counter-apologetics blog of Ben Wallis

Craig and actual infinites

2012-01-28T12:19:00.002-06:00

William Lane Craig uses Hilbert's hotel in an attempt to illustrate the impossibility of an existing actually infinite multitude, but I find several serious gaps in his arguments which, in my judgment, prevent them from having any force. His approach takes two forms: First, he claims that certain logical contradictions follow from the existence of actual infinites; second, his intuition tells him that an existing infinite multitude is absurd. In response, I want to resolve the alleged contradictions, and argue that intuition is an unreliable guide to the possibility or impossibility of an existing actual infinite.

Metaphysical and logical possibility.

In his "philosophical argument" against the existence of an actual infinite, Craig relies on the notion of "metaphysical" possibility, or as it is sometimes called (as I myself prefer), broad logical possibility, which he laments must follow from the relatively weak force of "intuitions and conceivability arguments" (Blackwell Companion to Natural Theology, p106). However given an accessible characterization of broad logical possibility, we should be careful not to think that just any intuition will do. Take, for instance, my deeply-felt intuition that a traditional God could never exist, which hardly counts as evidence against the possibility of God's existence. Similarly, if Craig has an intuition that Hilbert's Hotel could not exist, then that won't count as evidence either against its possibility---unless of course we have some particular reason to trust his intuition. The role of intuitions ought instead to be rather limited, whose appeals perhaps only serve to make up for our inability to precisely articulate a logical problem. So, for example, consider a person who first encounters the old challenge that an omnipotent God can create a stone so heavy he cannot lift it. Clearly, such a situation is not broadly logically possible. However not everyone can see precisely where the contradiction lies, and so these people must rely instead on their intuition that something is wrong with the picture the statement paints. Notice, though, that this intuition amounts to much more than merely a feeling of distaste for what we might view as a silly or sophistic suggestion. Instead, we genuinely cannot make sense of the statement given our understanding of its individual clauses and terms---that is, we don't know how to fit the statement's disjoint ideas into a consistent mental picture.

In principle, though, when faced with a broadly logically impossible suggestion, given sufficient reflection and ingenuity we ought to be able to find the precise nature of the inconsistencies, and express them as definite logical contradictions. In this way, we can interpret broad logical impossibility (or in Craig's parlance, metaphysical impossibility) as involving a strict logical impossibility which is perhaps hidden in a mass of ideas too tangled for us to penetrate. In other words, to assert that some state of affairs S is not metaphysically possible is to claim either that S involves an apparent logical contradiction, or else that there is some logical contradiction buried in S, but which is hidden from our immediate access. The role of our intuition, then, is to help inform us whether or not we can detect logical contradictions in those ideas where, for whatever reason, we cannot clearly explicate them.

Craig attempts to show an actual infinite is not possible by deciding that Hilbert's Hotel is "ontologically absurd" (p111), and he refers back to this idea of absurdity several times throughout the argument. It's not clear to me whether he intends the "absurd" to materially imply broad logical impossibility, or if he merely takes it as a strong probabilistic indicator; but in either case we have a serious problem. For if he has found no explicit logical contradiction in the actual existence of the hotel, then he must be appealing to an intuitive inability to make sense of it. However this is not the impression I get from his writing on the subject. It seems to me that, putting aside some extraneous confusions, he really does grasp, for the most part, the structure and mechanics of the hypothetical hotel, and can mentally manipulate it (at least apparently) in a logically consistent way. Though he may have a deeply-felt sense that its existence is not possible, this again does not count by itself as evidence against the possibility of the hotel as long as he has a coherent notion of what it means for it to actually exist.

Does the actual existence of the hotel, then, involve a logical contradiction? Craig argues that yes, it does, pointing to two distinct cases.

The first alleged contradiction.

Craig seems to affirm both that

(i) "there are not more things in a multitude M than there are in a multitude M' if there is a one-to-one correspondence of their members;" and

(ii) "there are more things in M than there are in M' if M' is a proper submultitude of M;"

whereas these are, at least according to Craig, inconsistent with the idea that

(iii) "an infinite multitude exists" (p110).

One of these may have to go, but as Craig points out we don't have an argument to keep (iii) over (i) or (ii). On the other hand, he doesn't offer an argument to keep (i) and (ii), either. Instead, he decides that (i) and (ii) are "innocuous," whereas (iii) is not, which he apparently takes as reason enough. However this seems to me entirely too hasty, another appeal to his personal intuition when we have no reason to think his intuition is a good indicator of truth. Further, (i) and (ii) do not seem innocuous at all unless we have already discharged (iii). Now, it is true that in ordinary language our uses of the terms "not more" and "more" are usually equivalent to (i) and (ii), respectively, for the simple reason that in ordinary language we almost invariably consider only finite multitudes. If we extend the meaning of these terms to contexts involving infinite multitudes, then we shall have left our comfort zone, so to speak. So the idea that (i) and (ii) are "innocuous" really depends on determining in advance that (iii) is false, which invites circularity if we wish to use that alleged innocuousness in our reasoning for rejecting (iii).

So if we take (i)-(iii) to involve a logical inconsistency, which is indeed the case as long as we give them appropriate interpretations, then we still haven't demonstrated a logical inconsistency in (iii) until we can first justify both (i) and (ii). Given that the only ready justifications of (i) and (ii) depend on (iii), this alleged contradiction fails to hold up under scrutiny.

The second alleged contradiction.

Craig writes:

In transfinite arithmetic, inverse operations of subtraction and division with infinite quantities are prohibited because they lead to contradictions... But in reality, one cannot stop people from checking out of a hotel if they so desire! In this case, one does wind up with logically impossible situations, such as subtracting identical quantities from identical quantities and finding nonidentical differences (pp111-2).

What is, after all, the result of infinity minus infinity? Well, that really depends on what we mean by "minus," especially as it relates to collections of objects. Craig notes that the mathematical stipulation on subtracting one quantity from another has "no force in the nonmathematical realm" (p112). That is true enough, but only because subtraction has a purely mathematical meaning in any case. Arithmetic, whether finite or transfinite, we apply to quantities, and not directly to the multitudes which those quantities can be said to measure. What we seek, then, in order to have Craig's objection track, is a way to link the arithmetic of quantities to real changes in existing multitudes. In particular, he'll need to affirm something like

(iv) If multitude M has quantity Q and a submultitude M' has quantity Q', then the multitude formed by removing the objects in M' from M has quantity Q minus Q'.

By affirming (iii) and (iv), along with a suitable notion of "quantity," we obtain a contradiction. However, here we seem to face the same sort of situation as we did with the previous alleged contradiction, whereby the most natural way to justify (iv) involves denying (iii) in advance, again threatening circularity. Meanwhile, as Craig himself points out, the set difference operator in mathematics (by which we remove objects of one multitude from another) works quite consistently, and we are free to use it to interpret what it means for guests to leave Hilbert's hotel. He objects only that this move "does not change the fact that in such cases identical quantities minus identical quantities yields nonidentical quantities" (p112). Yet although he is correct that the consistency of set difference operations will not change the inconsistency of transfinite subtraction, he still needs to first establish that indeed transfinite subtraction is required with infinite multitudes---that is, he needs to justify (iv) or something sufficiently similar so as to link transfinite subtraction with guests leaving a hotel. So far, he has not attempted this, and indeed it's hard to see how he could ever succeed apart from an independent argument against (iii).

From the hotel to the general case.

As an additional objection to Craig's appeal to intuition, Graham Oppy's observation that we don't get to infer from the impossibility of Hilbert's hotel the impossibility of an actual infinite in general seems quite powerful (cf. Oppy, Philosophical Perspectives on Infinity, pp51-3). So perhaps an infinitely-roomed hotel exists, but due to physical constraints it is not possible for guests to shuffle about so as to permit infinite arrivals or departures. To the extent that the intuitive absurdities Craig wants to find in Hilbert's hotel depends on such movements, since we have no justification for affirming their physical possibility then we cannot conclude from them that an actually infinite multitude is impossible by itself.

Craig offers two responses to this objection: First, he claims that "Hilbert's Hotel can be configured as we please without regard to mere physical possibilities" (p110). However this is quite obviously false; any reconfiguration of a hotel will still be a physical entity so long as it remains a hotel. In order to avoid minding physical possibilities, then, we must purge from the thought experiement of any significant appeal to physical entities. As it happens, this is precisely what Craig proposes in his second response. In particular, he suggests we generalize Hilbert's hotel by stripping it of all the characteristics which would cause potential mechanical problems, while preserving the same counter-intuitive results. However this does not so much defend against Oppy's objection as it concedes that Oppy has a good point, and that we need to go beyond the one example of Hilbert's hotel before we can infer that an actual infinite cannot exist.

Thus Craig writes: "If a (denumerably) actually infinite number of things could exist, they could be numbered and manipulated just like the guests in Hilbert's Hotel" (p110). So, what does he have in mind, exactly? If the objects in the infinite collection are physical, then he hasn't avoided his need to mind the unknown constraints of physical impossibilities. If on the other hand the objects in the infinite collection are abstract, then we are furnished with an abundance of counter-examples. The only option remaining that I can see is to say that the objects are mental (and non-physical). In that case, though, it's hard to see how he can carry over the concept of fullness of the hotel, and so we lose whatever counter-intuitiveness was associated with the notion of a hotel with no vacancies accommodating new guests. Instead we must imagine mental objects, ideas perhaps, divorced from physical bodies, and, say, blinking into and out of existence. Then we could have an infinite number of ideas existing, followed by the appearance of infinitely many more ideas; then infinitely many ideas suddenly cease to exist, but infinitely many extant ideas nevertheless remain---and so on. In this case, though, any violation of our intuition can easily be chalked up to the bizarre notion of having bodiless ideas pop into and out of existence.

Worse still, Craig seems committed to the position that the multitude of ideas can only be changed by having new ideas blink into existence, and not by having ideas blink out of existence. (This is due to his argument that a series of past events is an existing actual infinite.) This will interfere with his presentation of the second alleged contradiction, which requires us to somehow cut down infinite multitudes to proper submultitudes.

Conclusion.

I have tried to show here that Craig appeals to intuition to decide Hilbert's hotel is not possible, even though we have no reason to trust that intuition. Moreover, we have no means of moving from Hilbert's hotel to the general case without twisting the thought experiment so that it will be almost certain to violate our intuition independent of the presence or absence of infinite multitudes. In addition to these concerns, Craig wants to say that we have reason to think the existence of an actual infinite must involve two distinct logical contradictions, but in each case we find that the only ready justification depends on first showing that an actual infinite does not exist---an invitation to circularity. Given all this, it seems not only that Craig's arguments are insufficient for making his case against an existing actual infinite, but that they require further development before we can use them to throw any force at all to his desired conclusion.

an observation on William Lane Craig's divine command theory

2012-01-01T08:34:00.000-06:00

WLC suggests we characterize objective morality in terms of God's nature. In particular, he suggests a form of DCT, that "God's own nature is the standard of goodness, and his commandments to us are expressions of his nature" (On Guard, pp135-6). The obvious reply here is that we can conceive a God whose commandments are morally wrong; so for instance we can envision a God who expresses his nature by commanding, say, a father to sacrifice his son. Clearly this would be an immoral act, and since definitions are true essentially it shows that morality is not defined by God's nature. WLC anticipates this sort of objection, but complains that the envisioned scenario is "logically impossible," on par with suggesting that a square can also be a circle (p136). On his view, of course, that's true enough---but if the contradiction only manifests when we assume DCT in advance, then that just goes to show that DCT is wrongheaded. Since we know human sacrifice is wrong by our moral intuitions, and since we appear to be able to coherently conceive (apart from DCT) a God who expresses his nature by commanding human sacrifice, then clearly morality does not essentially accord with expressions of God's nature.

The solution, then, is not to invoke DCT and thereby beg the question, but rather to show that a God who expresses his nature by commanding human sacrifice is incoherent independent of DCT. Since we cannot define morality in terms of God, we might try instead to define God in moral terms, e.g. to claim that he is moral by definition. However this would prevent us from then defining morality according to God's nature on pain of circularity, hence undercutting the very DCT which WLC wishes to defend. The only remaining alternative in view is to argue without appealing directly to morality itself that God must be the sort of being to behave, ultimately, in accordance with our moral intuitions. But if we permit that sort of move, then we might as well define morality in terms of those moral intuitions directly, without having God play the role of a logical middle man. In other words, by defending against the objection, he concedes a more direct avenue for nontheists to characterize objective morality independent of God.

James Anderson and non-contradiction

2011-12-28T11:14:00.004-06:00

Dr. James Anderson has recently completed, with Greg Welty, the forthcoming paper "The Lord of Non-Contradiction," in which he argues for the existence of God from the laws of logic. We may divide the argument into two portions, the first where he holds that there is a necessarily existent mind, and the second that such a mind must be the mind of God. His summary of the first part of the argument proceeds thusly:

"The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind" (p20).

Of course this is a summary only, and in the full paper each step in this argument is carefully defended with sub-arguments. For my own part, while I am mildly suspicious of concluding that propositions are thoughts (as opposed to properties or contents of thoughts, or something along those lines), I only firmly disagree with two steps in this initial argument for a necessarily existent mind: First, it is not the case that the necessary truth of a proposition requires the necessary existence of a proposition; second, it is not the case that the necessary existence (as a thought) of some proposition requires the necessary existence of some particular mind. I do not discuss in this blog post the latter portion of the argument, in which he concludes that the necessarily existing mind is God's.

Regarding the first point of disagreement, we appeal to a distinction made by Robert Adams in his paper "Actualism and Thisness" (1981). Adams prefers to treat possible worlds as maximally-consistent sets of propositions which tell "world-stories," that is, which describe hypothetical states of affairs imagined by us. We can then distinguish between a proposition p being true at a world w, whereby it appears in the set associated with w, and being true in w. The latter sort of truth involves the proposition not only existing here in the actual world where we can use it to describe a hypothetical state of affairs and assign it a truth value in that capacity, but also existence within w, where denizens of that world can express it and assign it a truth value from their own point of view. Given that propositions exist in any world only insofar as beings with sufficiently-developed minds express them, this distinction seems intuitive and meaningful, and hence required in order to avoiding conflating existence inside a non-actual world of some truth there with its existence here in the actual world. Indeed it appears to have been championed quite independently of Adams, including by myself before I read his paper, and by Kit Fine under the labels "inner" versus "outer" truth (cf. "Plantinga on the reduction of possibilist discourse," 1985).

With this distinction in hand we may proceed to critique Anderson's inferences. To show that propositions which are necessarily true also exist necessarily, Anderson constructs two arguments: First, he points out that in ordinary language we are not permitted to utter something like, "the laws of logic are truths in [a possible world] w, but there are no laws of logic in w" (p14). So if ordinary language reflects what we can coherently imagine, it must follow from the truth of, say, the law of non-contradiction (LNC) in w that the LNC is itself in w. We can analyze the inappropiateness we detect in the sentence by asking ourselves what is meant by saying that the laws of logic "are truths in w." If by this we mean in part that the laws of logic exist inside w, then we have no business saying that the laws of logic "are truths in w." Instead, we must say only something like, the laws of logic are true at w. Once we change "truths" to "true" and "in" to "at," the modified sentence no longer sounds inappropriate: The laws of logic are true at w, but there are no laws of logic in w.

Although Anderson cites Plantinga's argument against weak necessity in his paper, Planting does not tackle the in/at distinction propounded by Adams and others. Instead, he discusses a more radical form of weak necessity whereby propositions are weakly necessarily true iff they "could not have been false" (cf. Plantinga, Warrant and Proper Function, 1993, p119). To rebut the Adams objection, then, Anderson in a blog post appealed to an argument from Thomas Crisp in his paper "Presentism" (2005, The Oxford Handbook of Metaphysics). There Crisp notes that a proposition p is true "at" a world w, on Adams' view, iff p is a true description of w, but complains that he knows no other way to make sense of p being a true description of w except to say that, "were [w] to be actual, [p] would be true" (p229). Such statements, of course, run quite contrary to Adams' analysis of truth at w. Thus we have no concept of a description of w compatible with the in/at distinction, and hence the distinction is not meaningful.

It seems to me, however, that Crisp's key premise that p describes w iff, were w actual, p would be true is false. Our intuitive understanding of what descriptions are informs our statements about descriptions---not the other way round. As long as we have such an understanding, we are not required, I don't think, to explicate it in English, or to construct a definition in terms of possible worlds semantics. If this bothers Crisp (or Anderson), then we can do as well with the following: p describes w iff, were w actual, p would be the case. Thus we have satisfied Crisp's demand for an account of descriptions compatible with Adams' in/at distinction.

So the ordinary language argument doesn't hold up to scrutiny, but Anderson offers a second argument, this time from "property attribution," and which he states succinctly: "If only existents can bear properties, and the laws of logic are propositions that bear the property of truth in every possible world, then we can only conclude that the laws of logic exist in every possible world, as the bearers of that property" (p15). However this line of argument depends again on the premise that propositions are true in each possible world, which given Adams' distinction is not evidently the case. Instead we can only say that propositions are true at each possible world, and we have no means of deducing from this that propositions have properties in each world.

Thus we have no defense for a crucial step in Anderson's argument whereby he concludes that necessary truth of a proposition requires its necessary existence. Indeed, this notion seems to be false; for to the extent that our imagination is a guide to what is (broadly) logically possible and what is not, then since we can imagine a world without sufficiently developed minds for producing propositions, and hence a world where propositions do not exist, it is possible that, say, the LNC does not exist in some world w. Thus there is no necessarily-existent (in the sense of being imagined) mind which thinks the LNC.

Still, it could be argued perhaps that our imagination isn't fully coherent when we attempt to drain it of our own point of view. So perhaps we can even imagine ourselves in the role of another, but we can never fully extract ourselves from our own imagined situation. Alternatively, one might argue for idealism of a sort where sufficiently developed minds for framing a model of the world also must be capable of conceiving propositions. In either case, we upset the in/at distinction that Adams wishes to make, preventing us from objecting to Anderson's argument on the grounds of propositions not necessarily existing. I should stress that Anderson declines to raise either of these points, and indeed I don't think they pan out in the end. Nevertheless, as an idealist they do concern me to some limited degree, and so we might wonder how they cash out in terms of Anderson's argument. That is, if Anderson is correct (but for the wrong reasons) that the laws of logic necessarily exist, can we resist any other premise in his argument to avoid the unwelcome conclusion that there is a necessarily existent mind?

I think so. For also demanded for Anderson's argument is the premise that the necessary existence (as a thought) of a proposition requires the necessary existence of a particular mind which thinks that proposition, a premise which seems to me quite false. His argument to support it runs thusly (p20, note 31):

(1) "thoughts belong essentially to the minds which produce them;"
(2) "consequently, the thoughts of contingent minds must be themselves contingent."

From (2), then, we can conclude that any necessarily-existent (as a thought) proposition is produced by a necessarily-existent mind. However, in order to deduce (2) as a consequence of (1), he appears to require the following additional premise:

(3) if a proposition p exists in world w and essentially belongs to a mind m, then m exists in w.

At least, without supposing something like (3), I don't see how to obtain (2) from (1).

Now, I happen to disagree with both (1) and (3) simply on the basis of how I understand thoughts and reference. However it turns out that if we assume they are true, along with the other premises required for Anderson's main argument, then they undercut his defense that the laws of logic are necessary truths. For in that case, since each human mind is contingent, it cannot be that any necessarily-existing proposition belongs (as a thought) to a human mind. Since furthermore Anderson requires that the necessary truth of a proposition implies its necessary existence, then it follows that human minds cannot have necessarily true propositions as thoughts. So for example, "2+2=4" cannot be the thought of a human being. This leads us to wonder, then, in what way shall we take human beings to conceive propositions? Obviously there is some sense in which a human being can conceive that 2+2=4, but if he is not actually having the proposition as a thought, then what is his thought which would lead us to say that he "conceives" that 2+2=4?

A presuppositionalist like Anderson might want to say that we conceive that 2+2=4 only imperfectly, i.e. that there is some unreachable ideal of "2+2=4" which only God can truly capture, and that "2+2=4" as we human beings can conceive it is not necessarily true, which on Anderson's view amounts to being possibly false. Yet if 2+2=4 is possibly false as each human being conceives it, then it's hard to see what "2+2=4" could mean for us at all; indeed a person would have to be deeply confused for his conception of 2+2=4 to be false in some possible world. Moreover, when we say that 2+2=4 is necessarily true, we do not typically refer to any external ideal, but rather to our own conception of what it means for 2+2=4. If a person is mistaken that "2+2=4" (as he conceives it) is necessarily true, then that seems to undercut any reason he would have for thinking that there is some ideal of his contingent propositional thought which exists necessarily. The same goes for the laws of logic as we can express them: By assuming (1) and (3), we find that the LNC as Anderson conceives it is not, in fact, necessarily true. Instead, he must assert the undefended (and probably indefensible) premise that there is some external perfect thought which is not within our conceptual reach, and which is necessarily true. In this way, his defense of the latter part of his argument appears to undermine his defense of the former.

Of course, whatever we mean by saying that we conceive 2+2=4 is true, or that the LNC is true, etc., it seems we must be able to say that whatever is our conception is necessarily true, on pain of violating the workings of natural language, and indeed any rigorously-constructed possible worlds semantics. Yet given (1) and (3), we cannot do this; therefore we ought to deny the conjunction of (1) and (3), preventing us from deducing (2) and hence also the necessary existence of any particular mind.

On his blog, Anderson denies that we need to attribute truth directly to human thoughts. So a human can instead represent a proposition by his thoughts, and we ascribe indirectly that representation a truth value by assessing the truth of the associated proposition. However in this case he makes a lot of work for himself by positing the existence of external objects, call them Anderson-propositions. For if we have no reason to think that such objects really exist, then obviously we cannot rightly take ourselves to refer to them when we talk about "propositions."

At first blush, this seems more of a denial of the premise that propositions are thoughts than that they must belong across all possible worlds to a single necessarily existent mind. For since we consider multiple thoughts to express a single proposition p, then since those thoughts are not identical to each other they cannot all be identical to p. Instead, we need to say something to the effect that p is a sort of "similarity class" of thoughts, i.e. that the different thoughts among human beings all exhibit some similar structure or character, as we might say that there is only one Ace of Spades, even though it has multiple incarnations. However this does not preclude the similarity class itself being a thought in my mind, and hence we need not deny Anderson's earlier premise. For although it must be unique to my mind in the strictest sense, leading us to posit again multiple "copies" of p instead of the single p which we might otherwise seek, that is tolerable for communication. Each of us, within his own sufficiently-restricted conceptual model, can understand p as a single similarity class of thoughts, and speak of p in that context. So p is still a thought in my mind---only not in the way Anderson envisions.

In summary, Anderson has failed to show that, first, a necessarily true proposition necessarily exists, and second, that a necessarily existent proposition requires a necessarily existent mind. Recall again that at least to the extent that our imagination is a guide to (broad) logical possibility, then since we can imagine a world without minds it certainly appears that there is no necessarily existent mind. Anderson's case to override this appearance breaks down in two places, and so we cannot accept it.

EDIT: Prof. Anderson has responded to this blog post here. You can also check out my counter-responses in the comments on that page.

a contextualist solution to skeptical problems

2011-12-16T08:32:00.003-06:00

Consider a skeptical hypothesis H, such as "I am a bodiless brain in a vat," and an ordinary knowledge claim O, such as "I have hands." Adapting the suggestions of Keith DeRosa (1995, "Solving the Skeptical Problem," The Philosophical Review 104.1), we may claim the following:

(1) I don't know that ~H;

(2) If I know that O, then I know that ~H;

(3) I know that O.

From these three individually-plausible premises a contradiction appears to follow, and this motivates us to seek a solution to what we can term the "skeptical problem." DeRosa's solution is to appeal to epistemic contextualism, which may allow us to affirm (1), (2) and (3) all at once without contradiction. In particular, an epistemic contextualist is free to suggest that the knowledge we have of O is a different sort of knowledge than that we seek for H. On this view, there is a context C1 in which we don't know that ~H, and a context C2 in which we do know that O. Thus the premises may be reformulated as follows:

(4) I don't know/C1 that ~H.

(5) If I know/C1 (know/C2) that O, then I know/C1 (know/C2) that ~H;

(6) I know/C2 that O.

Clearly, this interpretation allows us to affirm all three premises simultaneously without contradiction, hence solving the skeptical problem. So we may consider two remaining questions.

Is the contextualist interpretation of the skeptical problem correct?

At least we can be confident that some form of epistemic contextualism is true, as shown by DeRose's classic bank cases (1992, "Contextualism and Knowledge Attributions," Philosophy and Phenomenological Research 52.4) and other straightforward illustrations. So what we know in one context might be different than what we know in another context, and this makes it possible for us to simultaneously affirm for a fixed P what is expressed by utterances of the form "I know that P" and "I don't know that P," insofar as we may speak across contexts. However, just because sometimes what counts as knowledge can vary from context to context doesn't mean all knowledge is contextually varied. In particular, it is not necessarily the case, even given epistemic contextualism, that there exist distinct contexts C1 and C2 such that we can interpret (1)-(3) as equivalent to (4)-(6).

To investigate this, let us consider successively the context in which we decide that (3) is true and the context for deciding (1) is true. Regarding (3), our first instinct is to think of how silly we should sound were we ever to express genuine doubt for it. The idea here is that O is the sort of belief that people not only take for granted, but expect others to do the same. In this way, doubting O is likened, whether rightly or wrongly, to a kind of useless sophistry, which in turn is seen as a vice to be avoided. Even if we discover that can't logically justify O, our commitment to logical justification is weak enough and our commitment to O is strong enough that we all expect each other to remain nonetheless firmly and unshakably convicted of O. To doubt (3) is seen as betraying a doubt of O, and hence we deem it similarly intolerable.

The context, then, of (3) as we normally evaluate its truth appears to involve our widely-shared tendency not to question basic assumptions about the way the world works. In contrast, the context of (1) runs quite contrary to this tendency; for it consists in a direct challenge to those everyday assumptions. We conclude that (1) and (3) involve different contexts, and indeed since ~H is among the underlying assumptions of the context of (3), this quite clearly explains apparent inconsistency of (1)-(3). Thus the contextualist interpretation (4)-(6) of utterances (1)-(3) appears to be correct.

Do any further skeptical problems remain on the contextualist solution?

Philosopher John Koethe remarks of this contextualist interpretation that "as a response to scepticism it strikes me as a nonstarter" (2005, Scepticism, Knowledge, and Forms of Reasoning, p72). According to him, we must be able to affirm (3) given any "legitimate" context whatsoever. For he insists that the truth of (3) is "simply obvious," and to deny it even under the umbrella of something like C1 would be "just wrong." This makes C1 illegitimate as a context for knowledge claims, and hence (4) an unreasonable interpretation of (1).

Instead, he suggests that people tend to assume the allegedly fallacious principle that knowledge is incompatible with the possibility of the contrary. So, for instance, we might mistakenly suppose that since H is possible then we do not know that ~H. In this way, he implies that (1) only appears to be true if one holds to that principle, and on this view the natural solution to the skeptical problem is to deny (1) regardless of context.

On the other hand, I don't think Koethe's objection stands up to the contextualist interpretation when we consider that it offers a compelling explanation for why our intuition resists any denial of (3). In particular, even if it is appropriate to deny (3) under C1, our intuition persistently moves us to consider only C2, where (3) is clearly true; indeed this phenomenon seems evident upon self-reflection. So at the very least, my personal intuition is satisfied by the contextualist interpretation, and whatever remaining skeptical problems of the sort expounded in by Koethe have only to do with his own personal intuitions and those of others like him.

A stronger objection, in my judgment, to the contextualist solution, turns on the plausible principle that for any fixed contexts D and E, and proposition P,

(7) If it is not likely/D that P, then I do not know/E that P.

In other words, although we might be able to strengthen the likelihood of P by moving to a narrower context, something which is not likely at all in one context cannot be known in another. Furthermore, given a sufficiently broad context D, the following appears to be true:

(8) It is not likely/D that ~H,

and given probabilistic closure we also have

(9) If it is likely/D that O then it is likely/D that ~H.

It's easy to see that (6)-(9) are inconsistent, and so this constitutes a remaining skeptical problem which requires resolution. I shall not offer one here, except to say that while it might be intuitively tempting to deny (8), it seems to me instead that (8) is true but (7) is false.

Robin Collins' restricted principle of indifference

2011-11-24T08:48:00.003-06:00

In The Blackwell Companion to Natural Theology (2009), Robin Collins presents an argument for the existence of God from the fine-tuning of the constant parameters of our physics models. I see several great problems with the argument, but in this blog entry I want to focus on just one family of problems having to do with his invokation of the controversial principle of indifference (hereafter POI). Philosophers know quite well from a slew of paradoxes dealing with the principle that it is inconsistent in its most general form, and generally avoid appealing to it. However this has not prevented some from developing more rigorous forms of it which they believe are useful and intuitive. Robin Collins has followed in this tradition, and so he presents in Blackwell his own "restricted" version of the principle (hereafter RPOI):

...when we have no reason to prefer any one value of a variable p over another in some range R, we should assign equal epistemic probabilities to equal ranges of p that are in R, given that p constitutes a "natural variable." A variable is defined as "natural" if it occurs within the simplest formulation of the relevant area of physics. [§3.3.2, p234.]

To support the validity of the RPOI, Collins appeals to two lines of evidence:

(1) it has a "wide range of applicability" (p235); and

(2) we require some form of the POI as an assumption in order to draw many of the indispensable conclusions we do about the world.

However, it appears to me that both of these claims are false. In the case of (1), he appeals to the common use of uniform distributions when constructing probability models. However, while uniform distributions are certainly required for the RPOI, the converse does not hold. Uniform distributions draw their motivation from various sources, including but not limited to past observations of frequency, and especially pre-existing understandings of physical systems corresponding to the random variables we define. Furthermore, even if (1) were true, it would only show that the RPOI has application, and not that we are justified in applying it. Regarding (2), Collins' aims to show that inductive inferences from past experience are insufficient for developing a robust understanding of how the world works, and so the RPOI must complement induction as a sort of foundational principle. Yet in my survey of the supporting examples he provides for (2) I find that a POI is not indispensable for them as suggested. For instance, he asks us to consider the first balanced twenty-sided die ever produced; certainly, even though we have never encountered one in our previous experience, we ought to assign immediately, if tentatively, a uniform distribution for rolling outcomes. Yet how do we justify this uniform assignment? According to Collins, we must appeal to some form of POI, but is this really so? It seems to me that instead of applying an abstract philosophical principle, we instead draw from what we already know about the world, in this case the behavior of symmetrical bodies, as well as our instinctual expectations (whether gleaned from past experience or evolutionary history) for falling objects and other related physical systems. Perhaps in some cases we appeal to inarticulable intuitions, where those intuitions in turn have experiential (i.e. inductive) support, and in those cases too we have no room for the RPOI. To be fair, in Collins' opinion the clearest and best examples supporting (2) come from the science of physics (note: not "folk" physics), where sadly I cannot follow since I have no high-level training in that field. However it seems obvious to me that at least his examples outside physics don't hold up, and these are the most important for establishing that we ought to use some form of POI. For to the extent that physics is useful, it can be supported inductively apart from any POI; and to the extent that it is not, we are free to leave it behind. Of course there are other possible (though in my opinion similarly impotent) defenses of the RPOI outside (1) and (2); but Collins seems disinterested in them, and so I shall neither give them any attention here.

For these reasons, I don't think Collins has adequately defended the RPOI. However, I want to go a step further and suggest that we have positive reasons for thinking the RPOI is invalid, on account of two problems I see with its application.

The Zero Paradox: Consider a situation similar to the one Collins discusses in Blackwell, where we have a physics model with an unknown parameter p. Let L denote some statement about the physical world. Suppose the range of possible values for p is the interval [0,1], but that L is true if and only if p=0.5. In that case, the range of L-permitting values is a singleton, and hence has (Lebesgue) measure zero, whereas the parameter space has measure 1. Then provided we have no additional relevant knowledge, according to Collins we must apply the RPOI to obtain a probability that L is (possibly) true equal to the ratio of the measures of the respective ranges, which in this case is zero. Hence the epistemic probability that L is false is 1, which is to say that we must take a position of certainty that L is false. However this conflicts with the fact that we know by hypothesis L is possibly true, in particular it is true iff p=0.5. We can toy with this approach to bring it to bear more strongly on our intuitions. For instance suppose that L will be true just in case some term cancels in our physics model, and that this in turn occurs just in case p=1/n for some positive integer n. Then we have countably infinitely many values clustering about zero such that if p takes any one of them, L will be true; and otherwise L will be false. Then the previous argument will hold again, insofar as the RPOI will produce a zero probability that L is true, i.e. complete certainty that L is false, even though there are now infinitely many possible cases for L to be true in our physics model! Moreover, if we let L denote the statement p=x, where x is any value in [0,1], then we can apply the argument to show that for all x in [0,1] we must be certain that p≠x, even though we must also be certain that for some x in [0,1] we in fact have p=x. Since we are dealing with epistemic certainty, this is no mere lottery paradox. Collins, in effect, demands that we place absolute confidence in that which we know to be impossible.

The Continuity Paradox: (This is inspired by the criticisms of the McGrews.) Collins' argument assumes the measures of the "epistemically illuminated" ranges of the (EI) parameter spaces are all finite, even though the spaces themselves are infinite in measure. Suppose, however, that we increase our knowledge so that the EI range for the parameters of our physics models grows larger and larger. Provided that the life-permitting universe (LPU) range remains fixed, i.e. that we do not learn of any additional values which will permit life in the universe, then the probability of LPU will tend to zero. Suppose now that at some point we learn about the whole parameter space (which has infinite measure). According to Collins, we should then decide that LPU has probability zero. In other words, we must again be certain that LPU is false, even though we know that there is a positive-measure range of LPU values for the parameters. This of course re-introduces the zero paradox in an even stronger form. To avoid it, we might posit that there is some nonzero probability on an infinite-measure range. (Note: Collins does not do this, since he denies that the zero paradox poses any problem for us.) However if we assign a nonzero probability to the infinite case, then we have a discontintuity in the limit, which means that there is a point at which expanding the range of the LPU-inconsistent space results in a higher probability for LPU. Though not precisely a contradiction, this situation is clearly intolerable.

In addition to the zero and continuity paradoxes, it appears that the RPOI is inconsistent with Collins proposed rule of inference for the fine-tuning argument, the "restricted likelihood principle" (RLP). Recall that in his fine-tuning argument, he asks us to consider as a conceptual device a disembodied alien observer who witnesses the big bang and, using the information from those first few fractions of a second in the life of the universe, say up to time t*, develops the basic structures of the physics models which, once certain parameters are filled in, will accurately predict its behavior. Observing the ratios of measures between the sets of life-permitting and EI values of those parameters, he applies the RPOI to obtain an extremely low probability for LPU. However, I suggest that we go back further, not to time t*, but instead to the big bang itself. At that time, the alien has no information on which to base a physics model. So if he considers the hypothesis of LPU, then the natural variable is going to be, simply, true or false, i.e. will the universe permit life or not? Applying the RPOI he obtains a probability of 0.5 that the universe will permit life. Now, Collins denotes by k' the background information that the alien has at time t*. Let k'' denote the information in k', except for anything learned between the big bang and time t*. Let NSU denote, following Collins, the naturalistic single-universe hypothesis. Also, let CDL denote the hypothesis that the universe is consistent with the development of life at time t*. Then clearly P(CDL|LPU&NSU&k'') = 1 > P(CDL|(~LPU)&NSU&k''), and using Collins' RLP, we conclude that CDL confirms the LPU hypothesis on the background assumptions of NSU&k'', i.e. P(LPU|NSU&k''&CDL) > 0.5. Besides CDL, the only information involved in k' but not k'' appears irrelevant to the question of whether or not life will develop. Thus we conclude that P(LPU|NSU&k') = P(LPU|NSU&k''&CDL) > 0.5. However, this contradicts Collins' conclusion based on considering time t* exclusively that P(LPU|NSU&k') < 0.5.

In response to this objection, Collins argues that we must "update" the probability obtained from applying the RPOI at the big bang by re-applying it at time t*. Immediately we should note that even if this resolves the problem, it does so on pain of departing from the RPOI as stated in Blackwell, which requires that we have no existing reason to prefer one alternative over another. For when the alien arrives at time t*, according to the RPOI he already has reason to prefer the LPU range over the non-LPU range in the sense of taking it to have a greater probabilistic weight for intervals of fixed measure. Collins would have us modify his RPOI to read, "when we have no reason other than a previous application of the RPOI to prefer any one value...", or something of that sort. Moreover, he must also modify his RLP to ensure that any updates to the RPOI are performed prior to its application. Thus we must continually forget whatever we previously concluded as a result of the RPOI as new information becomes available. In this case, though, one might wonder why we cannot update our information from time t* to the present time. For instance, in the present situation the natural variable for the existence of God seems to me, again simply, true or false, i.e. God exists or not. If Collins wants this variable trumped by the parameter considerations at time t*, then he may be hampered by the additional restriction which we have seen he must add to the RPOI.

I suggest that the reason our intuition will not tolerate us endowing the RPOI with any greater persuasive force than this is that we intuitively understand that the RPOI doesn't give us any reason to prefer one hypothesis over another. So any actual reason to priviledge a particular hypothesis will always trump the RPOI. Indeed, the RPOI is so weak even on Collins' view that previous instances of the RPOI cannot inform its own application. Further, we find that not all of the paradoxes which are so-well known for the unrestricted POI are undercut by the RPOI. Most seriously of all, we don't appear to have any justification for its use in the first place. These problems, in my judgment, demands that we reject, at least tentatively, Collins' formulation of the fine-tuning argument.

clarification on "mixing models"

2011-11-21T08:52:00.002-06:00

[NOTE: This is a post on Pastor Seger's argument. For the discussion with Sye Ten Bruggencate, go here.]

This past Thursday Michael Long and I sat down to have a taped conversation (over Skype) with Sye Ten Bruggencate and Pastor Dustin Segers about the existence of God. We all had a great time, and plan to perhaps do it again at some point in the future. In the mean time, I'd like to clarify some comments I made.

Not surprisingly, they appealed to their "assumption" that God exists, and boldly asserted that God somehow "grounds" the so-called "laws of logic" (among other things). Michael and I expressed our concern, however, that they don't have a coherent idea of what it means for logic to have a "ground," and we asked them to explain how they took God to serve this purpose. (We're also rather skeptical that they have a clear notion of what they're talking about when they refer to "laws of logic," but unfortunately we didn't have much time to get to that in the podcast.) Towards the end, though, Pastor Segers told us that he took the laws of logic to be "necessarily existent thoughts" and suggested that a "ground" for the laws of logic consists of the mind or minds which contain(s) those thoughts. In particular, he said:

Laws of logic are necessary truths about truths. They are necessarily true propositions. Propositions are real entities, but they can't be physical entities. They are essentially thoughts. So laws of logic are necessarily true thoughts. Since they are true in every possible world they must exist in every possible world, but they are necessarily existent thoughts. Therefore there must be a necessarily existent mind. --1:25

[EDIT 2011 Dec 29: It turns out that this is a verbatim quote from a forthcoming paper by James Anderson and Greg Welty. For a fuller discussion of that paper, go here (on-site).]

Of course there are multiple problems with this argument, but I think it's most important for us to look at how possible worlds language operates, and consider in what ways we must be careful with its use. In the limited time available to me at the end of the podcast, I tried to point out to him that even if we take propositions to be "thoughts," they aren't guaranteed to exist as such within our possible worlds model:

Perhaps you could say that there are certain laws of thought that maybe in some sense exist as thoughts, or ideas or something. But within the model of looking at statements and truth-bearers, and possible worlds, and necessary existence and all that, within that model they aren't thoughts. They're just abstract properties of the model. So I'm suspicious that you're mixing models, there, in an inappropriate way. --1:30

I wish we could have explored this criticism during the podcast more than we did, but I will just take the present opportunity to clarify. To put it plainly, I accept that there are mathematical structures, elements of which we can label "possible worlds," and that these structures can aid in our use of modal language. A possible world, in this case, we might take to consist of the state of affairs described by some maximally-consistent set of propositions. On this interpretation, an entity E "exists" in world W just in case the set S(W) of propositions describing W includes the proposition P = "E exists." Notice, however, that this does not require S(W) to include some other proposition Q(P) = "proposition P exists." (Not only that, to maintain logical consistency we might be forced to stipulate that a possible worlds structure be non-self-referential, which is to say that no element of S(W) can refer to another element of S(W); but we shall assume for the present discussion that such self-reference is not logically incoherent.)

With this in mind, recall that Pastor Segers claims necessarily true propositions "must exist in every possible world." In terms of the possible worlds structure I've outlined, this is equivalent to the property that if for every world W in the possible worlds structure P is an element in the set S(W) describing W, then for every W we must have Q(P) be an element in S(W). However, there seems to be no reason to insist on always building this property into the models we use for our modal talk. Yet if we use a model without that property, then Pastor Segers' claim that necessary truths must exist in every possible world will be rendered false. Now, we can always abandon the use of models of the form I've outlined, and liken possible worlds to something other than states of affairs described by maximally-consistent sets of propositions. However that won't change the fact that we will still be using a model, and whenever we build something into that model, namely the necessary existence of certain propositions and/or thoughts, we can always ask, "why do so?" Pastor Segers has essentially demanded that we only use those models consistent with his view of necessary truths existing as thoughts in all possible worlds. However, it seems to me that this is only a roundabout way of assuming in advance what he is attempting to prove.

I suspect, however, that Pastor Segers hasn't thought about possible worlds in this fashion. Instead, it seems like he just conflates the possible worlds model with higher-level models we use to talk about it. So, he begins by observing within the possible worlds model that some proposition P is true. Jumping outside that model into a higher-level model, he (correctly) notices that P exists as a proposition, but then he mistakenly steps back inside the possible worlds model while still holding onto the existence of P from the higher-level model. This is clearly an intolerable move, and it's what I'm talking about when I suggest that he is "mixing models" inappropriately.

So, while I'm happy that Pastor Segers made a genuine attempt to explain what he means by having a "ground" of logic (which is more, in my experience, than most presuppositionalists would ever care to do), his account appears incoherent at worst and overly presumptuous at best. Of course, if he has a solution to this problem, naturally I would love to hear it. However I don't see any way around it, myself.

a discussion with Sye Ten Bruggencate

2011-11-19T08:28:00.001-06:00

This post originally consisted of an entirely different topic. However the comments for the post took on a life of their own, and so I'm re-posting the original topic here, and leaving this post open for further discussion on Sye's view. It comes after we interviewed him on the Goodness Over God podcast this past Thursday.

To summarize, Sye wants to know how we justify reason itself, and hence our subjective view of the world which we base on our reason. However I take justification to be a part of our reason, and so this is akin to asking, how does a person justify justification? My position is that we don't need justification for using any particular standard of justification as long as that standard is consistent with itself, and with its own application. While this situation may not satisfy us completely, it's the best we have available to us, since any would-be justification for our standard of justification must necessarily have a circular character.

In Sye's view, though, not all circular reasoning is bad, or "vicious." According to him, we should instead use a good or "virtuous" kind of circular reasoning involving the existence of the Christian God. Recall from the podcast (~48:00):

SYE: We're saying that we have a justification---revelation from God.

BEN: Part of what we mean by justification is to satisfy our reason. How could you have a non-circular argument given that that's what we mean by justification?

SYE: We're not saying that our argument isn't circular. We're saying that it's virtuously circular in that God can justify reasoning.

So that's the background to the following discussion. Enjoy!

an argument for agnosticism

2011-11-13T04:45:00.001-06:00

Let us take inductive inference to consist in extrapolating the broadest-according regularities of our experience to universal laws, each within some larger domain or context than the experiences themselves. On a small scale this is easy to envision, and we can appeal to such canonical examples as the inference that all swans are white from a large random sample of uniformly white swans. However, we must also take inductively-inferred laws to "accord broadly" with all of the regularities of our experience. For instance despite the fact that we have only ever personally encountered white swans, perhaps we have heard from a reliable source (wikipedia?) that there exist black swans. To infer that all swans are white under these circumstances might accord narrowly with our first-hand experiences of swans, but not broadly with our other non-swan experiences, namely the experiences which lead us to decide that our source for information on black swans is reliable. So inductive inferences must in this sense comport with the "big picture," so to speak, which is to say that wherever the narrow regularities of our experience conflict, induction must follow the most well-evidenced, i.e. the most well-represented, of these.

Suppose we have experiences which we wish to conceptually model according to induction, and consider the question, could God ever appear in such a model? More generally, suppose an actual object O causes us to have some set E of experiences. Let F denote the subset of experiences in E which follow some discernible order and/or regularity. Then in the best case scenario we can infer that there exists an object P which is like O in the sense that, in our conceptual model, it causes the sort of experiences contained in set F. (Here we are using some unspoken assumptions about uniqueness and maximality of subsets of regular experiences and the identity of objects whose existence we infer from them, but given the context this seems tolerable.) In this way, P is an object in the model which corresponds to the actual object O, i.e. P is a conceptual model of O. Now, O also causes the sorts of experiences contained in E-F, where E-F denotes the set of experiences contained in E but not F. Recalling that induction works only via regularities of our experience, we see that since the experiences in E-F follow no discernible order and/or regularity then we cannot inductively infer that P (nor any other object) is causing the experiences in E-F. So if it is an essential property of O that it causes experiences of a sort contained in E-F, then since we cannot infer that P causes those kinds of experiences it means that we have not inferred the existence of O when we infer the existence of P. Ideally, we would say that if a model object P whose existence has been inferred sufficiently resembles some object O which actually exists, then we have inferred the existence of O, thus permitting if not delivering knowledge of O. However in this case there is some essential property of O which is not shared by P, and so this prevents us from modeling O with P, and hence from inductively inferring that O exists.

To put it another way, when the object O in question has as an essential property that it transcends the regularities of our experience, then we can never inductively infer its existence. So we can never inductively infer the existence of an essentially omnipotent being like God, since omnipotence by definition involves the capacity to transcend the regularities of our experience. Notice, however, that we must use the qualifier "essentially," because it is nevertheless possible (in principle) to infer the existence of a being which possesses a non-essential property involving transcendence of the regularities of our experience. So, for example, it could be that Barack Obama can work a regularity-transcending form of magic. Although we could never inductively infer this hypothetical fact about him, we can nevertheless know that there is such a person as Mr. Obama---at least as long as we decline to take his supposed possession of magical powers to be one of his essential properties (which seems reasonable enough not to do).

In the case of God, we might possibly be able to infer the existence of an intelligent being B whose actions in the world correspond to some significant subset of God's own actions. However, we can never inductively infer that B has any of God's regularity-transcending abilities. Namely, we cannot attribute miracle-working to B, unless we water down our conception of what constitutes a miracle at least enough so that we can speak of miracles following the broadest regularities of our experience. So for instance, given that resurrections run afoul the regularities of our experience, we cannot currently infer through our experiences the existence of a being with (essentially) the power to raise the dead, unless those experiences change so dramatically that resurrections come to comport best with them.

Consider the following instructive example: Suppose we encounter a being B which has never failed despite extensive testing to deliver upon request perfectly truthful information. Perhaps we ask B a few dozen times for the winning lottery numbers in advance, and each time B tells us the winning numbers. Moreover, we could ask for descriptions of future events which we later observe to come to pass exactly as B has promised. And so on, every verifiable statement of B checks out to be true, despite the fact that we have no explanation for its remarkable truth-reporting abilities. Under these hypothetical circumstances, suppose further that B claims to be able to work a miracle, say raising Elvis Presley from the dead. In order to evaluate his claim, we must weigh the inductive evidence for his consistency in truth-reporting against the inductive evidence for the consistency of dead bodies to remain dead. If we decide that B's truth-reporting exhibitions have the greatest inductive weight between the two, then the "miracle" of raising Elvis will not in a broad sense transcend the regularities of our experience. If on the other hand we decide that the inductive evidence for B's truth-reporting is insufficient to outweigh the inductive evidence for dead bodies staying dead, then we shall be unable to infer that B has the power he claims to raise Elvis. So whichever turns out to be the case, we can never inductively infer that which runs against the broadest regularities of our experience.

In the preceding illustration we can see how it happens that miracles which we would currently regard as transcending the broadest regularities of our experience are not strictly epistemically off-limits, and we can infer their occurrence by accumulating sufficiently strong inductive evidence. To show that a miracle has occurred, then, we must weaken its status as a bona fide miracle, that is, we have to show that it broadly accords with the regularities of our experience. From a practical standpoint, though, this is as good as impossible; for example we cannot hope to prove through, say, examining historical documents and archaeological remains that the laws of physics were suspended in first-century Palestine. Moreover, in the case of omnipotence such weakening is impossible not just in practice but also in principle, since part of what it means to be omnipotent is to be able to transcend the regularities of our experience. So any being, namely God, for which omnipotence is an essential property can never be shown to exist by inductive inference.

To a great extent this is nothing new. Hume, for instance, and others after him have already dealt most brilliantly and succinctly with the subject of weighing inductive evidence for and against miracles, and I could not hope to surpass their marvelous eloquence. Rather, I intend for the preceding arguments and observations to show that we can go yet a step further from Hume and observe the consequences with respect to those hypothetical objects whose essential properties involve the transcendence of the regularities of our experiences. The existence of such objects can never be inductively inferred since by hypothesis they reside, so to speak, at least in part outside the context of those universal laws which extend the regularities of our experience; and through similar reasoning we see that neither can their nonexistence be inductively inferred. Immediately corollary to this conclusion, no causal argument for or against the existence of God shall ever succeed as long as we take omnipotence to be an essential property of God. Furthermore, no cumulative case can ever amass sufficient strength to show the existence or nonexistence of God as long as it depends on induction for its summed force. In fact, any justification we have for beliefs about the existence of God must have a non-inductive character. Given that induction appears necessary to learn about the world beyond our own present experience, internally-justified knowledge of the existence or nonexistence of God thus seems beyond our grasp.

more on the burden of proof for god's existence

2011-11-12T07:37:00.001-06:00

In debates over the existence of God, we often find atheists accusing Christians of having "the burden of proof." Defectivebit of choosinghats.com wants to remind negative atheists such as myself that we do indeed make positive claims, and according to him this leaves us with our own burden of proof. Now, in a very trivial sense, it is quite true that we must make a certain claim when identifying ourselves as negative atheists. Namely, we are making the claim that we do not believe in God. Furthermore, this seemingly benign statement draws on various concepts, which in turn suggests that by identifying as negative atheists we must take up the positions that they are collectively (and possibly also individually) meaningful. For instance it appears we must assign some positive meaning to the concepts of belief, God, the self, and so on, if we want to truthfully identify as negative atheists. Further still, what appears to me the usual context of accusations of "burden of proof" on the part of negative atheists involves the notion that negative atheism has a sort of "default" epistemic status, i.e. that we should all be negative atheists unless we have reason to adopt an alternative position, and this view will obviously require a defense if challenged.

I fully agree that we should remember all this in our conversations, and be willing to address such issues when the need arises. However, to the extent that we are interested in finding out reasons to think that God exists, these observations about implicit claims and underlying assumptions aren't going to help very much. If the presuppositionalist Christian can only dig up problems with, say, certain views on the self, epistemic humility, crypto-theism, etc., then we can talk about those problems of course (for example I have addressed here and here a couple of the supposed problems associated with crypto-theism); but to do so would depart from the topic of whether or not we can actually manage to scrape up some good reasons to believe in God. This is not necessarily inappropriate---it could be, for instance, that the presuppositionalist thinks those problems must first be resolved before we can move on to dealing with the existence of God. Nevertheless, that won't change the fact that such discussions regard dramatically different issues, and will not by themselves provide us with reason to believe in God.

In short, the "burden of proof" really depends on what kind of conversation you want to have. Do you want to discuss whether or not we have reason to believe in God? If so, then the ball is going to have to start in the court of the theist who thinks we can find it. That doesn't mean the negative atheist gets to sit back and leave all the heavy lifting to the theist; however, his role will be largely responsory to the arguments and evidence which the theist will presumably present in favor of the existence of God. To date, I haven't seen defectivebit present any case---not even a rough outline---for the existence of God. If this is an oversight on my part, and defectivebit has indeed published online some kind of argument for the existence of God, then I would certainly welcome a link! However, as best as I can tell, he's only pointed out potential problems with the views of selected atheists, and this doesn't get him very far even in those instances where his criticisms are valid. Whenever he finally does offer an argument for the existence of God, then he will have thrown the ball into the court of the negative atheist, and we will at that time have to either respond or end the conversation. Until then, however, there's not much we can do in our capacity as negative atheists but point out that he hasn't given us any reason to believe.

Pruss' grim reaper paradox

2011-11-10T06:00:00.001-06:00

Philosopher and mathematician Alexander Pruss in 2008, and again in 2009, discussed on his blog the following paradox: Consider an infinite collection of grim reapers indexed by the positive integers n=1,2,..., where the nth grim reaper is scheduled to kill Fred at 11:00am + 1/n minutes, and where Fred's life is otherwise safe during that period. By hypothesis, he dies from the hand of a grim reaper, say the kth grim reaper. However the (k+1)th grim reaper visited Fred before the kth grim reaper, which means that Fred must already be dead by the time the kth grim reaper visits him. This is a contradiction, and we conclude that there is a logical error in the construction of this unusual and hypothetical situation.

Naturally we ask, what is the error? Well, there are at least two highly questionable assumptions at work. Most infamously, we have the notion that there can be infinitely many physical objects (such as grim reapers) in the universe. But we also must assume that it is possible to subdivide time into infinitely small increments. Moreover, we ought to proceed cautiously given the danger posed by the odd and unfamiliar character of the scenario that we may have unwittingly assumed other potentially controversial facts of which we are not presently aware.

It's an impressively clever paradox, and Pruss goes on to use it in quite a creative way: For as it turns out, one can reduce the strength of the afore-mentioned assumptions required by the paradox by additionally assuming the past-infinitude of time. Instead of directly assuming the possibility of an infinite collection of physical objects, we can posit merely infinite spacial and material resources. For in that case, it is possible that for each time t=-n, where n is a positive integer, a physical object is constructed. Then by the time t=0, an infinitude of objects, say the grim reapers and/or the rooms in Hilbert's Hotel, have been constructed. Furthermore, if we take on the assumption that time is arbitrarily divisible (as opposed to infinitely divisibile) then for each positive integer n we can posit an event at time t=-n causing an event (such as a grim reaper trying to kill Fred) to occur at t=1/n. With these lesser assumptions in hand, we can have a grim reaper sent out from every room in Hilbert's Hotel at the appropriate time to kill Fred as postulated by the GR paradox.

Pruss tries to advance this as an argument against the past-infinitude of time, but here I must disagree with him. Rather, it serves only as an argument against that certain combination of all three of the unverified assumptions it requires. Furthermore, I suggest that we may also need one further controversial assumption, that the duration of time it takes to kill Fred can be made arbitrarily short. For suppose it takes at least some fixed positive length e>0 of time (in minutes) to kill Fred. Then we can find an integer N such that n>N implies 1/n < e and hence we have infinitely many grim reapers killing Fred during the period between 11am and 11am + e minutes. In this case it is not obviously problematic to say that Fred died at the cumulative effect of all those grim reapers working to kill him between 11am and 11am + e minutes. Of course, this raises in turn the question of when precisely it becomes the case that Fred is dead. We would like to say that this at least is an instantaneous event, but can we be so sure? On the other hand, we don't necessarily need to say that Fred's death occurs instantaneously as long as we assume there is no fixed length of time e > 0 required to kill Fred. So perhaps it takes the nth reaper 1/n^2 minutes to kill Fred. In that case, there would be no overlap between possible killing events, i.e. the nth reaper would already be finished killing Fred by the time the (n-1)th reaper comes to visit.

At any rate, it seems clear that there are more assumptions at work in Pruss' argument than just the past-infinitude of time. I thank him very much for describing the paradox---if it is his own invention then he deserves some significant credit for that---and look forward to any further thoughts he has on the subject. Of course, I would be especially pleased if he happens to address some of the above concerns.

another argument for God's control

2011-10-17T15:01:00.001-05:00

We wish to show that every individual event which occurs in God's creation is willfully caused by God, where we understand God to be the omnipotent and omniscient creator of the whole universe, i.e. the creator of everything that exists outside of God.

Consider first the case where God is in control of himself, and let E be an event that occurs. Then E is part of a (possibly trivial) causal chain with a set of (uncaused) root causes. Suppose towards a contradiction that there is some root cause F which is not part of God's will. It cannot be that F is a part of God, because that would mean God caused an event without willing it, violating his control over himself. So F is outside God, which means it is part of God's creation. By omnipotence, God could have created a world W' which is identical to the actual world W in every respect except that F is not an element in W'. Since God is omniscient and in control of himself, then he willfully created W instead of W'. Since the only difference between W and W' is the occurrence of F, then God willfully caused F, contradicting the definition of F as a root (uncaused) cause. So all root causes of E are part of God's will, which by transitivity of causation means God causes E to occur. So every root cause of every event is a part of God's will. Furthermore, by omniscience, if God wills the beginnings of a causal lattice then he wills every event therein. We conclude that if God is in control of himself, then God willfully causes every event to occur.

Next consider the case where God is not in control of himself, but where God's creative acts are always deliberate, i.e. an exercise of his will. Let H be an element of God which God does not control. If H causes some event E, then that event is either involved with God's creation or it is not. If it is involved with God's creation, then God considered in his decision of what to create this action of H on his creation. By omnipotence, he could have created a world W', identical to the world W which he actually did create in every respect except that H does not act on W' to bring about E. Since God's act of creation is deliberate, that means he wills the existence of W as opposed to W'. Since the only difference between W and W' is the occurrence of E, then it follows that God wills E, and moreover causes E to occur by creating W when he could have created W'. If on the other hand E is not involved with God's creation, then since all that exists outside God is God's creation, then E must be an event within God. Consider the last element E' of a causal chain beginning with E and not containing any event involved with God's creation. Then either E' is causally inert, or else the same argument applied to H can be applied to E' to show that whatever event involved with creation which is caused by E' is willfully caused by God. So any elements which are not willed by God are bound up within God, i.e. are independent of creation. Thus any element only ever acts on creation by the will of God.

We are left with the case where God's creation is not entirely deliberate. We claim that this case is impossible. For consider a (causally) first nondeliberate creation N of God. There are two senses in which N could be nondeliberate. On one hand, N could be nondeliberate in the sense that there is some other object N' which is different from N, and whose creation would satisfy God's will no better or worse than that of N. Let E be the event that God caused the creation of N (as opposed to N'), and let F be a root cause in the causal chain leading to E. Then since E (causally) precedes any nondeliberate creative act the previous arguments apply to show that E is caused by God's will. Thus God wills the creation of N over the creation of N', which contradicts the definition of N' as not willed by God over N. Alternatively, N could be nondeliberate in the sense that God did not intend to create N at all. Yet in that case the previous argument again applies, leading to another contradiction. Thus the hypothesis of a nondeliberate creation always leads to a contradiction. We conclude that God's creation is in fact deliberate, and therefore that every individual event which occurs in God's creation is willfully caused by God.

The sadness of nontheism

2011-08-27T19:26:00.001-05:00

Some folks experience conversion from theism to nontheism as a kind of awakening or liberation from the shackles of faith, and delight in their new-found freedom. Not so for me. When I lost my Christian belief, I flew into a panic which lasted several days, and after finally settling down and sorting through my thoughts, I found myself deeply saddened at the emptiness left for me in a nontheistic view of the world.

I've tried various ways of looking at the situation, taking hints from popular atheist authors such as Carl Sagan and Richard Dawkins. Sagan, for instance, once wrote,

How is it that hardly any major religion has looked and science and concluded, "This is better than we thought! The Universe is much bigger than our prophets said, grander, more subtle, more elegant?" Instead they say, "No, no, no! My god is a little god, and I want him to stay that way." A religion, old or new, that stressed the magnificence of the Universe as revealed by modern science might be able to draw forth reserves of reverence and awe hardly tapped by the conventional faiths (Pale Blue Dot, p50).

Dawkins echoes his sentiments:

...the universe is genuinely mysterious, grand, beautiful, awe inspiring. The kinds of views of the universe which religious people have traditionally embraced have been puny, pathetic, and measly in comparison to the way the universe actually is. The universe presented by organized religions is a poky little medieval universe, and extremely limited ("A Survival Machine").

I cannot disagree more with this kind of assessment. To be sure, the universe is a grand and mysterious place, and sparks our imaginations to wonder and awe. However, as marvelous as is the real world, the human stories told by religions such as Christianity and Judaism touch us in a far more personal way. Instead of nontheism's mysterious and mindless sea of stars, black holes and quantum fluctuations, Abrahamic religion offers to enrich our cultural history by weaving into it a sympathetic creator who has designed us in his image, and who cares about our well-being and shelters us from evil. And speaking of good and evil, religion tries to paint these concepts as monolithic forces vying for supremacy in this world---a romantic struggle in which we may take an active role. And on top of all this, theism still retains almost all the wondrous mystery of the physical universe!

I'm tempted to write that none of this means I wish I was a theist. But it wouldn't be true. Sure, I want to be satisfied by the truth, and by epistemic responsibility, but that doesn't mean I am. I may well be better off as a Christian, even if God doesn't exist. In fact, I'm inclined to think that I would be a much happier person.

I was recently reminded of this while reading George MacDonald's Phantastes. It's about a young man named Anodos who discovers he has fairy ancestry, and embarks on a journey through "Fairy Land," where he encounters all manner of wild and exotic fairy beings and elements. But after having been tricked by an ogre-woman, he is haunted by his "shadow," which follows him through Fairy Land and disenchants all upon which it falls. At one point, for example, he meets a wonderful little fairy child with magical fairy trinkets; but when the shadow wraps around him, Anodos suddenly sees only an ordinary boy with a straw hat and unremarkable toys. This sort of thing happens several times, whereupon Anodos begins to reflect on his situation. From the novel:

But the most dreadful thing of all was, that I now began to feel something like satisfaction in the presence of the shadow. I began to be rather vain of my attendant, saying to myself; "In a land like this, with so many illusions everywhere, I need his aid to disenchant the things around me. He does away with all appearances, and shows me things in their true colour and form. And I am not one to be fooled with the vanities of the common crowd. I will not see beauty where there is none. I will dare to behold things as they are. And if I live in a waste instead of a paradise, I will live knowing where I live" (pp103-104).

This passage struck me rather hard. What a lamentable position has nontheism put us in! On one hand, we value the truth, and knowing our place in the world. But this does nothing to mitigate the terrible absence of higher purpose, or of grand design.

What then, is left for us? Shall we accept Pascal's wager, as it were, and drown ourselves in Christian culture and influence in order that we might have a better chance of one day finding ourselves duped or seduced into believing the unbelievable? I think not. As wonderful as that might be for each of us individually, we have a moral responsibility to promote truth for the sake of those others who would benefit from it. But neither can I approve of those propagating the evidently false notion that religion is somehow smaller in imagination than nontheism. Honesty will not permit it.

Some comments on Brian Knapp's post

2011-07-28T19:21:00.000-05:00

Unfortunately it has become somewhat common for atheists to deny that they have any burden of proof in religious debates. While this may sometimes be true in some limited sense, I find it problematic for at least three reasons: First, it seems quite evident that many of the atheists who employ this tactic are in fact positive atheists, which is to say that they take the assertive position that there is no God, rather than the weaker position of unbelief in the existence of God. Now, it may be more interesting to talk about the justification for theism rather than that for positive atheism, but nevertheless the position of the nonexistence of God does indeed require some justification, and so anyone defending that position certainly has a burden of proof in that regard. Second, even a negative atheist has basic obligations to facilitate communication. In any two-way conversation, each party shares some measure of responsibility not just for communicating clearly, but also for assisting the other in doing the same. So for example, if a Christian offers an argument for the existence of God to an atheist, then the atheist, to the extent that he is part of that discussion, has a duty to respond in some substantive way. Third, although a negative atheist may not have any actual tenets to justify, depending on the context he may well owe the theist another kind of explanation for his position.

That said, there really isn't much to defend when it comes to mere unbelief. Once one notices that he has no reason to believe a particular proposition, then, given that we want to minimize such unjustified beliefs, we ought to give it up. The interesting question, then, is whether or not we can find a reason to think that God exists, and that is where the theist has a striking burden of proof.

Calvinist blogger Brian Knapp of choosinghats.com recently posted his own complaint to this situation. According to him, while we might not have a burden of proof defending unbelief in other gods, the Calvinist God is different, because it insists that we all know it exists (presumably this doctrine is based on his reading of Ro 1:18-25, and possibly other Biblical passages). He writes:

Now, if the God of the Bible was like any other god, they could get away with saying "no" and leave it at that---no burden of proof. However, the God of the Bible isn't like any other God. He claims that everyone knows he exists. He claims that he created the world. He claims that his existence is necessary for knowledge, ethics, aesthetics, etc. In short, he makes a bold claim about everyone's ability to reason, weigh evidence, draw conclusions, etc. He claims that none of those actions that we all do on a daily basis would be possible unless he existed as described in the Bible.

So that opens up an interesting challenge to the atheist. They aren't explicitly denying the existence of God when they say "I don't believe he exists", but they most definitely are *implicitly* denying his existence. Why is this? Well, it is because they are doing all these things that the God of the Bible claims ownership to, while at the same time they are saying "I don't believe he exists." They are relying upon all these basic beliefs that the God of the Bible claims *only* make sense if he exists.

To say they don't believe he exists is to say that it is *possible* to do these things (reason, weigh evidence, etc.) without him existing. But God says it is not possible to do them without him existing. Therefore (by implication) they are saying "This kind of God *does not* exist".

It isn't an explicitly positive claim that God does not exist, but is rather an implicitly positive claim. Either way, it is a positive claim, and therefore they own a burden of proof.

For Brian, the fact that we all believe God exists is corollary to something like an essential property of the Calvinist God. So to insist that we don't believe in his Calvinist doctrine is to deny the existence of his God; and this constitutes a positive claim in need of defense.

Now, before I address this, we may wish to make clear a certain distinction: for in one sense it is quite true that any self-professing atheist has his own sort of burden of proof with respect to the authenticity of his profession, insofar as a skeptic of genuine unbelief in God such as Brian might challenge him to defend it. This is not, however, the same as a defense of the negative atheist position itself. In other words, to challenge the accuracy of his self-identification as an unbeliever is not to challenge his justification for unbelief. The question of whether or not a person who declares himself negative atheist is justified in so doing is wholly separate from that of whether or not he ought to actually be an atheist, or other similar issues. So, maybe the Calvinist thinks this person is lying or self-deluded, and secretly believes in God despite insisting that he does not. Yet even if that's the case---indeed, even if we can prove it to be so---to the extent that we're interested in discussing the justification for negative atheism, we've made no progress.

Even so, Brian may be right to point out that in order to be consistent even a negative atheist must deny the existence of his highly specialized Calvinist conception of God (though even this is questionable). Yet the defense for disbelief he provides himself: our initial unbelief quite directly disproves the existence of the special Calvinist God which everyone knows exists. What additional proof does he require, the burden of which he thinks the atheist should shoulder? Now, he could always challenge our very unbelief, but that would, I think, move the conversation in a largely unproductive direction. We all trust our own ability to tell the difference between that which we do and do not believe. So for instance if I take myself not to believe one way or the other on the existence of a fifth moon of Pluto, that should be the end of the matter. It seems unlikely that any deeper self-reflection in that regard would be fruitful. Unless there is some outstanding reason to think ourselves in the throws of an unhappy delusion resulting in the subconscious repression of our belief in a fifth Plutonian moon, why should we consider the matter any further? I find myself in a similar situation with respect to my unbelief in God. It's possible that I'm just self-deluded, and that I really do believe in God, despite my second-order belief to the contrary. Yet we can say the same for any of our beliefs. Why afford this one special attention?

So while I appreciate Brian putting his finger on an interesting implication of Calvinist dogma, I must disagree that it has much bearing on the burden of proof had by negative atheists. Again, it seems like the most important issue is whether or not we have reasons to believe in God. It is certainly true that, as negative atheists, we should be responsible communicators and charitable interpreters, doing our best to understand and respond to the case for theism. However, in the end, the burden is on the theist to provide reasons for his belief.

Grim's Cantorian Argument Against Omniscience

2011-05-15T12:10:00.000-05:00

Philosopher Patrick Grim since the early 1980s has advanced an argument against the existence of God which turns on an incoherence he sees in the concept of omniscience, an essential property of God as understood by most orthodox incarnations of the Abrahamic religions.^[1] It runs as follows: There does not exist a set T of all distinct truths. For suppose towards a contradiction that T exists. Let f be a mapping from T into the set P(T) of all subsets of T, and consider the subset S of T of every truth q which is not contained in the set f(q). By definition of S, no truth q is mapped by f to S, and we conclude that f is not surjective. Since f is an arbitrary mapping from T into P(T), it follows that no such map is surjective. Now define a map g from P(T) into T. For each subset A of T (where A is a member of the set P(T)), define g(A) by the truth expressed by the sentence "A is a subset of T." Since every member of P(T) is distinct, then g maps them to distinct truths, which is to say g is injective. So there is an inverse map which induces a map g' from T into P(T), where g' is surjective. This contradicts our conclusion that no such map is surjective. It follows that our assumption must be false---that there can be no collection T of all distinct truths. However, in order to conceive the omniscience of God we must conceive that he knows all distinct truths. Since we can always conceive of known truths as sets, then conceiving the omniscience of God requires that we be able to conceive all truths as a set. Yet we have already shown that there is no such set, and so we cannot conceive all truths in this way. Therefore we cannot conceive the omniscience of God. Since omniscience is an essential property of God, this means we cannot conceive of God at all, and this prevents us from ever affirming that God exists.

I first encountered this argument on the internet, championed by an atheist mathematician who frequents a message board for religious debates. That it should find its greatest popularity among mathematicians seems natural, given that it is based on Cantor's power set theorem. At that time I reacted with amusement, struck by its obvious silliness. I asked Hans---that was the name of this mathematician---if he was serious, and although I don't recall his exact reply, it left me with the impression that probably he was not. Serious or not, though, Hans continues to this day to enthusiastically tout Grim's argument, and this led me to investigate its origins. For until recently I was not aware that this argument had ever been advanced by a professional philosopher, and when I discovered Grim had done so, I was simultaneously surprised and disappointed that such empty sophistry had found a home in the academic literature. I became even more dismayed when I discovered further that several more philosophers had published extensive responses to Grim. As if that weren't bad enough, it turns out that all but one of these responses which I took the time to read at any length have even deeper problems than Grim's original argument. This has contributed to my growing disillusionment at the desperate state of philosophy as an academic discipline.

John Abbruzzes published the worst of these objections to Grim in a 1997 paper,^[2] the first of which turns on a fundamental misunderstanding of Grim's argument. He writes:

Grim also makes a second assumption: that the multiplicity of truths, T, is a completed totality. This, however, need not be so, for the multiplicity of all truths may be, and in fact seems to be, infinite.^[3]

As Grim himself has pointed out, though, this criticism mistakenly limits Cantorian sets to finite collections, and this is not at all what we have in mind in the original argument.^[4] This of course calls into question Abbruzzes' remaining criticisms. Perhaps the least unreasonable of the bunch is that, according to Abbruzzes, Grim's argument can be adapted to deny the existence of the set of all propositions, where Abbruzzes insists that Grim quantifies over this set by asserting that there is no collection of all truths. In his own words:

His conclusion that 'There is no set of all truths' is equivalent to the universal proposition 'for all x, if x is a set, then x is not a set of all truths'. ...but [this] involve[s] universal quantification...over sets and truths...^[5]

Yet this analysis again seems obviously false. Even if we assume that Grim is asserting something logically equivalent to the statement "for all x, if x is a set, then x is not a set of all truths," this is not a case of quantification over truths or propositions, but over sets. We might instead try to follow in the spirit of Abbruzzes' criticism by pointing out that we are not justified in using T at all in our conclusion if we agree with Grim that T is incoherent. However, this is not at all required to feel the force of the argument. It is quite enough to conclude that the concept of omniscience shares the incoherence of T, and that this prevents us from ever coherently supposing that some entity is omniscient. In this way, Abbruzzes offers us nothing in the way of a valid or cogent critique of Grim.

Keith Simmons in his 1993 rebuttal to Grim discusses a more promising, but ultimately still unfulfilling consideration against his argument.^[6] I shall refer to this henceforth as the Liar objection, and it challenges Grim on the grounds that his argument depends on the allegedly question-begging assumption that

(1) There is a language in which the sentences of that language are too numerous to form a set.

To show that Grim in fact requires this key assumption, Simmons identifies another, seemingly innocuous assumption which Grim appears also to require, and generates from this a version of the liar paradox which has no apparent solution but to invoke (1). The reasoning goes something like this: Grim requires for his argument that for a given set, we can construct a distinct truth to correspond to the cardinality of that set. In particular, he must assume that for every cardinal number there is at least one distinct truth. To make this assumption, however, he must quantify over all cardinal numbers. Since cardinal numbers are too numerous to form a set, then whatever language we use to express his assumption must have the ability to quantify over such set-defying collections. It is therefore possible to make the following paradoxical statement:

(2) This sentence is not true in any language of any cardinality.

It's easy to see how (2) leads to a contradiction, whether it is true or false. Apparently, the only way Simmons sees to escape the paradox is to say that Grim's argument "stands above" the cardinal numbers. In other words, cautions Simmons, we need to assume on Grim's view that there is a language in which the sentences of that language are at least as numerous as the cardinal numbers. So (1) must be true, if Grim's argument is to succeed.

Though clever, this Liar objection has serious problems. First, I question the key assumption that we require a distinct sentence in order for each distinct truth to exist. While it may be the case that we need sentences in order to express truths, Grim's argument only requires that set-defying collections of truths exist, and not that they be expressible in some language. On the other hand, this position against truths depending on sentences is not at all obvious, and so we might be interested in the Liar objection as binding the success of Grim's argument to it, that is, to the assumption that truths can exist apart from sentences. Given uncertainty as to whether or not this assumption is accurate, the Liar objection, if otherwise successful, would limit the force of Grim's argument. Unfortunately, though, the Liar objection has further problems, and so it fails in this regard, as well. For if we are to interpret it as an objection to the truth of Grim's conclusion that omniscience is an incoherent concept, then we must further posit that (1) is false, since if it were true, then while Grim's argument might beg the question, on Simmons' view its conclusion would nevertheless be likewise true. Yet if (1) is false, and if Simmons' reasoning holds up, then it must also be the case that we cannot, as Grim does, use our language to talk about arbitrary cardinal numbers, which according to Simmons is tantamount to quantifying over them. Of course it seems clear that in fact our language is quite capable, one way or another, of expressing truths about set-defying collections like the cardinals. Simmons even does this himself when expressing his Liar objection, for example when he mentions entities such as "all cardinals." In defense of Simmons, we might say that we ought for this reason to take his argument as incoherent, but acknowledge that its incoherence somehow reveals a similar incoherence in Grim's argument. However, this recourse seems implausible since it entails a denial of the coherence of discussing arbitrary cardinals, which is required for modern mathematics. In short, Simmons' reasoning, though he aims it squarely against Grim, should it succeed, succeeds in undercutting the coherence of set theory. Yet it seems much more natural to affirm the coherence of set theory, and suppose instead that something must have gone wrong in the Liar.

Third, whatever solution we have to the similar paradox

(3) This sentence is not true in any language which exists.

must be sufficiently specific as to render it inapplicable to (2). Yet judging from his approach to (2), we might expect Simmons to prefer to object to (3) on the grounds that we cannot quantify over extant languages due to their numerousness. On this view, (3) is incoherent, and thus not paradoxical. This leads quickly to problems. For example, it commits Simmons to the implausible position that there are infinitely many extant languages; for since we can always quantify over finite quantities, then if there are finitely many extant languages then we can quantify over them. Next, if we consider the case where extant languages form a set, then Simmons must assume that there are certain sets too numerous over which any extant language may quantify, and this entails an even more direct challenge to the coherence of set theory than we have already mentioned. Otherwise extant languages are too numerous to form a set, which again seems implausible, and which Simmons seems to himself implicitly deny when he agrees with Bertrand Russell that the statement "to each set there corresponds a proposition" is untrue.^[7] So given these three counter-objections, it seems that the Liar is insufficient to overturn Grim's argument.

Most recently, Laureano Luna published in 2011 another creative yet inadequate defense against Grim's argument.^[8] Luna's objection to Grim had been foreshadowed by Abbruzzes' earlier remark to the effect that, whatever logic we human beings use, God needn't himself think in terms of set-theoretical objects in order to quantify the propositions he knows.^[9] Luna develops this idea further, writing that

if the traits of abstract objects depend on the peculiarities of the human mind, then the nonexistence of the set of all truths can be just a phenomenon relative to the human intellect (as a finite intellect, for instance) so that for other intellects (perhaps infinite ones) truths could form a completed totality. ...the nonexistence of certain totalities, such as the totality of all sets or the totality of all truths, is the consequence of a peculiar trait of the human mind, a trait related to its finiteness.^[10]

To put in in terms of the present discussion, suppose we can agree that Platonism is false or incoherent. Then, according to Luna, the properties of abstract objects like T depend in some way on the intellects which conceive them. In particular, the previous proof only shows that T fails to exist relative to our limited human minds. So, it could well be that relative to a superior mind such as God's, T may exist after all.

I'm a little suspicious of the leap from rejecting Platonism to supposing that all the properties of abstract object depend on the minds which conceive them. However, I don't want to criticize him on that point since, for reasons of my own, I do agree that the properties of abstract objects are indeed determined by our minds. Indeed, we can see this by noticing that abstract objects are completely characterized by definite conceptual procedures. So unless we have another way to make sense of abstract objects, it seems unavoidable that we should attribute to their properties a dependence on our minds. The real trouble with Luna's argument is that his conclusion that God might be able to make sense, in a manner of speaking, of the existence of T, does nothing to diminish the fact that we ourselves remain wholly unable to do so. There may well be a truth, call it u, which a super-intelligent being G knows, but which we are incapable as human beings of even comprehending. Unfortunately for us, if belief in the existence of G depends on a comprehension of u, then since u defies comprehension then we can never justifiably believe---and hence never know---that G exists. With this in mind, we can interpret Grim's argument along the following lines: since justified belief in the existence of an omniscient being depends on the our being able to make sense of T as a coherent concept, and since we find T to be incoherent, then we cannot justifiably believe, and hence we cannot know, that an omniscient being exists. Given this interpretation, it won't matter if some other being is able to make coherent sense of something like T. The fact remains, if Grim is correct, that we are not able; yet we must be the ones to make sense of T if we are ever going to justifiably believe in the existence of an omniscient being.

Even just to take the objection as far as we have, though, we must, as I alluded in the previous paragraph, speak loosely about T. After all, T does not really exist, even on Luna's view, with respect to human minds. In other words, neither the symbol 'T' nor the description which it abbreviates denotes anything of which we can make coherent sense. If T is incoherent to us, though, then any attempt on our part to appeal to T we shall find likewise incoherent. Yet Luna must appeal to T if he is to suggest that God can comprehend T. If Luna justifiably believes that God comprehends the existence of T, then he must find the sentence "God comprehends the existence of T" to be coherent. However, the incoherence (with respect to us) of T as a constituent part of the sentence infects the sentence as a whole, with the unhappy result that Luna believes something incoherent to him. If we take incoherence as undermining or otherwise preventing justification, then it follows immediately that Luna is unjustified in believing that God comprehends the existence of T. In short, when Luna asks us to suppose that God might comprehend T, he's asking us to suppose something which is at least incoherent to us.

Philosopher J.C. Beall also thinks he has discovered a way to avoid the force of Grim's argument. He contends that we ought to regard propositions as maps from possible worlds into truth values, and that on this view we cannot construct a collection of distinct truths corresponding to each member of P(T).^[11] I think it's fairly obvious, though, that the possible worlds interpretation of propositions is false. The reasons to reject this interpretation are numerous, but to give just one example we may turn to again to Beall, who acknowledges that on his view there is precisely one necessary truth; to disprove the possible worlds interpretation, then, we need only find two distinct necessary truths, for instance that Alvin is not identical to Patrick, and that 17 is prime. No doubt Beall would argue those sentences express the same proposition, but I think it's fairly clear that no such argument can ever be successful. A single super-proposition is simply not what we mean when we talk about necessary truths.

Despite this failing of Beall's approach, however, it's not too terribly far from what I think is the best response to Grim. The idea is not to claim that there is only one truth---for this is manifestly false---but rather that there is only one way reality actually is. In other words, if God has a perfect mental representation of the whole of the universe, past, present and future, then this is all He needs to know about in order for Him to satisfy orthodox doctrines relating to omniscience. So Grim is mistaken to suppose that omniscience involves the incoherent notion of T. Instead of thinking about knowledge as turning on individual truths, we can liken it to having an accurate picture of the world. To be omniscient, then, is something akin to having a perfect picture. Grim might object to this response by alleging that in order to know the way the reality is---in order to have that perfect picture---God must know every truth, i.e. he must know every element of T. Yet although this view might be intuitive, I see no good reason to think it is appropriate. Consider as an analogy the sentence "a baseball is smaller than a school bus." It expresses a true statement, and provided we have sufficient experience with American suburbia, we all know it to be true. However, it may never have occurred to us until just a moment ago to relate baseballs and school buses in just the way that sentence does, and pick out an arbitrary baseball as being smaller than an arbitrary school bus. Does that mean we didn't know prior to considering this sentence that a baseball is smaller than a school bus? Surely not. In this way, knowledge does not depend on logical constructions or expressions of particular statements. We don't need an omniscient being to hold in his mind a list of all possible truths. Instead, we merely require Him to have a complete understanding of the way reality is.

A defender of Grim might insist that on this view there are nevertheless truths which God does not know in the fullest sense. If we take truths to necessarily be about the world, then this of course contradicts the assumption that God has a complete understanding of the world. However, the only way I can see this objection to succeed is if there is a conscious creature which has a deeper apprehension of some truth than does God. For the only unique content to individual truths, as opposed to a general picture of the world, is the collective properties which mark them out for individuality. To see how this works, we can look at a sort of special case:

(4) The 76th digit of π is 6.

Consider a hypothetical reality R where no conscious creature thinks about (4) at any time in the whole existence of R. From our perspective outside R, we can easily verify that (4) is in fact true. Is then (4) also true from the perspective of a conscious creature within R? I would suggest that (4) is not a truth about R, but rather it is a truth about our perspective outside of R. Now, it may well be the case that the conscious creatures of R know an effective procedure with which, from our perspective outside R, we can say in some sense that they could discover the truth of (4). Even if they don't recognize this procedure for what it is, we can still say that there exists, at least beyond the boundaries of R, a procedure for them to find which would allow them to learn that (4) is true. However, all these things which we say about the truth of (4), and the possibility of conscious creatures inside R to discover (4), must be said outside of R, from our external perspective. For the creatures of R themselves, there is no truth about (4) as long as (4) never occurs to them. The "knowledge" that they are missing out on by failing to think about (4) is the knowledge of what could possibly be the case if only they took the time to investigate matters relating to (4). Yet if it really is the case, as we have stipulated, that nobody in R ever thinks about (4), then the only sense in which it could "possibly" be otherwise is from a larger perspective, i.e. from our external perspective. The God of R, if He exists, is not missing out on information about R by failing to know (4), because R is such that (4) is never conceived therein; from the perspective of the conscious creatures (including God) of R, (4) does not really exist to be conceived.

This view may seem radical, but I find nothing else tenable. To ease its strain on our intuition, we may consider the following sentence:

(5) God decrees an asteroid to destroy the earth.

It is in God's power to know (5), and yet God does not know (5) so long as he declines to decree an asteroid to destroy the earth. Is God missing out on knowledge because he does not know (5)? Clearly this is not the case. It's not that (5) is impossible for God to know, though. He could come to know (5) simply by making it the case that (5) is true. Yet we don't say for this reason that God is not omniscient. Similarly, the God of R could come to know (4) by conceiving the requisite procedures relating to (4). The moment the God of R conceives these procedures, (4) becomes true from within R. If God declines to conceive the procedures, though, which is to say that if God's mind does not operate in such a way as to calculate the 76th digit of π, then (4) is not true from within R. For there is nothing we can say about (4) which has any bearing on the conscious creatures of R except to relate R to our own perspective where (4) is true.

Now, I should note that I think this view is well-founded; for I can't make sense of its denial, nor do I think can anyone else. Even if we reject it, though, it should be clear that Grim's argument will still fail. For if we reject the view I just outlined in favor of one where we take truths to be so regardless of their conception by a real conscious creature, then there still seems to be no good reason to accept Grim's conception of omniscience. In fact, to the extent that Grim's conception is provably incoherent, we have good reason to reject it. This doesn't mean we can't make sense of omniscience in some other way, however. Philosopher and Christian apologist Alvin Plantinga, addressing Grim on this matter in a published dialog, explains succinctly:

My main puzzle is this: why do you think the notion of omniscience, or of knowledge having an intrinsic maximum, demands that there be a set of all truths? As you point out, it's plausible to think there is no such set. Still, there are truths of the sort: every proposition is true or false (or if you don't think that's a truth, every proposition is either true or not-true). This doesn't require that there be a set of all truths: why buy the dogma that quantification essentially involves sets? Perhaps it requires that there be a property had by all and only those propositions that are true; but so far as I can see there's no difficulty there. Similarly, then, we may suppose that an omniscient being like God (one that has the maximal degree of knowledge) knows every true proposition and believes no false ones. We must then concede that there is no set of all the propositions God knows. I can't see that there is a problem here for God's knowledge; in the same way, the fact that there is no set of all true propositions constitutes no problem, so far as I can see, for truth. So I'm inclined to agree that there is no set of all truths, and no recursively enumerable system of all truths. But how does that show that there is a problem for the notion of a being that knows all truths?^[12]

Grim's response to this objection is to point out that we have no semantics for quantifying over anything but sets. Yet Plantinga shows with his examples that indeed we do have just such semantics available to us---the only catch is that they are not formalized into a mathematical framework. So it seems plain to me that Plantinga's objection is perfectly successful, and that Grim has nothing to offer us in terms of a reason to accept his deliberately incoherent account of omniscience.

In sum, and at the risk of sounding overly harsh, I must once more express my profound disappointment at the audacity of Grim to advance such an obviously flawed argument, the willingness of numerous, conventionally "reputable" philosophical journals to publish it again and again, the eagerness with which his fellow philosophers took that argument seriously, and the miserable inadequacy, Plantinga excepted, of their various responses. I don't mean to suggest that these professionals are incompetent or unskilled, but it pains me to see them permit each other to publish arguments of such poor quality. It, along with similarly bad arguments found in the literature, has me worried for the discipline as a whole.

Notes:

[1] Grim, Patrick, "The being that knew too much," International Journal for Philosophy of Religion 47, 2000.

[2] Abbruzzes, John, "The Coherence of Omniscience: A Defense," International Journal for Philosophy of Religion, Vol. 41, No. 1, Feb., 1997.

[3] Abbruzzes, p32.

[4] Grim, pp147-8.

[5] Abbruzzes, p32.

[6] Simmons, Keith, "On An Argument Against Omniscience," Noûs, Vol. 27, No. 1 (Mar., 1993), pp. 22-33.

[7] Simmons, p26.

[8] Laureano, Luna, "Grim’s arguments against omniscience and indefinite extensibility," International Journal for Philosophy of Religion "Online First" 2011 Apr 23.

[9] Abbruzzes, p32.

[10] Luna, 2011.

[11] Beall, J.C., "A Neglected Response to the Grim Result," Analysis, Vol. 60, No. 1, Jan., 2000, pp. 38-41.

[12] Plantinga, Alvin, and Patrick Grim, "Truth, Omniscience, and Cantorian Arguments: An Exchange," Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, Vol. 71, No. 3, Sep., 1993, pp267-8.

Goodness Over God counter-apologetics podcast

2011-05-01T08:17:00.000-05:00

I'm pleased to announce that philosophy graduate Michael Long and I have successfully launched the counter-apologetics podcast Goodness Over God, where we tackle religious and philosophical issues on a weekly (more or less) basis. We would like to have guests as often as possible, including but not limited to religious believers who wish to defend their views in a civil and friendly environment. So if you would like to participate, feel free to drop us a line at the following email address: GoodnessOverGod@gmail.com

Here is a list of the episodes so far:

Episode 05 (2011 Apr 30) - God as an Explanatory Hypothesis and Causality (with special guest Rachael Morris)

Episode 04 (2011 Apr 23) - Easter, Miracles, and History

Episode 03 (2011 Apr 09) - Hell and Justice

Episode 02 (2011 Apr 05) - Secular Ethics, Theistic Ethics, and Faith

Episode 01 (2011 Mar 31) - Plantinga's Modal Ontological Argument

(Please note that we originally started under the name "Truly Free," so we introduce ourselves that way in our first three podcasts.)

You can also check out the Goodness Over God blog, where we discuss various issues related to the podcast.

If you don't like downloading mp3s, you can stream the podcasts directly from the website, or from right here!

And remember, if you want to be a guest, go ahead and email us at: GoodnessOverGod@gmail.com We can discuss just about anything religion- or philosophy-related. The format is also flexible---we can either have a nice informal conversation, or we can have a more structured (but still friendly) debate, and everything in between. It's up to you!

Enjoy the shows!

Mike Licona on Bart Ehrman's Forged

2011-04-03T13:07:00.000-05:00

Christian apologist and New Testament historian Mike Licona has written a review of Bart Ehrman's new book, Forged (2011). To my knowledge, it is the first significant review of Ehrman's book to make the rounds on the internet. In this response, I will address a number of Licona's most striking objections, and show that all but one of them are founded on serious mistakes of one kind or another. I will argue that he deeply misunderstands Ehrman in several instances, and that his objections are periodically irrelevant and fantastic. Given all this, it certainly appears to me that Licona has permitted his rather strong religious biases to cloud his reasoning. Overall, I'm very disappointed with his analysis, and can find little insightful in his critique.

Before looking at the arguments themselves, I would like to say something on the scholarly situation, as it bears on the dispute between Licona and Ehrman: Indeed, Licona primes his readers by painting Ehrman as "left of the middle," and recommending Christian scholars Luke Timothy Johnson and Raymond Brown as representing a more conservative but still moderate position. As it happens, I respect both of those scholars, and in fact I agree with Johnson over Ehrman on a number of issues, for instance the authenticity of the Pastoral epistles. I'm not sure how much help it is to mark out a center of the scholarly spectrum, though. New Testament studies seem to me to be hopelessly bothered by ridiculous religious biases on one hand and reactionary skeptical biases on the other. For instance, Licona himself counts among his historical conclusions that Jesus of Nazareth was raised from the dead by unknown powers which originate in a disembodied mind. If this was merely a religious belief on his part that would be bad enough, but he actually travels around the country to speak publicly and debate opponents in support of his view that historians ought to conclude based on their scholarly research that Jesus' corpse was supernaturally reanimated! The far left is considerably better off than that, but still advances conclusions dubious in the extreme (for example the claim that the historical person Jesus never even existed). With such obvious biases at play in the scholarly community, I can't bring myself to trust "the middle" in the same way I would ordinarily do with other branches of history. Instead, I insist on keeping a keen eye on the evidence, and weighing the arguments for myself without much concern for the academic authority (or lack thereof) of the person presenting them. I strongly encourage others to do the same.

To that end, we may investigate some of the arguments on the table in Licona's critique. Laying out his own view of the situation, he cites Eusebius' famous list of Christian Scriptures (Ecclesiastical History 6.20.1) as evidence that the proto-orthodox were quite careful in accepting books as canonical; in particular, he alleges that the "general tendency in the early Church was to exclude rather than include." If this is true, however, it is not evident from the Eusebian passage given. Nor is it obvious from any evidence with which I am presently acquainted. On the contrary, early Christians offered some notoriously bad arguments in support of canonization, for example Irenaeus' argument that we can know the four traditional Gospels are inspired because there are four "principal winds" and four "zones of the world" (Against Heresies 3.11.8), and also the initial acceptance by Serapion of Antioch of the Gospel of Peter as canonical simply because it was attributed to Peter (Eusebius, Ecclesiastical History 6.12). More importantly, however, canonical is not equivalent to authentic; the Church also took as authentic (but not canonical) a good number of dubious writings, for instance the Apostles' Creed and the spurious epistles of Ignatius. While we do know that the proto-orthodox were concerned about the issue of authenticity, I am not aware of any evidence which would indicate that they were in a good position to adjudicate on it. Instead it seems that they based their decisions largely on the perceived doctrinal content of the materials, which is to say that they tended to accept books which supported their theology and reject those which did not---a decidedly poor methodology to the purpose.

Licona next complains that Ehrman's arguments against authenticity are weak and unpersuasive. As an example, he cites Ehrman's contrasting of Eph 2:5-6, where the author takes the resurrection of the dead as having already occurred, and Rom 6:1-4 and 1 Cor 15, where the actual Paul propounds the opposite view that the resurrection is a future event. Licona agrees with Ehrman that the Roman and Corinthian passages do indeed show Paul's vision of a future resurrection. However, he contends that Paul also speaks of the resurrection "in a symbolic sense" in Rom 6:13:

Do not present your members to sin as instruments for unrighteousness, but present yourselves to God as those who have been brought from death to life, and your members to God as instruments for righteousness. (ESV)

He suggests we should interpret Eph 2:5-6 according to the same symbolism. Yet this counter-argument seems to me exceedingly weak. It is true that Paul thought Christians to have escaped in some sense the powers of sin and death, and spoke of this in terms of being "alive to God in Christ Jesus" (Rom 6:11, ESV), and that this is how we ought to interpret Rom 6:13. However, this present-day life in Christ is contrasted with the future physical resurrection of dead bodies, of which Jesus was the "firstfruits," and in which Christians would follow at His second coming (1 Cor 15:20-3, ESV). Eph 2:5-6 seems to address this actual, physical resurrection:

...even when we were dead in our trespasses, made us alive together with Christ---by grace you have been saved---and raised us up with him and seated us with him in the heavenly places in Christ Jesus... (ESV)

So while it is possible that Paul was simply using more symbolism in his epistle to the Ephesians, it seems more natural to me to interpret that particular passage as referring to a literal resurrection of the dead. So it seems that Ehrman is quite right to marshal this as evidence against authenticity. That said, I should add that I don't believe Ehrman's argument is especially compelling on its own. However, he does raise a fair point of evidence against the authenticity of Ephesians which ought to be considered alongside the other evidence available. We are also free to consider Licona's interpretation, which I agree is quite plausible, but this in no way undermines Ehrman's point about the physical resurrection.

Next Licona disputes some of Ehrman's historical observations and conclusions. I find his complaints quite bizarre, however. His most serious allegation is that Ehrman misleads his readers in the following passage:

The New Testament emerged out of these conflicts, as one of the Christian groups won the arguments and decided which books would be included in Scripture. Other books representing other points of view and also attributed to the apostles of Jesus were not only left out of Scripture; they were destroyed and forgotten. As a result, today, when we think of early Christianity, we tend to think of it only as it has come down to us in the writings of the victorious party. Only slowly, in modern times, have ancient books come to light that support alternative views, as they have turned up in archaeological digs and by pure serendipity, for example, in the sands of Egypt. (p183)

Licona openly acknowledges that Ehrman is factually correct, here---"in a technical sense," he adds---but insists that it gives unsuspecting readers the wrong impression nonetheless. Yet he believes that Ehrman here gives the implication that "the only thing distinguishing the literature that made it into the New Testament from the literature that did not is the results of a vote."

This allegation seems to me inexplicable. Does he perhaps think that when Ehrman tells us the early church "decided" on the issue, this somehow suggests a decision by vote? I certainly don't get that image from Ehrman's language. Incredibly, Licona even hints that this may constitute a deliberate deception on Ehrman's part, telling us that "in a book where he is identifying deceit, it's ironic that Ehrman himself engages in misleading his readers." On the contrary, Ehrman wrote an entire volume expressly devoted to clearing up such gross misconceptions, and in which he bluntly countered that "there was certainly no vote to determine Jesus' divinity," and that "the formation of the New Testament canon was instead a long and drawn-out process that began centuries before Constantine and did not conclude until long after he was dead" (Truth And Fiction in the Da Vinci Code, pp15,74).

This is not the only clear instance where Licona has misunderstood Ehrman. For example, in one passage Ehrman wards against the misconception that Christianity was systematically persecuted in the early days of the Roman Empire, writing that, before the year 249 CE, "there were...no declarations that it was illegal, no attempt throughout the empire to stamp it out" (Forged, p164). In response, Licona objects that Nero had Christians executed in 64 CE in Rome, and that Pliny the Younger had the same in Bithynia et Pontus in the early second century. While these events really did occur, they do not seem relevant to the point Ehrman makes in Forged (and other works), which is that we have no evidence of an empire-wide persecution. It appears, then, that Licona has mistaken Ehrman to be saying instead that, in all the empire, there were never any persecutions up to the year 249 CE. Yet this certainly does not follow from anything Ehrman wrote, and on the contrary, it betrays a woeful unfamiliarity with Ehrman's other writings, where he details the persecutions under Nero, Pliny, and numerous others instances of persecution in the empire, including the rooting out of Polycarp in 155 CE, the executions of Perpetua and Felicity in 203 CE, and the persecutions in Lyons and Vienne in the late second century, among others; all of these have been discussed in some length by Ehrman. And even if Licona is ignorant of all this, how could he possibly think a professional scholar of Christian history could be unaware of these events? Does he think Ehrman suddenly forgot all that learned in his many years of training? Licona seems to have no excuse for this grievous error.

Or consider the following description of the book of Acts from Forged, and quoted in Licona's critique:

a book that scholars have as a rule been loath to label a forgery, even though that is what it appears to be (p199)

Despite this clear indication on the part of Ehrman that most scholars avoid calling Acts a forgery, Licona claims that "Ehrman speaks of Acts being a forgery as though this is the conclusion of scholarship." Now, it's not as if Licona simply overlooked on accident Ehrman's denial of this---he quotes it himself! So, why on earth should he think Ehrman to have suggested otherwise? Does he perhaps have the wrong idea about what it means to be "loath" to perform some action? Again, I'm very much perplexed as to what could possibly be the source of his strange views.

Licona continues on to dispute Ehrman's criticism of the book of Acts as historically inaccurate. According to Ehrman, we ought to believe Paul when he outlines in Galatians his movements following his conversion to Christianity. According to that epistle, Paul

went away into Arabia, then back to Damascus, and did not go to Jerusalem for another three years (1:15-19). This makes the story of Paul's conversion in the book of Acts very interesting. Here we are told that Paul is blinded by his vision of Jesus on the road to Damascus; he then enters the city and regains his sight. And what's the very first thing he does when he leaves town? He makes a beeline straight to Jerusalem to see the apostles (Acts 9:1-26). Well, which is it? Did he stay away from Jerusalem, as Paul himself says, or did he go there first thing, as Acts says? (Forged, p205)

According to Licona, this reading of Acts is uncharitable. Instead, he believes we should interpret Acts as a dynamic narrative which tends to "fast-forward" through certain events without comment, though he doesn't give us a reason to prefer his more stilted interpretation. Moreover, he highlights the fact that according to Acts, Paul converted outside Damascus, and then entered the city before moving on. Yet, I would ask, how does this bear on the issue? That is not at all clear to me, but I wonder if Licona is simply confused, here, and thinks that Ehrman believes Acts has Paul going to Jerusalem immediately after his conversion; but as we can clearly see in the quoted passage, this is not at all the case. Instead, the contradiction between Acts and Galatians is just as Ehrman describes it, whereby in Galatians Paul goes (apparently from Damascus or its outskirts) to Arabia first, then back to Damascus, and not to Jerusalem until years later; while in Acts Paul goes inside the Damascus, then to Jerusalem, and never to Arabia. The tension is made worse by Paul's comment in Galatians that he "did not immediately consult with anyone" (1:16, ESV), whereas in Acts it was only three days before he began visiting other Christians and preaching the Gospel in Synagogues (9:3-20). Now, it is certainly possible that the author of Acts simply left out Paul's trip to Arabia, but I can find no evidence in support of this view. Apparently the only reason to prefer Licona's reading is if one is already committed to harmonizing the Biblical accounts, and this is hardly acceptable if we are interested in historical methodologies or indeed truthseeking in general.

Licona's impressive commitment to creatively harmonizing the New Testament is especially evident in his treatment of Acts 9:26-30, where Paul meets with "the apostles" (ESV), despite the fact that Paul expressly tells us in Gal 1:18-20 that he did not meet with any apostle except Peter and James. According to Licona, we can explain this by noticing that

if the Jerusalem Christians were fearful that Paul may have playing a trick on them in order to infiltrate their ranks and identify the key leaders of the entire Christian Church, we can understand why only two leaders were willing to meet with him until they could be certain of the genuineness of his conversion to Christianity. A wise move indeed. No contradiction is necessary.

I cannot help here of being reminded of Heinrich Paulus' colorful interpretations of Jesus' miracles, for example his suggestion that Jesus' walking on water was the result of the disciples' erroneously thinking themselves to be in the middle of the sea when in fact they were just by the shore. Licona's speculations seem no better than that, and so it's difficult to feel any force behind his criticisms of Ehrman.

Despite Licona's many mistakes, not all of his criticisms are completely off-target. He points out that Ehrman himself admits that many of the reasons for thinking the epistles were forged take for granted that they were not extensively modified or otherwise influenced by the thoughts and expressions of secretaries. Yet Ehrman seems unable to provide good reason for making this assumption, except perhaps that there is no precedent for it in Greco-Roman antiquity. However, Licona correctly points out that such an argument is by no means decisive, especially considering that Paul is known to have used secretaries for his undisputed letters. So, this seems to me a valid defense against Ehrman's stylistic charges. On the other hand, just as Ehrman's arguments are not absolutely compelling, neither is Licona's counter-argument. There seems to me no way to decide the issue of a secretary on the basis of the existing evidence, and in the face of this uncertainty we must take stylistic arguments against authenticity to have significant force. Only we must be careful to remember that there is at least one possible explanation to resolve most of them. Fortunately for Ehrman, the most powerful arguments against the authenticity of most New Testament books are not stylistic, but rather based on external data, as well as their substantive (i.e. style-independent) internal content. So Licona's objection isn't going to hold much weight in the face of the totality of the evidence.

In sum, then, it seems plain to me that Licona has allowed his religious biases to get the best of him. His understanding of Ehrman's points appears garbled in many important respects, and as we have seen this too leads him to make a number of serious mistakes in his critique. I am sorry to report then, that as a result, he has little here of value to offer.

Anderson and the Epistemic Status of Theism

2011-03-13T08:54:00.000-05:00

Philosopher and Calvinist apologist James Anderson, in Paradox In Christian Theology, devotes a chapter spanning 62 pages to outlining the epistemic status of Christian theism. I would like to highlight two observations regarding this chapter which I think are important for best understanding his position: First, he does not present an argument for the existence of God, nor does he attempt to lay out any good reasons for taking a theist position; and second, he neither attempts to show that Christian theism is warranted, but only defends the more modest assertion that it is warranted if it is true. Given these observations, we are obliged to conclude that Anderson's purpose in this chapter is not to secure a convincing case for the existence of God, nor for the truth of Christianity.

Anderson borrows his position on epistemic warrant from Alvin Plantinga. On their view, warrant is "that epistemic quality enough of which transforms mere true belief into knowledge."^[1] This is to be distinguished from mere justification, which is widely thought to be insufficient for warrant. Now, even though Anderson, again following Plantinga, assures us that theism is indeed justified, this justification he only understands in the weak deontological sense expounded by Plantinga in Warranted Christian Belief. For example, Plantinga tells us that a justified belief may be primarily if not entirely founded on ineffable impressions and sensations, and may even sometimes amount to mere "wishful thinking."^[2] For Plantinga, we do not require good reasons in order to satisfy the epistemic responsibility sufficient to deontologically justify our beliefs. To quote him directly:

How could [a Christian] possibly be blameworthy or irresponsible, if she thinks about the matter as hard as she can, in the most responsible way she can, and she still comes to these conclusions? Indeed, no matter what conclusions she arrived at, wouldn't she be justified if she arrived at them in this way? Even if they are wholly unreasonable, in some clear sense?^[3]

For my own part, I would like to insist that we demand much more of justification, and indeed of epistemic responsibility itself, than what Plantinga allows in his illustration. I want to find people accountable for willfully holding unreasonable beliefs. If a Christian theist has no good reasons for her Christian theism, and recognizes that deficiency, then she is epistemically duty-bound on my view to renounce it. Anderson, however, shares Plantinga's position, not mine; yet while he is correct that Christian theism is justified on Plantinga's account of justification, that won't be particularly helpful if wish to hold our beliefs to a higher standard.

Beyond giving good reasons or providing justification, however, Anderson strives to show that, if Christian theism is true, then it is also warranted. To this end, he again turns to Plantinga, whose account holds, in his own words, that a belief is warranted only if

(1) it has been produced in me by cognitive faculties that are working properly (functioning as they ought to, subject to no cognitive dysfunction) in a cognitive environment that is appropriate for my kinds of cognitive faculties, (2) the segment of the design plan governing the production of that belief is aimed at the production of true beliefs, and (3) there is a high statistical probability that a belief produced under those conditions will be true.^[4]

To endow Christian theism with warrant, Anderson turns to a doctrine he attributes to Thomas Aquinas and John Calvin, in which God brings forth in his human creatures a sensus divinitatis, that is, an innate, authentic sense of the divine. According to this view, the Christian God has built into our cognitive faculties a strong tendency towards theistic belief, indeed towards Christian belief. So, even though we might not have good reasons to believe in God, our innate proclivities urge us to accept Christian theism nonetheless, as intended by God's design. This, Anderson assures us, satisfies Plantinga's account of warrant, and thus, if God exists and the Aquinas-Calvin doctrine is true, then believers have warrant, and therefore knowledge, of God's existence.

For Anderson, an important corollary of Plantinga's analysis is that the question of warrant for theism is tied up with the question of its truth, and that we cannot rightly consider either issue independently of the other. For the most part, I agree with this conclusion: If God exists and has endowed us with a sensus divinitatis or something analogous, then it seems fair to say that theism is warranted on Plantinga's account; conversely, if God does not exist, then we do not seem to have any access to epistemic warrant for theism. In other words, as long as we limit ourselves to Plantinga's definitions, I don't disagree with Anderson's thesis that "if the basic contours of the Christian narrative are true, then there is good reason to suppose that the Christian's beliefs are warranted."^[5] Rather, I would like to point out that we still lack good reasons for Christian belief itself. Put another way, I'm interested in higher epistemic standards than those which Anderson borrows from Plantinga. Even if Anderson's vision of Christian theism is true, and God has designed our cognitive faculties to gravitate inexorably towards theistic belief regardless of reason or evidence, I would still be unwilling to call his belief knowledge; I demand more than just a divinely-programmed belief tendency to constitute warrant.

In my judgment, the most important observation we can take from Anderson's treatment is that he declines to offer any good reasons to think that theistic belief is true. This omission seems deliberate, and so I don't mean to suggest he tried and failed. However, I nevertheless find it extremely interesting that, in his discussion of warrant for Christian theism, he avoids any hint that we might be able to find rational justification of the strongest sort we typically desire. Furthermore, Anderson remains unable to conclude from his outline that theism really is warranted; the most he can say is that, if Christian theism and the Aquinas-Calvin doctrine both happen to be true, then belief in God satisfies Plantinga's weak account of warrant. In the mean time, if we seek to epistemically justify God-belief according to stricter standards, as I think any theist should, then we must look elsewhere to achieve that goal.

Footnotes:

[1] Anderson, James. Paradox In Christian Theology: An Analysis of Its Presence, Character, and Epistemic Status (2007), p158.

[2] Plantinga, Alvin. Warranted Christian Belief (2000), pp100-1. http://books.google.com/books?id=BypSHmoozV0C

[3] Plantinga, p101.

[4] Plantinga, Alvin. Warrant and Proper Function (1993), pp46-7. http://books.google.com/books?id=4OqJbrwcHtoC

[5] Anderson, p209.

A Simplified Account of Moral Objectivism

2011-03-06T08:17:00.000-06:00

In religious discussions, among other situations, we often raise the issue of whether or not moral values are objectively determined. By "objective" moral values, we typically refer to moral values which are not determined by human opinion or disposition. For instance, CSUSB philosopher Tony Roy characterizes objective moral values as those which are not "dependent on the attitudes of a person, group of persons, tradition, practice, or the like directed at" accepting that value.^[1] Apologist-philosopher William Lane Craig considers an objective moral value to be one discovered "independently of whether anybody believes it to be so."^[2] In this way, moral objectivism springs from the sense of morality laying in large part beyond our creative power, either as individuals or even as a society. Indeed, I take the view that circumstances far beyond our control determine the most fundamental moral values, and that no mere human opinion or social trend can change the morality or immorality of a given behavior. I thereby propose a trim but rigorous account of moral objectivism designed to capture the spirit of the typical view of objective moral values, and which might serve as a reference for future discussions.

We begin by noticing that a moral code assigns to each of a certain set of behaviors under one of a variety of possible conditions a particular moral value. For our purposes, we require two natural simplifications: First, we restrict the range of possible moral judgments to three distinct values: moral (M), immoral (I) and non-moral, i.e. neither moral nor immoral (N). So, we do not permit one moral behavior to be somehow "more" or "less" moral than another, and similarly with immoral and non-moral behaviors. Here we treat the non-moral judgment as a catch-all for behaviors which are neither moral or immoral, even if they are not explicitly addressed by the given moral code. So, if a moral code is silent concerning some behavior, then we take that behavior to be non-moral. Our second simplification is that, instead of distinguishing between behaviors and contextual circumstances, we shall merely take otherwise identical behaviors performed under differing circumstances to be distinct. So, for example, we might be tempted to say that crying 'fire' is a behavior which is moral when there is a dangerous conflagration nearby, and immoral when seated in a non-blazing but crowded theater. On this account, however, we shall instead regard these two behaviors as distinct insofar as they are performed under different conditions. This way, we can consider sets of behaviors exclusively, without any additional regard for contextual circumstances. Given these simplifications, we may identify moral codes with functions mapping a set of behaviors into the set of possible moral value judgments.

With these considerations in mind, we may proceed to construct our account. Let F be the set of all possible societies S made up of agents, at least some of which may be rational, and let G be the set of all possible behaviors by individuals living in a society S∈F (even if those behaviors are not possible across all societies S∈F). For each society S∈F, fix a moral code φ_S:G → V, where V:={M,I,N}. Now we put H:={φ_S:S∈F}, and define a moral code Φ_H:G → V as follows: Let T∈F be a society. If for each society S∈F we have φ_S(B)=φ_T(B), then Φ_H(B)=φ_T(B); otherwise Φ_H(B)=N. We also define a new term: A rational agent x of a society S∈F is sufficiently informed regarding a behavior B∈G if and only if x takes B to have a particular moral value y, and given any arbitrary body of true information, if x learns it, then x still takes B to have the value y.

We say that Φ_H is an objective moral code if and only if it satisfies the following three conditions:

(1) For each S∈F and B∈G, we have that φ_S(B)=M if and only if, for each rational agent x of S, if x is sufficiently informed about B, then x takes B to be moral;

(2) For each S∈F and B∈G, we have that φ_S(B)=I if and only if, for each rational agent x of S, if x is sufficiently informed about B, then x takes B to be immoral.

(3) There is B∈G such that Φ_H(B)≠N.

If Φ_H(B)=M or Φ_H(B)=I for some behavior B∈G, then we say that B is objectively right or objectively wrong, respectively. If B is objectively right or wrong, then we call that fact an objective moral value.

It follows immediately from our account that any objective moral code is unique. However, we have not guaranteed the existence of such an objective moral code. Notice also that our account does not specify what moral values are. So, we should not mistake it for some kind of ethical theory. Instead, however, I suggest we regard it as a partial framework for communicating an actual ethical or metaethical view. In this way, should we decide how to interpret moral values, we shall at once have a plan for investigating moral objectivity.

Footnotes:

[1] Roy, Tony. "Objective Moral Values and Metaphysical Queerness," p3 (online article). http://philosophy.csusb.edu/~troy/obj-val6.pdf

[2] Craig, William Lane, "The Indispensability of Theological; Meta-Ethical Foundations for Morality" (online article). http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5175

Inductive Standards and Calvinism

2011-02-28T13:12:00.000-06:00

Over the course of my various exchanges with presuppositionalist apologist Chris Bolt, he has repeatedly and mistakenly boasted that he has a satisfactory answer to the problem of induction which involves the Calvinist God (he calls it the "Christian" God). Until now, I've largely ignored this unusual (and, as we shall see momentarily, obviously false) claim, instead preferring to vigorously defend my own view of induction. It's usually fairly easy to go on the offensive, and poke holes in another person's argument; but it's considerably more challenging to defend one's own positive arguments for a given position. So, I've been more interested in meeting that challenge of defending my views than I have been in the comparatively simpler task of criticizing Chris's. In the case of induction, I think I've presented a solid case for my view over the course of my Skype debate with Chris and our subsequent written correspondence in the blogosphere. At this time, I'd like to capitalize on that defense by taking a more offensive-minded approach, that is, by pointing out just a few of the myriad of problems I see in Chris's position.

To begin, we should notice that Chris hasn't clearly articulated the reasoning behind his central objection that induction is unjustified on a secular view. In particular, even after six months of debate and blogging correspondence, he has never explained what his standards of justification are. I warned him about this deficiency back in November of 2010, writing that

there is a second possible interpretation of your criticism, which is that any non-deductive inference should be taken as invalid and therefore irrational. But if that's what you're saying, then I would simply reject whatever standard of rationality leads you to make that judgment. Non-deductive reasoning, e.g. inductive reasoning, is not irrational simply because it's not deductively valid---at least, not by my standard... But whatever you are using as a standard of rationality, I must insist that on my standard, there is at least one form of non-deductive reasoning which is perfectly rational: inductive reasoning. (source)

In our latest correspondence (which he has as yet declined to make public), I pressed the point:

I need you to explain, what are your standards of reasoning? What criteria do we use to distinguish good reasons from bad reasons? For me, my standards of reasoning cover inductive inferences directly. In other words, according to my standards, a cogent inductive argument IS a good reason to believe some conclusion! It seems to me that most people, including scientists and philosophers, use similar standards. But you apparently don't want to use a standard which directly grants inductive inferences as reasonable/rational/justified/etc. Well, okay. But then I have to ask, what DOES make for good reason, on your view?

For causes unknown to me, he has persistently declined to volunteer this rather essential information---and, to be sure, it is essential. He clearly intends to use different standards of rational justification than I do; but if he cannot articulate those standards, then how can he ever show that induction is "justified" by presupposing the existence of the God of Calvinism?

Indeed, his case for getting induction from Calvinism is extremely vague. Consider his remarks from our Skype debate in August 2010:

If God exists, then he created and hence caused us, our minds, and the world that we know with our minds, and the way that they all work. On this presupposition our conceptual scheme is automatically in touch with and corresponds to objects of experience with God as the connecting link. If we deny this view, then there's nothing to connect the [unintelligible] to God. But God is the connecting link between everything else. What is left is a loose and disjointed epistemology. There are, in this case, random objects of knowledge not connected together by God's creative, sovereign, fore-ordaining Word. There are not objects connected to the mind of man and his conceptual scheme. By definition, this world view cannot answer the skeptic, because it begins with a separation between the mind and objects in the world. Since God has not been brought into the picture at the start, we have what we might call an egocentric predicament. On the other hand, there is no egocentric predicament for the creationist. (source)

This is all I could find in his opening statement which resembled any kind of positive case for taking inductive inferences as justified. Since then, I have asked him to clarify his position, but thus far he has declined. This is unsurprising, considering the difficulty of his task. In fact, the alleged existence of God, whether Calvinist, Catholic or Muslim, simply does not help us along to finding appropriate standards of justification; given that induction is required to hold onto any conception of the external world (and even our private thoughts), it's easy to see that religious doctrines are likewise incapable of providing us the means of using a given standard to justify induction indirectly. The attempted solution which Chris presented in our debate falls into circularity, as I explained in our correspondence:

The problem with this position is that it already assumes induction. God's causal powers, as Hume pointed out in his famous essay, like all causal powers, consist only of our inferred or assumed regularities set in the context of other such inferred/assumed regularities. So, you can make all the assumptions or inferences you like, but they will only be rationally justified if they meet with some standard of rationality/justification. And since this is what we're after, an (unjustified) assumption that God has such causal powers, i.e. that the regularities you wish to infer already hold, isn't going to help us in the least. That's why I said you haven't been able to show any coherent and uniquely religious answer to induction. You're not adding anything relevant to the conversation when you talk about a creator-deity.

All Chris can do is to assume what we all assume---that induction is justified---and then, on top of that, assume that the God of Calvinism exists, that He created the universe and everything in it, that he inspired the 66-book Protestant Bible, that only his favorite strain of Calvinism properly interprets that Bible, etc. He's not giving us a novel way to deal with induction. Instead, he's only adding superfluous nonsense to what we already accept about induction!

In fact, we can generalize on this approach: Notice that inductive inferences are justified if and only if they meet with our standards of justification. If those standards are independent of the existence or nonexistence of God, then so too is the justification of induction. If on the other hand those standards depend on the existence or nonexistence of God, then we require from Chris an explanation of how his standards differ from non-Calvinist standards, and furthermore why we should be interested in using those standards. After all, how can we ever suppose that induction is justified on Chris's view if we don't know what his standards are? And even once we are able to identify them, why should we exchange our pre-existing non-Calvinist standards for his uniquely Calvinist standards? So far, he has declined to address either of those issues.

It's hard to anticipate what Chris might want to use as a standard for justification, but I suspect it must have something to do with the Protestant Bible. However, in order to make sense even just of the words on the pages---the very strokes of ink which make up the Hebrew, Greek and Aramaic characters---we need to have some kind of coherent conception of language already in place, and this requires induction. If we wish to make sense of the thoughts expressed by that language, for example the notion of Delilah having her lover's hair cut, we must first know what cutting and hair are, which is to say that we rely on the regularities of the world which make cutting hair possible. So, if Chris wants to use the Bible as a part of a standard of rationality or justification, he can only do so against the backdrop of some kind of uniformity of nature. In short, Chris would have the cart before the horse: induction is required in order to make sense of the Bible, not the other way around. If he wishes to use the Bible as part of his standards of justification, then it will only be on top of the inductive standards he must also use. Again, Chris would not be contributing anything relevant to the discussion of induction, or providing a uniquely Calvinist substitute for secular inductive standards; he would only be tacking on superfluous religious dogma to the inductive standards we already use.

Moreover, the Bible actually conflicts with the inductive standards we ordinarily use, as I informed Chris in our correspondence:

If you want to re-define the word "rational" in that way [such that accepting the Calvinist interpretation of the Bible is rational a priori by our standards of justification], then you are welcome to do so, though I will not follow you in your peculiar convention. The result, however, is a great inconsistency, unless you jettison some of the word's current meaning. In particular, induction compels us to accept truths which are plainly at odds with your form of Christianity, for example that the earth is billions of years old, and that we evolved from lower forms of life. Induction shows us that prayer is ineffective in curing disease, and that at least a few of the books of the New Testament were forged. (source)

Chris's defense against these charges consists of little more than claiming that they are merely unsupported assertions on my part. Yet clearly this is not the case. While it may be true that I have not personally marshaled all the evidence in favor of geologic time, biological evolution, the medical inefficacy of prayer, or the forgery of certain New Testament books, who can credibly deny that geologists, biologists, historians and other scientists have not done so in my absence? It seems an act of desperation to demand that I personally reproduce the arguments and experiments developed by these experts before we can accept their results. In the mean time, anyone familiar with these issues ought to know very well that the evidence points against the respective religious dogmas. These kinds of radical denials ought not even be taken seriously, a lesson we should have learned from our experience with Kent Hovind, Ken Ham and Kirk Cameron, among others. The only reasonable response available to Chris, it seems to me, is to acknowledge that the physical evidence really does point us away from his brand of Calvinism, but that we have other reasons to accept Calvinism which somehow trump that evidence. Unfortunately, this defense only works out if we can actually produce those reasons, which thus far he has not done, and which indeed it appears he cannot ever succeed in doing.

In contrast, secular standards of justification appear to me quite sufficient for accepting induction as rational. In the course of our debate and ensuing correspondence, I have addressed three particular concerns regarding inductive standards: First, we might ask, is it rational to choose to use induction? As I pointed out in the debate, however, we don't have a choice, here; we will use induction, whether or not we make a conscious choice to do so. This was the position of David Hume, and indeed Chris agreed with it at the time of our debate, even though he inexplicably thinks we need God to be able to agree. Second of our concerns is this: are individual inductive inferences rationally justified? Recall again that inductive inferences are justified if and only if they meet with our standards of rational justification. Along with philosopher Peter Strawson, I suggest that those standards deal directly with induction. In other words, a strong inductive case is part of what we mean by rational justification. To put it another way---and to borrow Strawson's analogy---asking whether or not inductive inferences are rationally justified is a bit like asking whether or not laws are legal. I furthermore suggest that Chris must use similar standards if he is to make sense of the world---even if he is to make sense of God---since induction is a prerequisite to that purpose. Third, and finally, we could inquire as to whether or not we have any motivation for using a standard of justification which permits inductive inferences. The answer to this question seems a resounding yes, since as I illustrated in great detail in our Skype debate, induction is absolutely required if we wish to develop any plans or strategies for predicting and controlling our experiences. So, if we want to be actors in the world, we ought to use inductive standards.

Although these three issues all regard induction in some way, they differ quite dramatically from one another, and accordingly demand differing responses. Chris, however, seems not to agree. He writes (emphasis original):

...the various answers that are being provided are not the same answer to the problem of induction. For example, an a priori solution to the problem of induction is not the same as a pragmatic solution to the problem of induction, however Ben has used both. This is not necessarily a problem insofar as the attempted answers are consistent with one another, but I am not sure Ben is even aware that he is offering multiple answers, and whether or not they are consistent with one another is debatable. (source)

Needless to say, I'm very much aware of the differences between my answers, and this all stems from the fact that there are different issues which demand our attention. Why, then, should Chris express surprise at my varying points? Perhaps he thinks we should only deal with one single issue, and ignore the others; but then on which issue does he want to focus our attention? He has not indicated to me anything which might suggest an answer to this. Alternatively, maybe he just doesn't appreciate the distinctions I've drawn. Yet if that is the case, then he seems to be in no position to disagree with my view, since one must first understand a view before one may sensibly oppose it. So, all this underscores the deficiencies in his own position. At best, Chris has neglected to offer uniquely Calvinist account of induction, while ignoring no less than two essential concerns regarding induction. At worst, he has conflated several of the distinct issues involved, causing him to adopt an ultimately incoherent position on induction and engage in a fundamentally unintelligible criticism of mine.

Whatever unspoken content his caginess has hidden from us, one fact stands out from our correspondence as abundantly clear: Calvinism is useless for helping us deal with induction. Chris is in exactly the same boat that we all are---that is, whether or not we realize it, we all use inductive standards of justification whenever we make sense of the otherwise disconnected experiences we have. Chris is not somehow exempt from this unavoidable human situation. Presuppositionalist Calvinists like to say that non-Calvinists "borrow" from the Calvinist world view, but ironically enough, in this case it is the Calvinist who is using independently secular standards without realizing it. The only difference between us is that, in addition to using those secular inductive standards, Chris has lumped in a host of arbitrary religious dogma along with them. If he thinks he can justify that dogma, he is welcome to continue to try to do so. However, he will make no progress towards that goal by invoking the circularity of using induction to make sense of Calvinist theology, then in turn claiming that Calvinist theology justifies inductive inferences. To the extent that the task depends on that circularity, Calvinism is thusly impotent for justifying itself.

debate with Jamin Hubner on the existence of God

2011-01-16T08:54:00.000-06:00

This past Thursday, 2011 Jan 13, I debated the Calvinist apologist Jamin Hubner, who according to his web page is the professor of theology at Jesus Bible Institute in Rapid City, SD, on the existence of God. You can listen to that debate online here, and read a transcript here. The debate was held over Skype, with moderator Joshua Whipps. Jamin is involved with Prof. James White's Alpha and Omega Ministries, though I do not know in what capacity (except that he blogs on their website). He's a presuppositionalist apologist, and has authored/edited at least three books on that subject in the past few years.

The debate went rather well, I think, for showing some key problems with presuppositionalism. Jamin's case for the existence of God was predictably vague, and the lengthy cross-examination periods allowed me to make that plain to the audience. On the other hand, I can hardly claim to have performed perfectly! Although I answered all of his central points, I did not always do so clearly, for instance when I implied but failed to explicitly state that what makes a judgment objective is its dependence on a standard, and not merely on a specific type of standard (e.g. a divine standard).

Even so, I think I successfully communicated my objections to Jamin's case. He had neglected to actually present any explicit argument for the existence of God, despite thinking himself to have done so. Instead---and just as I had predicted---he made a series of bold claims about the existence of God, to the effect that God explains all that we observe and experience, when nothing else can ever hope to do so. He declared in his opening statement,

Nothing can be explained---not facts, laws, biological information, the uniformity of nature, objective morality, the metaphysical preconditions of science, dogs, cats, or sauerkraut---nothing can be explained, let alone exist, without the Triune Creator of them all.

Anticipating this move, I told him in my opening statement that

this kind of rhetoric would be far more convincing if only it could be accompanied by an explanation of those lofty philosophical foundations which the presuppositionalist claims to have.

In other words, he needs to actually demonstrate how his presuppositions explain what he claims they explain, something he did not do in our debate. Moreover, he needs to show us why we always need such explanations, and also why we should think agnosticism disallows us from obtaining them. During our cross-examination, for instance, we had the following exchange:

WALLIS: Maybe I can't answer certain questions, but what about my inability to answer some particular question would lead you to believe that my views are inconsistent? [discussion of order]

HUBNER: Well, first of all, you believe that unanswered questions lead to inconsistency, otherwise why did you ask me to answer your unanswered question?

WALLIS: Again, let me clarify, I'm not suggesting that unanswered questions make for inconsistency.

HUBNER: Well I don't think you've ever asserted that unanswered questions makes for inconsistency. I think that assertions, multiple assertions that have no explanation and no foundation. And that has been demonstrated by unanswered questions. It's simply a demonstration that your world view really isn't much of a world view. It can't really be lived out. It can't function, except in terms of re-affirming self-autonomy.

In this way, he was unable to make the essential link between, on one hand, identifying unanswered questions on a secular view, and on the other hand, concluding that the secular view is somehow flawed, or that the Christian view is justified.

Beginning with his opening statement, and continuing throughout the debate, Jamin also stressed the following points (my paraphrase):

(1) We absolutely must presuppose the truth of the 66-book Protestant Bible.

(2) We should clearly perceive God when we look at creation.

(3) Christianity offers objective, infallible ethical and epistemological standards, when agnosticism relies on changeable and subjective standards.

(4) Nobody should listen to my attempts to address any such philosophical issues, because as an agnostic I can only state my own subjective opinion.

First and foremost, I reminded him that none of his assertions actually constituted, either individually or collectively, an argument for the existence of God. I took (1) to be a mere re-statement of the position which he needed to defend, and therefore in no need of a direct rebuttal. Rather, I answered it insofar as I pointed out that Jamin had failed to adequately defend Christianity.

Thesis (2) I took as an allusion to the teleological argument, and responded by explaining how we need to have some background of experience with the creative processes before we can learn to identify creative explanations. Since we have no recognizable experience with God or his manner of creative process, we are not in a position to detect divine purpose or creation. Jamin, in turn, responded by denying that he was appealing to the teleological argument. Instead, he told me, he simply believes that "creation presupposes the Christian creator," i.e. we can't make sense of the universe without presupposing the existence of Yahweh. Unfortunately for that position, however, he made no recognizable effort to defend it.

In response to (3), I pointed out that we have no guarantee God will not change his standard, and that furthermore we could easily capture an unchanging standard without appealing to God, if only we wished to do so. I also reminded him that no one standard is any more objective than another. In particular, I told him that

any claim that I make is going to appeal to some standard, sure. And, to the extent that it's a standard, it's objective. What else do we mean by "objective"? So I don't understand why you would suggest that my standard isn't objective.

With respect to (4), I told him that, first, we all have to use our own judgment, whether we are Christian or not, and, second, I'm not acting as an authority---that is, I expect people to weigh each issue for themselves, and not just take my word for it when I assert something.

In addition to those four points which I answered in some form or another, there was one other point which I let by. We may summarize it thusly:

(5) As an agnostic, I deny that I have any knowledge at all.

I was surprised he made this point, and essentially ignored it since there seemed to be more serious criticism to lend my attention. Needless to say, I only affirmed my agnosticism with respect to the existence of God. Of course, I know lots of things besides whether or not God exists! I have no idea why he thought otherwise, since I gave a detailed description of my agnosticism in my opening statement.

So, in sum, I believe I successfully rebutted his most serious and far-sweeping claims in favor of Christianity. After all, the only thing I really needed to do was to point out that he had not presented an argument, much less a good argument! His only defense to that very serious (I think) objection was that the substance of the argument had eluded me since its subject-matter ensured that it must be unlike any other, i.e. not deductive, inductive or abductive. I spent the rest of my time responding to miscellaneous objections to my agnosticism which he had (mistakenly) taken as relevant.

The only thing that really disappointed me about my performance was my hemming and hawing, and my occasional awkward pauses. I need to learn to speak more fluidly, and to master the art of rhetoric. Hopefully I will improve in that regard, for my next debate. Otherwise, I had a great time, and I hope Jamin felt the same. Moreover, I really hope he thinks carefully about the problems with his position, which seem to me to be abundantly obvious, yet which he---and many other presuppositionalists, it seems---somehow fails to recognize.

Collett's Transcendental Argument

2010-12-26T07:30:00.000-06:00

Here I reply to Don Collett's online paper "Van Til and Transcendental Argument Revisited" [sic], by denying his implication that arguments following Bas van Fraassen's presuppositional semantics are distinct from deductive arguments, and also by pointing out the invalidity of his sole stated example of a transcendental argument.

Twentieth-century developments in the Reformed tradition of theology have led a number of apologists to assert that there exist arguments which they call transcendental, which are neither identical with nor reducible to arguments of deductive or inductive form, and that only these arguments are faithful to God's plan for ministering to the unregenerate, that is, to non-Christians. However, this position leads us to certain problems---namely, if transcendental arguments are not deductive or inductive, then in what sense ought we regard their conclusions as justified? Collett's paper appears framed at least in part as an attempt to help answer this question by appealing to the logical system induced by van Fraassen's presuppositional semantics, since he evidently believes that this system is something altogether different from either induction or deduction. However, we shall see that Collett does not, in fact, accomplish this task, nor does he suggest any strategies for doing so, for the very simple reason that, contrary to Collett's analysis, van Fraassen's system is indeed one of deduction.

While Collett never unequivocally states that he believes transcendental arguments to be distinct from deductive arguments, the implication remains strong throughout his paper. For example, he writes (emphasis original):

Thus in contrast to both deductive and inductive forms of argument, a transcendental argument allows the concept of God to function as a logically primitive rather than logically derivative proposition, thereby bearing witness to the non-derivative character of God's existence on an argumentative level. To state matters another way, in [Cornelius] Van Til's Christian-theistic construction of transcendental argument, the truth of God's existence is not a deductive consequence of the premises of the argument, but rather the ontological and logical ground for the very possibility of the premises themselves. This is undoubtedly one of the reasons, if not the chief reason, why he believed that transcendental arguments were uniquely suited for the task of placing into sharp relief the non-deductive character of the truth of God's existence.^[1]

This is not an isolated passage; he peppers similar suggestions throughout his paper to the effect that, according to Van Til's conception of transcendental arguments, they are "non-deductive." In this way, a natural reading of Collett gives us the clear impression that he shares Van Til's view in this respect; if this is so, however, then he requires a further defense of it. Now, this is not to say that he intended such a purpose for his paper; on the contrary, he seems to have voluntarily restricted himself there to attacking one particular mode of reduction, namely that once argued by apologist John Frame,^[2] instead of generally condemning all possibility of reduction. Nevertheless, Collett's choice to describe transcendental arguments in terms of van Fraassen's presuppositional semantics, which induce an unmistakably deductive system,^[3] leads him ultimately to a view of transcendental argumentation entirely incompatible with the notion that transcendental inferences are always distinct from deduction. In other words, however Collett thinks his transcendental arguments cash out, they must do so deductively if we are to frame them using van Fraassen's semantics. With this in mind, we may examine his deductive method.

Following Peter Strawson,^[4] van Fraassen characterizes the two-place presupposition relation in the following way: If A and B are sentences in a presuppositional language, then A presupposes B if and only if the following hold:

(a) T(A) only if T(B); and

(b) T(¬A) only if T(B),

where we read 'T(A)' as 'A is true.'^[5] So the following is deductively valid in van Fraassen's system:

(1) P presupposes Q;

(2) P;

(3) therefore Q.

This is because we have by the presupposition relation that T(P) only if T(Q), while taking P as a premise gives us T(P); and from this it follows by modus ponens that T(Q), which is to say that we conclude Q is true.

Notice that even though we applied modus ponens, we can still construct (albeit not in van Fraassen's system) deductively valid arguments which do not make use of it. This is because deduction is not limited to a single kind of logic, e.g. classical logic. In fact, in this case we are not even using classical logic! for van Fraassen's system does not always obey the principle of bivalence; that is, we permit some sentences in his language to be neither true nor false. Instead, all we need in order to make deductive inferences is a language, semantics, and a set of rules of inference. Strawson, for instance, describes a deductive system thusly:

A small number of logicians' statements or rules (e.g., to the effect that certain formulae are analytic) are taken as premises, and further rules derived from them by the use of one or two higher-order rules of inference.^[6]

It is under the umbrella of such rules that we may understand arguments as valid or invalid. So, we might wonder, then, what does Collett have in mind when he asserts on one hand that his transcendental argument is valid,^[7] yet implies on the other that it is non-deductive? Ironically enough, the only argument Collett explicitly identifies as "transcendental" is not actually valid at all under the logical system in which he frames it. For this is what he provides (numbering added):

(4) Causality presupposes God;

(5) Not God;

(6) Therefore neither causality or not causality [sic].^[8]

First of all, none of these strings are sentences in the English language, unless we read 'causality' as an abbreviation for the sentence 'there is such a thing as causality,' or 'causality exists,' or some such; and similarly with 'God.' If we assume that this is his intent, which seems natural enough, then we may further abbreviate his 'causality' and 'God' sentences by 'C' and 'G,' respectively. Then his argument consists of:

(4’) C presupposes G;

(5’) ¬G;

(6’) therefore ¬(C ∨ ¬C).

Notice that there are no rules in van Fraassen's system which allow us to deduce (6’) from (4’) and (5’). Moreover, no argument with (6’) as its conclusion could possibly be valid in van Fraassen's system, because (6’) is always false by the law of excluded middle.^[9] However, we can construct the following valid argument, which perhaps Collett had intended instead to communicate:

(7) C presupposes G;

(8) ¬G;

(9) therefore ¬(T(C) ∨ T(¬C)).

For since we take (7) as true, we have T(C) only if T(G), and T(¬C) only if T(G), by the properties of the presupposition relation.^[10] By contrapositive, ¬T(G) only if ¬T(C), and ¬T(G) only if ¬T(¬C). Meanwhile, we have that (8) is true if and only if G is false by the valuation rules for statements.^[11] Then T(G) is false,^[12] which is to say, ¬T(G). It follows by modus ponens that ¬T(C) and ¬T(¬C), which gives us (9).

On this more charitable interpretation of Collett, he still commits himself to the position that at least some transcendental arguments are deductive, which seems unsatisfactory given his presumed intent to follow Van Til; for he believes Van Til held that "the truth of God’s existence is not a deductive consequence of the premises of the argument,"^[13] which is clearly inconsistent with argumentation under van Fraassen's semantics. Perhaps more importantly, if there really is a class of arguments which are neither inductive nor deductive,^[14] but deserve the unique label 'transcendental,' then what are they? No mere appeal to van Fraassen's presuppositional semantics, which afford us only rules for deduction, will answer this question.

What, therefore, is the solution to the Reformed apologist's unusual conundrum? How can we compel a uniquely transcendental inference, whatever that might mean? If an answer is possible, then regardless of its content, we have sufficient information even now to know that any argument distinct from deduction and induction, whether we call it transcendental or not, will have to satisfy at least two obvious criteria: First, it mustn't consist of recognizing some kind of order or constancy of the universe, our cognition or language, nor any other aspect of reality; indeed, such abstracting of regularities falls squarely within the scope of inductive inference. Second, it cannot have us follow a system of carefully-constructed logical rules in order to draw a conclusion from a body of existing knowledge or belief, since this describes a deductive procedure. Unfortunately, once we have set all those aside, it seems difficult to imagine that any other kind of inference should remain; so I do not envy the apologist's task in this matter.

To sum, we have seen that Collett's solitary example of a transcendental argument given in his paper is invalid by the very system he borrows in order to construct it. Further, his characterization of transcendental arguments, even charitably interpreted, requires that we understand them as plainly deductive. In this way, van Fraassen's system, the basis of Collett's analysis, seems fundamentally unfit to serve Reformed apologists in their efforts to distinguish between deductive and transcendental inferences, on account of its own unavoidably deductive nature.

Notes:

[1] Collett, Don. "Van Til and Transcendental Argument Revisited," pp6-7.

[2] Here we refer to Frame's Cornelius Van Til: An Analysis of His Thought (1995), p315, as cited by Collett, p9. Frame has since retracted some of his views, attributing his shifts to Collett, in the online essay "Reply to Don Collett on Transcendental Argument" [sic] (2003).

[3] van Fraassen, Bas. "Presupposition, Implication, and Self-Reference," The Journal of Philosophy, Vol. 65, No. 5 (Mar. 7, 1968), pp. 136-152.

[4] Strawson, Peter. Introduction to Logical Theory (1952), p175.

[5] van Fraassen, pp137,43.

[6] Strawson, p58.

[7] Collett, p34.

[8] Collett, p33.

[9] van Fraassen, p142.

[10] Namely, property (3) from van Fraassen's paper.

[11] This is by rule (8b) from van Fraassen.

[12] By rule (18a).

[13] Collett, p7.

[14] Here I class, not uncontroversially, abductive arguments among inductive.

A Limited Response to Anderson's Sketch

2010-12-19T11:33:00.000-06:00

Here I respond briefly to James N. Anderson's online essay entitled "The Theistic Preconditions of Knowledge: A Thumbnail Sketch" (2006) by pointing out two serious problems I see in his outlined case for theism. To that end, I critique his central argument against naturalism, as well as his contention that epistemic normativity cannot be subject to human convention.

Following a tradition of presuppositionalist apologetics, Anderson takes up the position that God stands among the necessary preconditions for knowledge itself, and that we must assume the existence of a divine author of the universe if we are to free ourselves from a paralyzing epistemological skepticism. He bases his outlined case, a kind of transcendental argument for theism, on the observation that one of same notorious difficulties of metaethics also frustrates inquiries into epistemology, namely the question of how normative standards can arise out of the impersonal properties of the universe; for the very concept of rationality presupposes epistemological norms to which we ought to conform. Similar to certain moral arguments for the existence of God, he suggests that we cannot derive the prescriptive standards we need for epistemology from a Godless description of reality.

As we might expect, then, Anderson's argument features some of the very same strengths and weaknesses as those moral arguments he emulates. For example, when addressing the Platonic approach, he rightfully observes how difficult it is for us to imagine how abstracta governing personal relationships could just happen to exist in a universe without a personal author. On the other hand, though such an argument from incredulity may have some inductive force, its controversial form leaves it potentially vulnerable to a variety of serious criticisms, chief among them the dubiousness of taking our personal experience with finding explanations for certain phenomena as evidence concerning which explanations may ever be found and which may not. So, a Platonist could respond that our present inability to conceive an impersonal accounting for epistemically prescriptive abstracta hardly constitutes evidence that no account can ever be found. Anderson in turn might point out that it does indeed serve as an inductive argument against Platonism, and that clinging to the hope of some day discovering how to explain the existence of personal normativity in an impersonal universe only ignores real difficulties through ad-hoc assumptions. In this way, a dispute over epistemic normativity may closely resemble more familiar moral points and counterpoints.

Anderson devotes the bulk of his essay to attacking what he calls (metaphysical) "naturalism," which he takes to be "the thesis that only 'natural' entities exist, i.e., entities which can be described (at least in principle) in terms of the methods and inventories of the natural sciences (e.g., physics and chemistry)." For the most part, though, he frames his criticisms of naturalism in sufficiently general terms such as they may apply to certain non-naturalistic positions nearly or even equally as well. So, we should not misunderstand him to have constructed merely a critique of one metaphysical view. In fact, his principal argument seems to turn on his position that any ontology whose foundation limits itself to descriptive terms can never inform us "how things ought to be," a required component for epistemic normativity. Since science is a "purely descriptive" enterprise, then naturalism, which is founded exclusively on scientific principles, leaves no space for epistemic normativity and thereby rational warrant. Yet, if beliefs can never have rational warrant, then knowledge itself is impossible. Organized into a deductive form, this reading of his argument consists of the following:

(1) Naturalism is a purely descriptive ontology;

(2) A purely descriptive ontology excludes epistemic normativity;

(3) Knowledge is impossible on any ontology which excludes epistemic normativity;

(4) Therefore knowledge is impossible on naturalism.

Since clearly we do have knowledge, it follows further that "naturalism must be false."

We may wonder, though, what is stopping us from applying this argument to any ontology at all, given that ontologies are always by their very nature descriptive? Put another way, since descriptions can only ever describe, then what advantage has a non-scientific description of reality over a scientific description? Perhaps, then, Anderson means to suggest that scientific descriptions in particular, i.e. not merely by virtue of being descriptive, are somehow incompatible with normative standards. For instance, one might argue that standards, and possibly also the very relationship between standards and human beings, are abstract objects, the reality of which the scientific method disallows or ignores. However, Anderson explicitly rejects this view later in his essay, where he denies that "impersonal abstracta could give rise to epistemic duties." Alternatively, he might try taking the position that standards can only influence conscious minds, but that consciousness cannot in principle have any explanation on naturalism; so he writes that, on naturalism, "mental phenomena...must either be reduced to the physical (i.e., explained in terms of more fundamental physical phenomena) or eliminated (i.e., explained away altogether)." This position would require significant defense, though, which he declines to offer in this particular essay. It seems most likely, then, that he would prefer to argue along the lines that, on naturalism, we must treat epistemic standards as a kind of human convention, and that this view carries with it certain serious, even insurmountable problems.

Now, for clarity, we needn't treat human convention as mutually exclusive with respect to biological evolution and development. In other words, it may not be biologically possible, even in principle, for a human society to hold to radically different epistemic norms than they do in actuality. It could be, for instance, that we are developmentally or even genetically predisposed to adopt certain kinds of standards. Perhaps we are wholly unable, again by virtue of our biology, to reject them. So, convention ought not be confused with whimsy. Understood in this way, that is, as rooted in biology, human convention seems an attractive characterization of epistemic standards, whether or not one is a naturalist. Anderson, however, argues that human convention, though it might do for founding, say, moral standards, can never provide a suitable foundation for epistemic standards. Using an analogy similar to that introduced a few years ago by Laurence Bonjour (In Defense of Pure Reason (1998), §7.4, p199), he invites us to consider a population which takes by convention wishful thinking to constitute a form of rational warrant, and furthermore which rejects beliefs formed from "reliable perceptual faculties" as non-rational. If epistemic norms are just human conventions, then this hypothetical community of wishful thinkers really could come about, at least in principle, and they would have no less powerful a claim to rationality than the actual population of non-wishful thinkers. "But clearly this can't be right," he protests, thereby concluding that epistemic norms must be more than simply human conventions. Indeed, he adds, human conventions are always "subject" to such norms. He appears to be arguing, then, that no description of reality can be correct which has as a consequence that normative standards develop as human conventions.

I agree that something has gone wrong in his thought experiment, but it is not the assumption that epistemic norms can develop through human convention; for Anderson has quietly taken on the additional assumption that there can be a population which rejects its perceptive faculties and functions as a community. Yet what does it mean for a community of people to reject their perception? It seems to me that any person who failed to yield to his own sensations and perceptions could never interact successfully with his environment, even to the smallest degree. In order to, say, communicate with other people, he must be willing and able to interpret his perception such that he even recognizes that there exist such other people with which to communicate! If we amend the analogy such that the hypothetical community recognizes perceptive faculties as important for acting in the world, then we are left with the suggestion that in addition to ordinary rationality, it also embraces wishful thinking. In that case, however, the problem with the community is that their standards are self-defeating insofar as they are inconsistent even when evaluated with respect to themselves---a criticism (hopefully) inapplicable to the epistemic standards we all actually use. It seems to me, then, that he needs other grounds on which to argue that epistemic standards cannot be taken as human conventions. As long as the naturalist---or the non-naturalist, for that matter---appeals to convention for the origin of this kind of normativity, Anderson shall require more than just the criticisms given in his essay to make his case for the impossibility of knowledge on such a view. In particular, he requires further, independent defense of his position that any account of epistemic standards "must posit a fundamental ontological distinction between that which grounds or originates epistemic norms and that which is subject to epistemic norms," a key component in his stated case for theism.

In sum, though many of Anderson's observations deserve (and, to the extent that others have preceded him, have received already) serious attention, his overarching argument for theism requires significant development. This does not in itself constitute a deficiency in his essay, which he clearly intends only as a "thumbnail sketch;" we should therefore refrain from complaining that it falls short of a robust defense of theism. However, Anderson's criticism of naturalism as purely descriptive seems fundamentally unable to function as a defeater for naturalism, regardless of development; furthermore, his resistance to understanding epistemic norms as human conventions seems to me entirely unsupported. Inasmuch as his case for theism depends on these two points, we cannot properly take it as persuasive.

An Argument Concerning the Trinity

2010-12-05T05:28:00.000-06:00

Although I can identify certain sentences which educated Christians take as descriptive of the Trinity, I remain unable to meaningfully interpret those sentences as a cohesive whole, or to otherwise find any substance to the various supposed descriptions of the doctrine. I suspect that this is not my own failing, but rather caused by a genuine lack of meaningful content therein. Indeed, I submit that even those Christians who claim to understand the Trinity doctrine may not actually understand it. However, I make this suggestion humbly, and with an earnest desire for correction in case I am mistaken. So it is that I have sought at some length to meaningfully interpret it, by inquiring after Christians how to do properly so. Yet this process has proved invariably unsuccessful, for a number of different reason, chief among them, in my experience, the supposition on the part of certain Christians that a non-Christian is simply incapable of understanding the doctrine in the first place. These Christians are unwilling to discuss the matter because, according to them, I must come to know God, or some such, before I can appreciate the meaningfulness of the Trinity. In this discussion, therefore, I shall outline a defense for my position that the following three statements are inconsistent when taken together:

(I) Non-Christians cannot understand the Trinity.

(II) Christians always understand the Trinity.

(III) Accepting the Trinity is rational.

The purpose of my defense is to promote discussion about the Trinity doctrine's meaningful content, or lack thereof, by resisting objections to the effect that non-Christians cannot understand it.

My defense turns on the important status given to the Trinity doctrine by orthodox Christians. Indeed, with its long history of difficult formulation, the Trinity stands today as a particularly controversial doctrine in Christian theology: On one hand, many Christians consider it to be an essential tenet of faith, such that anyone who denies the Trinity is not, by their reckoning, a true Christian. Yet while educated Christians are often able to articulate the doctrine precisely and with basic agreement, many other Christians have considerable trouble expressing it, and find serious disagreement in its various aspects. It strikes me as strange, however, that an essential doctrine should appear so widely misunderstood within the Christian community. Having observed this, we might ask, if the Trinity is to be taken as an essential doctrine, then in what sense is it really essential, given that so many self-professed Trinitarian Christians cannot communicate it? Perhaps the key is not in acceptance, but rather denial: So, one may, for whatever reason, fail to accept the Trinity, and still be Christian; however, if one denies the Trinity, then he ought not be called Christian.

Actually accepting the doctrine of the Trinity, then, seems both unnecessary and insufficient for being a Christian. To illustrate this intuitively, we can consider four distinct types of people, by no means an exhaustive list, who do not accept the Trinity, but who neither reject it: Firstly, there are agnostics who claim to understand the Trinity, but who have declined to believe it for some other reason, for example the perceived lack of evidence for the Trinitarian God's existence. This shows rather unequivocally, and believers should for the most part be happy to agree, that merely declining to deny the existence of the Trinitarian God is not sufficient to define a Christian. Second, we have self-described Christians who claim to understand the Trinity, but who profess agnosticism as to whether or not it accurately represents the relationship between Jesus, the Father and the Holy Spirit. These Christians might, for instance, accept the divinity of Jesus without being sure how to properly reconcile that doctrine with monotheism. Thirdly, we may encounter Christians who freely admit that they do not understand the Trinity. Even if such Christians claim to be Trinitarian, they cannot possibly be so if their profession of ignorance is correct; for one cannot accept a doctrine, except by proxy, unless one understands it. Fourth, and finally for our purposes, many Christians who describe themselves as Trinitarian, and who believe they deeply appreciate the doctrine, in actuality have little or no understanding of it. We should not expect such Christians to be few in number, and indeed I suspect they are the most common of all four groups we have discussed thus far. As with those Christians who openly acknowledge their ignorance, these Christians whose non-understanding remains hidden, at least to themselves, cannot really accept the Trinity if they do not know what it entails. Certainly more deserves to be said regarding these types, especially for those Christians who fail to understand the Trinity, whether knowingly or not. For now, however, it suffices to have briefly surveyed various groups of people who do neither accept nor reject the Trinity, in order to show that they are not all obviously Christian or non-Christian.

If the Trinitarian acknowledges that not all Christians understand the Trinity, then hopefully this will enable him to consider the possibility that he himself hasn't properly understood it, either. In that case, we might seek discussion along those lines. Nevertheless, some Christians may insist that even if a person fails to deny the Trinity, if he does not accept it he cannot be a Christian. However, this view, when taken with certain uncontroversial assumptions, has serious consequences, in particular, that either non-Christians are able to understand the Trinity doctrine or else all Christians make an irrational decision when they accept the Trinity. For, if non-Christians are unable to understand the Trinity on one hand, and on the other hand Christians always accept (and therefore understand) the Trinity, then this means that a person only begins to understand the Trinity at the very instant of becoming Christian. So, there can be no time for rational deliberation, which of course means that any such decision to accept the Trinity must be irrational. Presumably the Christian will wish to preserve his sense of rationality, and so when confronted with this choice, should he recognize its necessity, he is likely to acknowledge that non-Christians are capable of understanding the Trinity. The conversation can thereby move forward to exploring that doctrine.

In case the Christian insists that non-Christians can never understand the Trinity, while simultaneously holding that anyone who does not accept the Trinity is not a true Christian, then we can drive home the point with a formalization of the afore-mentioned argument:

(1) A person x is a Christian at time t only if x accepts doctrine Y at t.

(2) Person x understands doctrine Y at time t only if x is a Christian at t.

(3) Person x makes a rational decision to accept doctrine Y only if x deliberates on doctrine Y.

(4) If person x deliberates on doctrine Y, then there is a time t at which x understands but does not accept doctrine Y.

(5) If person x accepts doctrine Y at time t, then either x makes a rational decision to accept doctrine Y, or else x makes an irrational decision to accept doctrine Y.

(6) Therefore, if person x is a Christian at time t, then x makes an irrational decision to accept doctrine Y.

The deductive validity of this argument may be verified using the following symbolic representation:

(1) (t)(x)(Cxt → Axt);

(2) (t)(x)(Uxt → Cxt);

(3) (x)(Rx → Dx);

(4) (x)(Dx → (∃t)(Uxt ∧ ¬Axt));

(5) (t)(x)(Axt → (Rx ∨ Ix));

(6) therefore (t)(x)(Cxt → Ix);

where Uxt symbolizes the statement "Person x understands doctrine Y at time t," Axt symbolizes "Person x accepts doctrine Y at time t," Cxt symbolizes "Person x is a Christian at time t," Rx symbolizes "Person x makes a rational decision to accept doctrine Y," Ix symbolizes "Person x makes an irrational decision to accept doctrine Y," and Dx symbolizes "Person x deliberates on doctrine Y." Clearly, we take "doctrine Y" in all cases to denote the Trinity, but the generalization allows us to apply the argument to any doctrine whose acceptance is perceived as essential to salvation.

Here we wish to show the consequences holding to both of the first two premisses. In contrast, premisses (3)-(5) seem fairly straightforward, though objections may be thrown up against these, as well. For example, a Christian might wish to quibble over premiss (5), claiming that there is a difference between irrational and non-rational decisions. Yet even if we allow such accommodations, we should still feel the force of the argument.

Recall again statements (I)-(III) from earlier: If a Trinitarian is willing to deny (III), then while it may end any discussion of the meaningfulness of the Trinity doctrine, it presents an opportunity for exploring the rationality or irrationality of Christianity, a worthy subject on its own. Otherwise the Christian can deny (I) or (II); if (I), then clearly the conversation can continue unabated; if (II), then, as mentioned previously, this motivates the Christian to reflect upon his own meaning, and we can foster care and attention in that task.

Alexander Pruss on Self-evidence and the PSR

2010-11-21T07:17:00.000-06:00

As long as I have seen it used, I've had no end of trouble interpreting the term "self-evident." The only way I know to make sense of self-evidence is to understand it as a kind of intuitive obviousness. So, when Alexander Pruss writes in one of his papers that he finds the principle of sufficient reason (hereafter the PSR) to be self-evidently true, I interpret him as having a strong intuition of it. Unfortunately, this cannot be all he means by "self-evidence;" for he speaks about it as if it were an objective property about which we can be correct or incorrect. So, on Mr. Pruss's view, if I do not find the PSR to be self-evidently true, then it follows that one of us is factually right and the other wrong. Yet on my interpretation, the difference in opinion amounts to varying intuitions. So, while we may disagree as to how to handle our often unique intuitions, we are not necessarily mistaken about having them or not having them. I shall not hesitate to point out, for instance, that Mr. Pruss commits a substantial error when he decides to trust his intuition uncritically, and urges others to do the same, but I do not dispute that the intuition is genuine (though I strongly suspect that in this case it is contrived).

It cannot be, then, that Mr. Pruss shares my own concept of self-evidence; but then how does he envision it? One might suggest that Mr. Pruss combines my own concept of intuitive obviousness with a standard detailing under which circumstances it is appropriate to accept such intuitions. So, Mr. Pruss might embrace an epistemic standard such that he would claim one ought to accept a proposition as self-evident if one has a strong intuition that it is true, and his standard justifies accepting that intuition. So a subjective element plays a role on this view also, which is consistent with Mr. Pruss's treatment, but the addition of an epistemic standard to our considerations provides an objective component about which we can make factual claims and thereby judge them as correct or incorrect. If this is indeed what Mr. Pruss has in mind, then the PSR is self-evident to Mr. Pruss because his epistemic standard permits or perhaps even compels him to accept his intuition that the PSR is true. In contrast, I am mistaken that the PSR is not self-evident to Mr. Pruss, because even though I lack his intuition, I should nevertheless acknowledge that, if only I shared the intuition, then I too would be epistemically justified in trusting it.

If this is what Mr. Pruss believes, then he clearly holds to a different epistemology than myself, and one which I am disinclined to accept. I don't see any reason to trust intuitions uncritically, which is what it seems like Mr. Pruss would have us do. This is not to say that I reject using intuitions at all; for I do believe that we are justified in employing intuitions under certain circumstances, most notably those when we lack the time or interest to examine their contents more closely. For example, suppose I wished to estimate the number of NIU graduates who attended the graduation ceremony with me in 2010. One way to do this would be to draw on my intuition of how many people I must have seen that day in gowns. I can even cross-reference that intuition with my additional intuition of roughly how many names I remember seeing in the program booklet. These appeals suggest to me that about five hundred graduates attended. If these intuitions are strong enough, and cohere well enough, then perhaps I am justified in accepting them. However, I submit that this acceptance must be tentative, and that more importantly it must yield to a critical examination. So, if I learn from the NIU website that there were over a thousand graduates at the ceremony, then even though my intuitions might strongly tell me that there could not have been more than five or six hundred, those intuitions simply do not stand up to the hard evidence against them. In this way, intuition is not exempt from critical examination.

What about the PSR, though? How can there be "evidence" against a principle like that? In response, I suggest that we have two very good reasons to reject whatever intuition we might have that the PSR is true. First, I believe that once we examine what constitutes an "explanation," and how we find such explanations, then it will become apparent that Hume's account is the only workable one available, and moreover that the PSR cannot be true on a Humean view. This contention, however, requires significant development and defense, and so it will not be convincing until I offer such a defense. However, there is a second reason to reject whatever intuition one might have that the PSR is true: For I submit that the only reason to trust intuitions at all is inductive---that they have proved useful in the past and are therefore likely to serve us similarly well in the future. If we can show, therefore, that some intuition differs radically in character from those intuitions which have proved generally accurate and reliable, then the inductive argument loses nearly all its force for that intuition.

Recall the graduation ceremony example. The reader very likely noticed that the intuition I described therein has a very different character than whatever intuition we might have regarding the PSR. In fact, a defender of Mr. Pruss might go so far as to say that the judgments I described of how many gowned participants I witnessed and how many names I saw in the program are so vastly different from what they have in mind that they should not be called "intuitions" at all---and they would be quite right at least to notice that manifest and extensive qualitative difference. However, if a PSR intuition should be so far removed from a graduation ceremony intuition, then this only serves to show us that we ought not misconstrue past successes of intuitions of the latter sort as inductively supporting unverified intuitions of the former sort. We therefore require inductive evidence which is compatible with our PSR intuitions, or else a non-inductive argument for trusting PSR-type intuitions. Yet I can find neither of these things.

I therefore suggest to those who regard the PSR as intuitively obvious that they reflect on their intuition by examining it thusly: Can we find any cases where an intuition of similar character to our PSR intuition has proved true or otherwise accurate? Keep in mind that unverified intuitions which have merely failed to be proved false or inaccurate will not do for an inductive argument. For myself, I can find none, and thus I am unable to construct any argument to support PSR-type intuitions. Mr. Pruss, on the other hand, believes that the law of excluded middle is self-evidently true, and his defenders might regard an intuition for it as having a similar character to the PSR. However, I contend that they are not similar at all; for the LEM deals with language, with which we have intimate and daily experience, and the PSR we mean to apply to the origin of the cosmos, a domain of inquiry foreign even to the experience of the best and brightest physicists. In order to make an inductive argument for the PSR of the sort we have discussed, we must find a class of intuitions which do not apply to everyday experience, but which exhibit a demonstrable pattern of accuracy or truth. This appears to me an unlikely result. In the mean time, it remains only to point out that we should not trust that which we have no reason to trust, and so on these grounds we may hold that no appeal to intuition will constitute justification for accepting the PSR, even on the part of the person doing the intuiting.

Of course, all of this presupposes that I have adequately captured Mr. Pruss's concept of "self-evidence," which is in no way assured. If I have not, then what does Mr. Pruss mean when he declares the PSR to be self-evident? I cannot answer that question, but whatever the case, it seems that he needs to further defend his position that he is justified, even if only from his subjective point of view, in accepting the PSR.

A Recap of the Debate with Chris Bolt

2010-10-24T06:56:00.000-05:00

EDIT: Chris has responded to this blog entry here.

A few weeks ago, Chris Bolt and I held an over-internet debate on the existence of God (audio, transcript). He and Brian Knapp proved to be gracious hosts, and I came away from the event having had a splendid time of it, and with the impression that they both felt similarly. More than just having a fun time, however, I learned a great deal both in my preparation for and during the debate. In all respects, then, I'm very happy with how things turned out. At some point in the future, we may try our hands once again at persuasion, perhaps picking up where we left off. In the mean time, this blog post aims to summarize some highlights from the debate, and to examine Mr. Bolt's two key arguments which he presented on that occasion. I do not intend to exhaustively criticize those arguments, but I will point out what I believe are serious problems with them.

During the debate, Mr. Bolt argued for the existence of God, whereas I expressed agnosticism on the subject, and explained why I found his presentation unconvincing. In particular, Mr. Bolt focused on two chief arguments: one for his preferred flavor of Christian theism, and a second against my own agnosticism. He also presented a number of counter-arguments to my responses. I will try to address most of these in this summary.

His argument for Christian theism was borrowed from Reformed apologist James Anderson:

• If theism is not the case, then one cannot account for the uniformity of nature presupposed by inductive reasoning;

• If one cannot account for the uniformity of nature presupposed by inductive reasoning, then beliefs based on inductive reasoning are not warranted;

• Beliefs based on inductive reasoning are warranted;

• Therefore, theism is the case. [18:05]

This argument succinctly captures the spirit of Mr. Bolt's claim that the existence of a supernatural creator-deity is the only satisfactory solution to the infamous problem of induction. Suggesting that deductively valid inferences must underlie all our reasoning, he pointed out that we nontheists have no such justification for our use of induction. According to Mr. Bolt, nontheism leads us to a paradox, since inductive reasoning is deductively invalid without the invocation of the Judeo-Christian deity Yahweh:

Reasoning invalidly is not reasonable at all; it is irrational. However, everyone reasons inductively. The conclusion is that humans are irrational. [10:35]

In response to this argument I offered two objections, the first of which is that we simply must use induction, because we have no other means of planning for action in the world; so, no epistemic "problem" of induction need cause us an abundance of concern. From the debate:

In short, to reject induction is to paralyze onesself with skepticism. So, to the extent that we don't want to be paralyzed, we simply have to go use induction. And if Mr. Bolt wants to remind us that we have no guarantee induction will hold, I'm happy to agree; but that won't change the fact that we haven't any other alternative. [45:55]

Several times during the debate, Mr. Bolt agreed that indeed it is "necessary" [75:40] for us to use induction. However, he argued that such an observation does not help us solve the problem of induction, pointing out that, on nontheism, "it's still unsupported, regardless of its alleged necessity for inferences" [60:50]. However, he appeared not to take my point that such an epistemic problem does not threaten nontheism, and that we can live comfortably with a non-epistemic justification for induction. He furthermore complained that even if we have a non-epistemic solution now, only induction will allow us to apply that solution to the future, in which case, he argued, we will be guilty of circular reasoning. So, even though he agreed that we must use induction, he concluded that, on nontheism, we cannot "know" [61:20] that we must use it, remarking, "that this assumption has been necessary for past inferences does not require that it be necessary for future inferences" [61:00].

However, I don't find this terribly threatening, either. It's quite true that we need induction to draw the conclusion that induction is required for acting in the world. If this seems like a case of circular reasoning, remember that I'm not trying to reach induction from some more primitive position. Instead I want to point out that, from our current induction-using perspective, we may recognize the fact that we simply can't give it up. Inductive reasoning is not something we can just discard if it grows too uncomfortable for us. So it's not as if we have a choice to make---as if we must decide whether or not to continue to use induction. Rather, we simply will do so, because we have no alternative. In other words, we have no need to keep on seeking an epistemic justification for induction, because, from our position of using induction, we see that we are utterly unable to respond to the results of whatever search we perform.

My second objection to Mr. Bolt's argument for the existence of God pointed out that theism is just as ill-equipped as nontheism to answer the epistemic problem of induction. I said:

If we want to justify our assumptions, for example our assumption of induction, then it won't do to invoke new assumptions, unless those new assumptions are themselves justified. In other words, it doesn't help us to trade in one unjustified assumption for another, because if that's all we do, then we're still going to have unjustified assumptions on our hands. [28:20]

Mr. Bolt responded by offering "faith" as an alternative to induction, pointing out that whereas unjustified assumptions are unacceptable on a nontheist view, his version of Christian theism "provides for faith in our epistemic structure" [57:50]. With faith in the Testaments of the sixty-six-book Protestant Bible, we can get everything we need for reasoning, including induction. He continued:

So it's not the case that having assumptions is a problem for the Christian, though I would say that it is a problem for the rationalist---the non-Christian---who will not allow faith in an epistemology. [58:20]

And indeed I will not. "We should always question our assumptions," I said in the cross-examination period [34:15], adding that "I don't think that blind faith is ever a good idea" [36:00]. Even if faith were somehow a worthy means of knowledge---and I think it's fairly clear that it is not---why should we privilege it over induction? Why does faith need no justification, but induction does? In any case, it seems redundant to turn to faith in order to get for ourselves induction (even assuming we really can get induction from faith, which is not at all obvious) when we can simply accept induction directly.

In addition to his argument for the existence of God, Mr. Bolt also presented an argument against agnosticism:

• If God exists, then everyone knows that God exists;

• Mr. Wallis does not know that God exists;

• Therefore, God does not exist. [5:00]

Of course, here Mr. Bolt is assuming that the only "God" on the table is his own Reformed conception of Yahweh, the God of the sixty-six-book Protestant Bible. In response, I pointed out that, since I don't believe in God, any hypothesis which holds that I do believe in God must be false in that respect. So, I can rule out the existence of any God which is said to make all people believe in him, since I am living proof that such a God does not exist. From the debate:

[My unbelief] does contradict his view of God---absolutely, yes. So, if you want to be strict about it, yes, I'm denying that his particular idea of God exists, at least insofar as it includes the idea that I really believe in God, because I know that I don't! [67:10]

So it could be that there exists a God which does not enforce belief, such as the God of Islam or Judaism. It could be that the Biblical God exists, and that Mr. Bolt has simply misinterpreted Romans 1---the principal text from which he concludes that even self-described atheists believe in God. There are a myriad of such possibilities, none of which I can rule out. This is what makes me an agnostic; yet Mr. Bolt's argument overlooks that key point.

In sum, I think it's fairly clear that Mr. Bolt's argument for the existence of God, while undoubtedly clever, falls well short of convincing. His theistic reliance on faith is as epistemically unjustified as he claims is the nontheist's reliance on induction; and in any case we have no need of an epistemic justification since we are not in the position to make any actual decision on whether or not to continue to use inductive reasoning. We simply will use it, whether or not we think it's usable. Mr. Bolt's argument against agnosticism is still less satisfactory, as he ignores the plethora of possible creator-deities (including different conceptions of Yahweh) outside his own personal view. So, while I thank him for forcing me to think carefully about my position, I must remain agnostic to the existence of the Christian God.

NOTE: Chris Bolt also has his own blog, where we have already exchanged some thoughts regarding our debate.

Debate on the existence of God, Thursday, Aug 19, 8pm CST

2010-08-15T07:50:00.000-05:00

EDIT: The debate is now available for download! Get it here. (Thanks to Brian Knapp for generously recording and mastering the event!) A complete transcript is now available here.

EDIT 2: Post-debate discussion is underway! Check out Chris's blog post on self-deception and my general recap.

On Thursday, August 19, at 8:00pm CST (9:00pm EST), I will be streaming a prerecorded audio debate with philosophy graduate Chris Bolt through the internet, while listeners and myself may engage in live text chat. To listen and/or participate, just go to paltalk.com and visit the room called Chris Bolt Ben Wallis debate Does God Exist. The room will open at approximately 7:45pm CST, fifteen minutes before the stream begins.

The debate itself is scheduled to take place at 6:00pm CST. So, the stream you will hear at 8:00pm will be unedited and raw, having just finished recording only a few minutes earlier!

I will also post a download-able mp3 of the debate here, so feel free to check back for an update.

Chris Bolt is a presuppositionalist Calvinist apologist, a fan of Bahnsen and Van Til, whom I expect will use a transcendental argument in our debate. He is a philosophy graduate, theology student, and regular poster on the website choosinghats.com.

I hope to have a lot of fun, and anyone interested is welcome to share in that for the Paltalk stream this coming Thursday!

Enjoy!
--Ben Wallis

Free Will and Determinism

2010-07-04T08:29:00.000-05:00

In my last blog post I presented an argument that if God has the omnipotence and omniscience typically ascribed to Him by God-believers, then he is in control of our choices.^[1] There I carefully avoided using the terms "determinism," "free will," "compatibilism" and "libertarianism," and for this present post I would like to discuss my reason for keeping distance from them. In short, with a few possible exceptions, I no longer wish to use those terms because I find them all enormously problematic insofar as I cannot ever easily identify any coherent content behind them.

Surely, one might say, this is not so. For instance, is it really so difficult to define determinism? It seems almost obvious on its face, but as it turns out, determinism is notoriously difficult to define. Take, for instance, causal determinism, which the Stanford Encyclopedia of Philosophy defines thusly (emphasis original):

The world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law.^[2]

The author, philosopher Carl Hoefer, dutifully recognizes that this definition is vague and largely unhelpful until such time that its italicized phrases should be properly defined. However, I have found, both with lay and educated persons, that few if any have well-developed notions of those component terms, and, when they claim to, their accounts are either internally incoherent, mutually incompatible, or else conflict with popular or otherwise attractive accounts of the same terms used in different contexts. This situation makes it difficult to communicate effectively when we permit the use of the word determinism.

The same sort of trouble applies, to I dare say an even greater degree, to discussions about free will, which is so poorly defined in most contexts as to render it utterly useless without first explicitly elucidating one's own account in advance of each employment. However, others are not often prepared, in my experience, to accept such stipulative definitions, and so it becomes necessary instead to solicit an account from one's partner in conversation. This in turn is only possible if that person has already spent some time developing such a definition, or is willing and able to do so on demand. Clearly, we should expect few to meet that criterion. For those who do, we must, at a minimum, acknowledge that it is a serious inconvenience to lay down precise stipulative definitions before every conversation regarding free will or determinism. How much worse if, after spending the time to do so, it turns out that the proposed definitions are incoherent or otherwise disagreeable!

Besides that, we really have no need to provide content to a word or phrase which lacks it. We are instead perfectly able to simply acknowledge that they lack content, and accordingly abandon them. These terms, apparently as a rule, invite misunderstanding and tension where they do not require significant commitments of time and energy in defining, and I therefore feel inclined to avoid them altogether. As a consequence of my decision, I must likewise avoid discussion of compatibilism or libertarianism, since those terms are defined based on the concepts of free will and determinism. To clarify, I don't mean to suggest that these terms cannot be endowed with precise and meaningful conceptual content, but only that to do so seems unnecessary and, in light of the serious cost of convenience for defining them, woefully inefficient. As metaethical philosopher Richard Double once wrote, regarding whether or not moral claims bear truth, "The inability of 'I am thinking of the largest integer' to be true does not provide reason for thinking the statement is a disguised exhortation, command, or wish."^[3] I find relevance in his observation likewise to the present discussion; for, if free will and determinism lack meaning on some account does not somehow compel us to provide them with such. I contend that, in order to encourage limpidity and efficiency of communication, we ought to leave them unapologetically behind.

Let us keep in mind, though, that restricting our language does not necessarily prevent us from communicating a given idea. Unless one of the four terms in question is a primitive term with a meaning which cannot be communicated alternatively, then whatever content lies behind them all may be discussed using a reduced vocabulary. This is precisely what I would like to do from now on, avoiding the four problematic terms, and instead discussing directly whatever objects we happen to find of interest in a particular context. So, for example, one might ask whether the God of Calvinist theology is morally praiseworthy or blameworthy. A dispute on that subject could take the following form: a non-Calvinist argues that Calvinism teaches determinism, which cannot be true since human beings have libertarian free will; a Calvinist in response argues for compatibilism. However, whether or not compatibilism versus libertarianism is true is only interesting in that context insofar as it relates to the topic of immediate interest, which regards the moral status of the Calvinistic God. It is entirely possible to discuss that topic without mentioning libertarianism, compatibilism, etc. Indeed, I suggest that it is easier and relatively painless to avoid those terms.

Nevertheless, some may insist that their terms are indispensable. If so, then I believe it is possible to show them that they are either mistaken, or else they are taking the terms to have primitive content. If the latter is true, then the conversation is doomed unless all parties already share the concepts in question, in which case it remains only to point out that one lacks such concepts. For instance, I myself only understand determinism and free will to the extent that they can be defined using component terms; so, I will be unable to communicate effectively with anyone for whom the conceptual content behind their own use of the terms is primitive. Otherwise the terms are not primitive, which is to say that their underlying conceptual content is alternatively communicable. So we are free to opt for that alternative; indeed, I believe we should do just that, for the reasons given thus far.

Yet this is not to require that we must never make mention of the terms, but only that we do so in reference strictly to the terms themselves, and their status as objects of philosophical positions. So, in this document for example, I have extensively discussed free will as a term which may be employed in the English language, and this kind of use I fully appreciate. Naturally, if we do wish to avoid the terms as they are typically used, that is, as representative of some supposed philosophical concepts, then it will not do to simply ignore them when a person employs one or more of them in the course of a conversation. Rather, we must patiently and politely explain to that person why we cannot permit their continued use, and suggest alternatives.

Finally, we may observe that this policy of avoidance is primarily motivated by conversations with non-specialists. I freely confess that I have not had much occasion to discuss free will and determinism with professional philosophers who have spent time developing those terms. However, since the vast majority of persons are not professional philosophers, and even among philosophers we should expect few to specialize in free will or determinism, I do not anticipate this seriously impeding my proposed conversational strategies. If I happen to discover in the near future that resisting the problematic terminology of free will and determinism in this way results in unforeseen difficulties outweighing those which accompany the terms themselves, then I may revise my plan of action, and make less limited use of that language. However, in the mean time, I very much hope to avoid doing so, and I hereby encourage others to follow my example.

Notes:

[1] Although the statement "God is omnipotent and omniscient," call it A, does not appear in the deductive argument, of those premises which do appear, call them P₁,P₂,...,P₇, the rhetorical points discussed beforehand may be taken to defend the heretofore unspecified statement A → P₁∧P₂∧...∧P₇ from which A → B follows, where B is the argument's conclusion, that God completely controls the choices of all agents.

[2] Hoefer, Carl. "Causal Determinism," Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/determinism-causal

[3] Double, Richard. Metaethical Subjectivism (2006), ISBN 0-7546-5417-6, p36. http://books.google.com/books?id=M3PMl1vVN6EC

A Sketched Argument for God's Control

2010-06-20T06:58:00.000-05:00

Introductory remarks

Here we offer, in accordance with our title, an argument for the doctrine that God controls the choices of all agents, which I regard as the key underlying principle of Calvinism. So, by the term "God" we have in mind the creator-deity Yahweh from Judeo-Christian tradition. The argument is deductive, with seven premises, each intended to cause comparatively less controversy than the conclusion. Defenses of the premises are not given in this document. However, we do present an initial set of six points, along with a rhetorical appeal for each, intended to elucidate the reasoning behind the argument. These points do not themselves make up any deductive argument; rather, each one, save the last, will serve as an aid to rhetorical defenses for subsequent points, and suggest strategies for defending the premises of the final argument.

Point (i): God is the creator of an entity iff He has complete control of its existence.

Here we assume that the definition of "create" is satisfied by complete control over existence. That God is in complete control over that which he creates seems fairly uncontroversial. However, the converse is not necessarily obvious; can God be in complete control over the existence of an entity without being its creator? I cannot make sense of such a suggestion, especially if we say that God is omnipotent and omniscient, such that he is in control of his actions and fully appreciates their consequences.

Point (ii): God and His creation comprise everything that is real.

The motivation for this point is fairly clear: Suppose that God and His creation are real, which seems necessary for theism, but that, additionally, (ii) is false. Then something, say, X, is real which is not part of God and His creation. Now, this seems to deny some of the majesty of God, and so is unattractive for that reason alone. However, we may further argue that X is out of God's complete control. For suppose God could completely control the existence of X; then by (i) God is the creator of X, which is false by hypothesis. However, if X is out of God's control, then this impedes upon His omnipotence, which we presumably wish to preserve.

It may also be helpful to observe that, given (ii), inaction on the part of God is quite different than inaction on the part of other agents, since there are no external forces to God and His creation to take over, so to speak, when God declines to act, whereas this is always the case with respect to other agents. Since objections to Calvinism often deal with the distinction between God's action versus inaction, noting this observation may assist in persuasion.

Point (iii): God is in complete control of Himself.

If God is omnipotent and omniscient, then it seems natural to say that He is in complete control of His own responsiveness to whatever external forces He happens to encounter. If (ii) is true, then God is in control over the existence of such external forces, and so He is able to incorporate them into His plan for His own state of being. In this sense, he is in complete control of Himself.

Point (iv): God is in complete control of His creation.

If we accept points (i)-(iii), it seems hard to deny that (iv) is also true. For if God is omnipotent and omniscient, then He fully controls the existence of His creation, and appreciates all the consequences thereof. So, for any entity X, God controls the existence of X, and fully appreciates its role and consequences with respect to the remainder of reality. If God does not want X to behave a particular way, then he may create instead an entity Y which behaves as God wills, and which is the same as X in all other important respects. Since God is in complete control of Himself, then he is responsible for his own choices, including the choice to create X instead of Y. In this sense, God is in control of the behavior of X, which since X is arbitrary means God is in complete control of all entities within His creation. Indeed, we may view His entire creation as a single entity which is under His control in this respect.

In order to resist this conclusion, apologists may claim that God voluntarily withholds his control. If so, then we must point out that, according to (ii), God and His creation make up the whole of reality, such that there are no external forces to take the place of God when He stays His hand. Whereas in our human context we are accustomed to a sort of background of regularities which proceed whether or not we act, in the case of God this is not necessarily so. Indeed, if God is omnipotent and omniscient, then God controls the existence of everything, which, as we suggested previously means that God is the creator of everything outside Himself. So, for God, He is equally responsible for inaction as well as action, if we can distinguish between those at all, since He fully orchestrates the respective consequences of each alternative. For, if (ii) is true, then whatever forces are at work in God's creation ultimately come from Himself.

Point (v): The choice of an agent is an event which occurs within the context of God and His creation.

It seems fairly natural to say that the choice of an agent is an event, but does it occur within the context of God and His creation? By this last question, we are asking if there are forces external to God and His creation which influence in any way, however small, a choice event. If (ii) is true, then we ought to conclude not, since nothing is real apart from God and His creation.

Point (vi): God is in complete control over the choices of every agent.

If points (i)-(v) are true, then it seems almost impossible to deny (vi). For if God is in complete control of Himself and His creation separately, then we tend towards the conclusion that God is in complete control of Himself and His creation as a whole. Since the choice of any agent is an event in this context, then it occurs under the umbrella of that control.

The argument

We presently introduce the following notation: Let N symbolize the statement "Everything that is real is among God and His creation." Let S symbolize the statement "God completely controls the existence of every entity, real or hypothetical, in His creation." Let Cx symbolize the statement "x is an event in the context of God and His creation." Let Tx symbolize the statement "God completely controls x." Let Hx symbolize the statement "x is a choice of an agent." Let Ix symbolize the statement "x is an entity in God's creation." Finally, let g and c symbolize the individual constants "God" and "God's creation," respectively. The argument thusly proceeds:

(1) premise: N

Everything that is real is among God and His creation.

(2) premise: N → (x)(Hx → Cx)

If everything that is real is among God and His creation, then every choice of an agent is an event in the context of God and His creation.

(3) premise: (Tg ∧ Tc) → (x)(Cx → Tx)

If God completely controls Himself and His creation, then God completely controls every event in the context of Himself and His creation.

(4) premise: Tg

God completely controls Himself.

(5) premise: S

God completely controls the existence of every entity, real or hypothetical, in His creation.

(6) premise: Ic

God's creation (in its entirety) is itself an entity in that creation.

(7) premise: (N ∧ S) → (x)(Ix → Tx)

If everything that is real is among God and His creation, and God completely controls the existence of every entity, real or hypothetical, in that creation, then He completely controls every such real entity.

(8) conclusion: (x)(Ix → Tx) (from 1,5,7)

Therefore, God completely controls every entity in His creation.

(9) conclusion: Tc (from 6,8)

Therefore, God completely controls His creation.

(10) conclusion: (x)(Hx → Cx) (from 1,2)

Therefore, every choice of an agent is an event in the context of God and His creation.

(11) conclusion: (x)(Cx → Tx) (from 3,4,9)

Therefore, God completely controls every event in the context of Himself and His creation.

(12) conclusion: (x)(Hx → Tx) (from 10,11)

Therefore, God completely controls every choice of an agent.

Final words

As anticipated, the desired conclusion, (12), follows from seven premises. Of those, premises (1)-(4) seem relatively uncontroversial, and in need of little defense from a Trinitarian Christian who accepts divine omnipotence and omniscience. We may expect that (5) and (6) are likewise easy for many to accept, but unlike (1)-(4), they are sufficiently unintuitive that some who wish to avoid the conclusions may feel inclined to attack them. Premise (7), on the other hand, will require a significant rhetorical defense. We have outlined one such possible defense in the previous rhetorical appeal for point (iv).

On the other hand, even premises (1)-(4) may fall victim to doubt if the apologist demands and in turn attacks specific definitions. In particular, what does it mean to say that "God completely controls x"? Can we use the same such definition when x is an object versus an event? Answers to these questions may not be immediately obvious, and so we tentatively plan further clarification and rhetorical defense. However, such an expansion we leave to compose for a later time.

The Laws of Thought in Formal Calculi

2010-06-13T09:29:00.000-05:00

In philosophical discussions with laypersons I often encounter references to three so-called "laws of logic." Although they may take any of a wide range of different expressions which convey an arguably greater diversity of meaning, I shall adopt for the purposes of this document a simple and specific set of formulations, given thusly:

The law of identity: Every entity is the same as itself.

The law of noncontradiction: No proposition is both true and false.

The law of excluded middle: Every proposition is either true or false.

I wish briefly observe the role and expression of these laws in certain formal logical systems, namely that of the statement and first-order predicate calculi. As we shall shortly see, the laws of noncontradiction and of excluded middle appear as theorem schemas but not axiom schemas of the statement calculus, given an appropriate overlaying theory and interpretation thereof. The law of identity, in contrast, is not a theorem schema of the statement calculus, nor any pure predicate calculus. However, it is an axiom schema of equality, the results of which are commonly absorbed into first-order formal theories.

Before we begin our outline, I should say a few words regarding our motivation: For mathematicians and logicians usually perceive nothing special about these laws, and in the context of formal logic we have little reason to pay them any great attention relative to other theorem and axiom schemas. However, they are well-known in certain circles as Aristotelian "laws of thought"^[1] which, according to certain philosophy enthusiasts I've encountered, lie at the root foundation of our ability to think and reason. This view has become especially popular among what are called "presuppositionalist" Christian apologists, who argue that the God Yahweh is the only possible explanation for the existence, as they describe it, of these laws. Needless to say, such arguments have failed to convince most academic philosophers, and this author, although not a philosopher himself, follows in their skepticism. Let us now explicitly clarify that our discussion shall not further involve those arguments. Neither will our outline deal with the possible role which some versions of the Aristotelian laws may play in understanding our ability to reason. Instead, we will restrict our attention to the appearance, or lack thereof, of the laws strictly within the context of axiom and theorem schemas of formal statement and first-order predicate calculi, with the hope that it will spark the interest of those who are involved in some manner or another with apologetics.

We do not intend it to be necessary to have any knowledge of formal logic in order to appreciate our forthcoming observations. Instead, we will introduce the reader presently to formal systems by providing an example of a very basic formal logical calculus. To that end, the following is Jan Łukasiewicz's refinement of Gottlob Frege's statement calculus, as reorganized by Robert Stoll:^[2]

We define a string of the primitive symbols ¬, →, (, ), A, B, C, A₁, B₁, C₁, ..., as a formula if it meets the following inductively-applied criteria:

(F1) Each statement variable (a primitive symbol of the form X_i) is a formula.

If A and B are formulas, then

(F2) (A) → (B) is a formula, and

(F3) ¬(A) is a formula.

(F4) A string is a formula only if it is the last in a column of strings, each of which is a statement variable, or which is obtained from strings appearing earlier in the column by the application of (F2) or (F3).

Regarding (F2) and (F3), we almost always abbreviate formulas by omitting parentheses where their place is otherwise unambiguous.

Given the above definition, we present the axiom schemas for the statement calculus: If A,B,C are formulas, then

(S1) A → (B → A),

(S2) (C → (A→B)) → ((C→A) → (C → B)), and

(S3) (¬A → ¬B) → (B → A).

A proof is a finite column of formulas, each of which is either an axiom or else inferred by modus ponens (B if A and A → B) from two (not necessarily immediately) preceding formulas in the column. A theorem is the last formula in such a column.

As we can plainly see, none of the three laws of thought make an appearance in the axiom schemas of the statement calculus, nor in its essential definitions, that is, the definitions of formula, proof and theorem. The same goes for at least one if not all first-order predicate calculi, namely that of Alonzo Church, as presented by Robert Stoll (which we shall not reproduce here).^[3] However, something like the law of noncontradiction we incorporate into the definition of consistency of formula sets:

A formula A is deducible from a set Γ of formulas iff it is possible to construct a column of formulas such that the last formula in the column is A, and each formula in the column (including A) is either an axiom, a member of Γ, or else inferred by modus ponens from two preceding formulas in the column. Γ is consistent iff for no formula B can we deduce from Γ both B and ¬B; otherwise Γ is said to be inconsistent.

Although not quite the same as the law of noncontradiction, we can see the parallel. Every consistent set of assumptions, for example the axioms of a first-order theory, over the framework of the given statement calculus (and indeed Church's predicate calculus), upholds the principle that for no formula A do we have both A and ¬A as theorems. Nevertheless, the definition of consistency is an identifier, not a rule, and as such does not behave as a "law" in the sense we have in mind.

Therefore we may consider presently how to state the law of noncontradiction as such a theorem schema. Now, the concepts of true and false do not automatically accompany the statement calculus. However, the concept of a theorem schema is usually intended as the formal analog of a tautology, that is, a statement form which is always true, regardless of its interpretation. Meanwhile, the logical connectives ∧ and ∨ are usually associated with the concepts of and and or, respectively, whereas ¬ we read as not, or, more explicitly, it is not the case that. Furthermore, the concept of a law we take as analogous to a theorem or axiom schema in formal calculi, that is, a theorem or axiom for which we may substitute any individual or predicate constant for all instances of any free or predicate variable, respectively. To this end, we offer the following formulations of the laws of noncontradiction and of excluded middle as possible theorem schemas of the statement calculus:

The law of noncontradiction: For any formula A, we have ¬(A ∧ ¬A) as a theorem.

The law of excluded middle: For any formula A, we have A ∨ ¬A as a theorem.

By definition of the ∧ and ∨ symbols, we write these theorems using formal notation as A → A and ¬A → ¬A, respectively. Each are theorems, regardless of our choice of A. The proof of the former is quite straightforward:

(1) A → ((B → A) → A) (S1)

(2) A → (B → A) (S1)

(3) (A → ((B → A) → A)) → ((A → (B → A)) → (A → A)) (S2)

(4) (A → (B → A)) → (A → A) (1,3,MP)

(5) A → A (2,4,MP)

We obtain the result ¬A → ¬A by substituting all occurrences of A with ¬A in the preceding proof.

On the other hand, the law of identity makes no obvious appearance among the axiom schemas of the statement calculus which we have stipulated, and indeed the same goes for Church's predicate calculus. This may seem surprising to those with only knowledge of semiformal mathematics, since the = symbol is employed in just about every informal system of note. However, in a formal system, the = operator must be explicitly defined into existence, which is not the case in either Łukasiewicz's or Church's calculi. We describe such predicate calculi as without equality, to distinguish them from those calculi for which we wish to explicitly define = as a logical symbol.

We shall presently begin a discussion of predicate calculi with equality. However, in order to do so, some general understanding of predicate calculus notation is required. Readers lacking a familiarity with this notation may refer to wikipedia's page describing the formulation rules of first-order logic.

With predicate calculus notation in mind, we describe the constant = as a special kind of two-place predicate symbol, such that we may construct the formula (x=y) for any individuals x,y. As a predicate, then, it is absent from the statement calculus regardless of its specific formulation. In order to incorporate it into a predicate logic, we append to the initial set of predicate logic axiom schemas the following two additional schemas:

(E1) x=x, where x is any individual symbol.

(E2) (x=y) → (A → B), where B is obtained by substituting y for all free occurrences of x in A.

Axiom schemas (E1) and (E2) are absent from what we call a "pure" predicate calculus, which, among other characteristics, excludes by definition all constants. Since = is a logical constant, then it cannot appear in a pure predicate calculus. Informally, we may expound axiom schema (E2) as follows: If A is a 1-place predicate, then (x=y) → (A(x) → A(y)), if A is a 2-place predicate, then (x=y) → (A(x,z) → A(y,z)) and (x=y) → (A(z,x) → A(z,y)), and so on for all n-place predicates A. Similar implications hold for formulas which are not precisely of the n-place form, but rather incorporate a subformula, so to speak, which is an n-place predicate. Needless to say, this informal description is inadequate for a precise understanding of (E2), but we offer it for the benefit of those lacking familiarity with formal predicate calculus.

Plainly, the statement schema x=x has a striking interpretive similarity to the law of identity as we stated it in English: every entity is the same as itself we may read as every entity x is the same as x, or, in the context of predicate calculus, for every individual x we have x=x. It seems clear, then, that (E1) best represents the law of identity in predicate calculus with equality. Axiom schema (E2), meanwhile, describes the intuitive consequences of the law of identity.

Now that we have identified the laws of thought in the axiom and theorem schemas of predicate calculus with equality, we may turn to address their spirit. In our formal system of predicate calculus these schemas establish the mechanical rules for the organization of symbols. For example, axiom schemas (E1) and (E2) govern the behavior of the = symbol. This is all any such axiom or theorem schema could ever do in systems such as the statement and predicate calculi, which have been stripped of meaning by logicians, and act as self-contained mechanisms.

Finally, we may observe that second-order logical calculi may offer a method of formalizing the laws of thought, so that we may state them as theorems rather than theorem schemas. However, we shall not pursue that avenue here.

To summarize, we have observed that certain formulations of the laws of noncontradiction and excluded middle appear as theorem but not axiom schemas of the statement calculus and of the first-order predicate calculus, and we have presented the single proof schema sufficient for both. They are therefore theorem schemas of any expansion on the statement calculus, including any first-order theory which uses it. Since it would therefore be redundant to include them as axiom schemas of any theory overlaying the statement calculus, we can expect them never to appear as such. On the other hand, although the law of identity is absent in any natural form from the statement calculus and from the pure predicate calculus, it appears as axiom schema (E1) of the predicate calculus with equality, and therefore as an axiom schema of any associated formal first-order theory, for example certain common formulations of set theory. Since any axiom is also a theorem, we therefore acknowledge that all three laws are theorem schemas of any formal theory overlaying first-order predicate calculus with equality.

Notes:

[1] We may wish to note that some have questioned whether the law of identity authentically originates with Aristotle, but for our purposes we will ignore that somewhat arcane controversy in favor of popular convention.

[2] Stoll, Robert. Set Theory and Logic (originally published 1963, this edition 1979), ISBN 0-486-63829-4. The statement calculus is described on pp375-377. According to Stoll, the system of Frege was published (not necessarily originally) in Die Grundlagen der Arithmetik, Eine logischmathematische Untersuchung Über der Begriff der Zahl (1934); Łukasiewicz is credited without citation as having contributed to Stoll's formulation.

[3] Stoll, pp388-390, citing Church, Alonzo, Introduction to Mathematical Logic, Vol. I (1956).

The Q-device

2010-04-11T09:11:00.000-05:00

In a blog post dated 2010 Mar 17, mathematician and philosopher Alexander Pruss expressed some interesting ideas regarding probability and countably infinite samples in an attempt to show an absurdity which would, in his judgment, lend support to the claim that the existence of what he and others call "actual" infinite collections of physical objects is impossible.^[1] He suggests a set of hypotheses which, taken together, appear to violate our intuition regarding probability. While I do not believe this constitutes evidence against actual infinities, I find the argument interesting in another way which I shall discuss here. In particular, I maintain that we ought not assign probability values under certain conditions whereby the probability measurements in question are insufficiently interpreted. Paul Castell calls this position abstention,^[2] and Pruss's ideas yield an opportunity to give an example of how we might find reason for adopting it.

Pruss asks us to consider the following: Suppose that a random process bestows the unobservable property Q on a subset of a population with total size N, where each person has the constant probability p ∈ (0,1) of being granted Q. Let K denote the total number of people who are actually given property Q; then we can expect the value of K to be approximately pN. So, consider Mary, a member of that population. With only the approximation pN for K at her disposal, she would correctly conclude that the probability she has Q is precisely p. Indeed, that is true practically by hypothesis. However, if she were to discover the actual value of K, then that knowledge would supersede the estimate pN. No longer would she say that the probability she has Q is p; instead she would assign herself a probability of K/N for having Q.

Now suppose we alter this hypothetical scenario by considering not a finite population of size N, but rather a countably infinite population. In that case, what is the probability that Mary, if she is a member of that population, has Q? We might be tempted to say that the probability is p; indeed, Pruss insists that this answer is "obvious," although ultimately contradictory, since he invites us to infer from p that there are infinitely many members of the population with Q, and infinitely many without. However, I believe his judgment is too hasty, for reasons I shall presently expound.

As described thus far, the scenario is deceptively ambiguous. What exactly does it mean that each person in the population is bestowed Q with probability p, especially if that population is infinite? This point is not at all clear from Pruss's description, but I suggest that we need to know exactly what we are measuring with the value p before we can draw any conclusions from it. We can endow p with any one of a number of particular meanings: For example, we could consider what would happen if the same process which acts on the infinite population instead acted on a population of finite size N, interpreting p as the anticipated value of K/N for that case---and here I simply mean the value which we should think most reasonable, not the formally-defined expected value. Alternatively, we could hypothesize that the process in question is drawn out over an infinite period of time, and never actually completes; then we may interpret p as the anticipated value of the limit of k_n/n as n approaches infinity, where k_n is the number of people endowed with Q after n have been passed over by the process.

However, I prefer the following interpretation: Suppose there is a Q-device which passes over a denumerable population with such rapidly increasing speed that the device assigns either Q or no-Q to every member in a finite time interval. In particular, suppose that it only takes the device half the time to assign to some member of the population Q or no-Q as it did the previous person. So, if t is the time it takes for the device to assign the first member of the population with Q or no-Q, then the total time required by the Q-device to pass over the entire population is ∑t/2ⁱ=2t, where i=0,1,2.... In this way, we may interpret p as the propensity of the device to assign each person with Q, that is, the anticipated value of the limit of k_n/n as discussed in the previous example. One may notice that the possible existence of such a Zeno-reminiscent device remains dubious. I freely acknowledge this difficulty, and I do not claim it is realistic or physically possible. It is merely a hypothetical construct for the present conceptual exercise.

We turn now to what I regard as the central matter: What is the probability that, being part of a denumerable population after the Q-device has completely passed over it, Mary has Q? Before we can answer this question, we must consider what it means to talk about this probability. For ease of notation, let M denote the event whereby Mary has Q, given that the device has passed over the whole population. Then the probability of interest is P(M), and we ask what P(M) is actually measuring. This does not seem to be immediately clear. If only the population had finite size N, we could interpret P(M) as the anticipated value of the ratio of correct guesses to N, should every person in the population guess whether or not he has Q. However, this interpretation will not do, since the population of interest is infinite.

Many of us might be tempted to give P(M) in a folk interpretation. For example, we could imagine a set of trials where Mary attempts to guess whether or not she has Q, then time is rewound and Mary guesses again, repeated as needed. Of course, it is naive to talk about rewinding time, and presumptuous to suppose Mary's guess should be different from trial to trial even if it were somehow conceivable. Such interpretations are inappropriate for a consistent analysis.

We might wish instead to interpret P(M) as the anticipated value of G/S, where a subset of finite size S is chosen randomly, without privileging one member over another, from the population, and G is the number of people in that subset to correctly guess whether or not they have Q. However, such a definition turns out to be incoherent; for it is impossible to assign a uniform distribution to a denumerable sample space. In other words, one cannot select elements from an infinite set without privileging certain elements over others, and so it is nonsense to suggest that we can choose a finite subset of the population in that manner.

Although these examples hardly exhaust the myriad of possible approaches to providing P(M) with some meaningful interpretation, I believe they help illustrate the difficulties involved. While I have no cause to claim it is impossible, I nevertheless remain highly skeptical that we will ever find an appropriate definition for P(M) which would satisfy both mathematical convention and intuition. In any case, we learn an informative lesson from this exercise, that, at least under certain circumstances, we ought not leave probability measurements ambiguous or otherwise undefined. In these situations, we cannot always draw conclusions about or assign values to those measurements until such time they are endowed with sufficient meaning.

This difficulty is the primary motivation behind the abstention position. Castell, who I should add is not at all concerned with the sort of exercise I have outlined here, offers a number of reasons for opposing it, responses to which I shall save for another occasion, except to mention that I find his arguments unpersuasive if insightful. For the present time, I wish only to have shown that the Q-device provides a helpful illustration of how insufficient meaningfulness of probability measurements may lead us to prefer abstention.

Notes:

[1] Pruss, Alexander. ``Another argument against actual infinity,'' 2010 Mar 17. http://alexanderpruss.blogspot.com/2010/03/another-argument-against-actual.html

[2] Castell, Paul. "A Consistent Restriction of the Principle of Indifference," The British Journal for the Philosophy of Science, Vol. 49, No. 3 (Sep., 1998), pp. 387-395.

An English translation of a small portion of The Qalémentos

2010-02-28T06:19:00.000-06:00

Earlier this month I became aware of a document (or collection of documents) called The Qalémentos (or Pseudo-Clement). I have had great difficulty in determining its origin, but from what I can make out, it survives in Ethiopic (or perhaps Coptic) mss. which are in the possession of Ethiopian Orthodox churches. The surviving text is thought to have been translated from Arabic (apparently it was among a large batch of Christian texts translated from Arabic into Ethiopic or Coptic). However, the Arabic may have itself been a translation, perhaps from Greek, Coptic or Latin. Unfortunately, the information I have is very sketchy, and I cannot provide any solid details regarding its earliest origins. Arguably the most important information---the place and date of authorship---remains entirely unknown to me.

What I do know for certain is that at least the first portion of the document was translated from the mss. in Ethiopia into French, in or shortly before 1911, by the French scholar Sylvain Grébaut, and published in volume 16 (1911) of a series of French journals called Revue de l'Orient chrétien. This volume has been generously scanned and uploaded to archive.org, and may be downloaded there in full-color pdf format, or a text file which was generated through OCR from that pdf file.

In addition to the raw data from archive.org, I hereby offer this zip file, which contains the following additional text files: The file pseudo-clement-french.txt contains the original OCR data from pp72-84 only, since those are the pages which deal with The Qalémentos. In the file pseudo-clement-french-formatted.txt, I corrected as many OCR errors as I could find, including formatting issues. Please note that my corrections are not exhaustive; I'm sure there are many errors I overlooked, especially given that I do not speak or read French. The file pseudo-clement-english.txt is a Google-translated version of the previous file into English.

The Qalémentos appears to be an epistle from Saint Peter to Clement of Rome. Obviously it is spurious, but whether it is an ancient or medieval forgery I cannot say. Consider the following Google-translated remarks by Grébaut:

The Qalémentos, which includes seven books, is divided into two parts... [In part I] Clement tells the creation and birth of the Blessed Virgin with the history of the world to Joram what Christ taught him the secrets of heaven and the future, the creation of heaven and earth, the Trinity, orders of angels, the heavenly Jerusalem, paradise, creation of angels, their appearance The fall of Satan, the future of Christianity on earth, he defers to tell what will happen at the resurrection, he lists 70 heresies of Simon Magus to Apollinaire. [In part II it deals] with laws and the order of the Christian Church, St. Peter to St. Clement gave orders that he should send anx metropolitans, bishops, etc.., it outlines the duties of bishops and clergy and dictated a lot of rules and special penitential canons... The Qalêmentos appears as a compilation of ancient documents, such as Recognition, the Cave of Treasures, the Testament of Adam and perhaps V Apocalypse of Peter, which were fused together by an anonymous writer. According to Dillmann, the original Arabic would be the work of a Christian, living and writing in Egypt from 750 to 760. The Ethiopian version was made later directly on the original. ...we know four mss. of this work, namely: three at the British Museum, Or n04 751, 752, 753, and one in Paris, Abbadie No. 78. This latter ms. we translate.

Who exactly Dillmann is, however, I have not been able to ascertain (though admittedly I haven't tried very hard). Perhaps in the future I will track down his work and attempt to decipher it. As for his dating, we should distinguish here I think between the idea of an "original Arabic" and an original composition. In other words, if the Arabic dates from the eighth century, then the Greek, Latin, Coptic, etc., or whatever language in which this document was first written, must date from the eighth century or earlier. Then again, the Arabic may indeed be the original language, in which case, if Dillmann's hypothesis is correct, we are apparently looking at a medieval composition.

With all this in mind, I offer the Google translation of The Qalémentos, verses 1.1.1-1.3.7, as taken from archive.org's OCR of the French journal Revue de l'Orient chrétien, Vol. 16 (1911):

1.1.1. After the climb Our sky-Seigîieui 'and Xotre-Sauvenr Jesus Christ, the disciples were separated (from) the ends of the world to preach the new gospel of the Holy convert people to faith and knowledge (of Jesus Chnst), and the baptism of the holy baptism of new birth. Therefore the Apostles wanted to search for them disciples, which went with them into the country. Then (F 1 r0 b) Simon Peter took me and made me his own disciple. Indeed, I believed in him and in him who sent him, and I realized he was the chief apostle, because speech has called our Lord and Savior Jesus Black - Christ in the Gospel: You are Peter and upon this rock I will build my Church and the gates of Sheol shall not prevail against it. I'll give you the keys of the kingdom of heaven. After many days it took two brothers and made his own disciples. Then, when I lived with him twenty years, he took me, took me to my father and (to) my mother called (F. 1 v0 a) Metroryà, and revealed to me the mysteries of Our Lord Jesus Christ had taught on the Mount of Olives.

1.1.2. At that time, the Apostles and all believers suffered great persecution of the Jews infidels. Indeed, the Jews continued to kill all the faithful that they met. So, the good Peter went and entered a city. Me too, (I left) with him. Here we found a great persecution, (caused) by the quarrels (from) the infidel Jews, and questions about the genealogy of St. Mary, because they said it (F. 1 v0 b) it was no strain of Judah, to ruin the coming of Our Lord and Our Savior Jesus Christ in the world. Indeed, they themselves continued to give much money to bribe the Greeks and Romans, so they aid him for the extermination of the faithful. They prevented the Apostles to read the law, so we did not know the original creation of the world.

1.1.3. When I saw all this persecution, which came at me from the Jewish infidels, I inquired with my Master Simon Peter, and I asked him to let me know and how to expose myself (F. 2 r0 was) had held the original creation of the world. Indeed, he even knew all the mysteries from Jesus Christ our Lord. As for me, I knew the language of the Greeks, their books, all their mysteries and their philosophy.

I told my teacher all the hatred and (all) jealousy, which had come against me. (I told him) that Jews outraged and scolded me about St. Mary, (saying) that I had no knowledge of the Law and the Prophets, and (said) they don ' many had questioned the creation of our father Adam, they had greatly blasphemed against Notre Dame St. Mary, and (F. 2 r0 b) I was pa? found an argument by which their malice and confound their speech impure.

1.1.4. When I told all this to my teacher, he was enormously sad. Zeal entered into him and he told me: Myself, I will reveal to you, O my son, everything that you asked me and I'll make you understand the original creation of the world, and I will demonstrate on Sainte Marie Mother of Light, it is clearly without confusion (possible), the strain of Judah, son of Jacob. In addition, I'll tell you how Satan fell from heaven.

1.2.1. Understand then, O my son Clement, as the Lord originally existed and before the origin (F 2 v0 a) he who has no beginning or end. He was raised well above the (people) high, it is not known by the intelligence nor the understanding that it has no bottom, or inner, or outer . It is the principle of days and times of ancient. 11 is inconceivable and inexpressible. It is above all. There's beauty in his divinity over his creatures. With the creatures in the creature (it still is) the beauty. It creates a bright light, a light which do not approach the darkness, he who goes into the lights, that her eyes are not aware. There was (W 2 v0 b) before the creatures. 11 is the author of everything and the creator of everything, he whose fame comes from himself. He is the creator of everything that is glorified, that the greatness of his majesty and strength of his power is manifested. He is the author of the heavens and the earth.

1.2.2. Here I expose you, O my son Clement, the Most High (created) before (another) creature, his Angels, (divided) into nine families, and it has established for them glorified with songs, rhythms and sweet melodies, each according to its degree. The larger (family) of them approach the throne of the Lord. This family Sâtnâ'êl. This is the first of all (the families) angels. (Angels of the family) make up (F. 3 r0 a) their glory to the Lord, without being silenced.

1.2.3. The first day holy is to say, the beginning days, the firstborn from the day the Lord created the heaven above and earth family of angels above, is to tell the family Sâtnâ'êl of the Angels, Archangels, Virtues, Powers, Thrones, Principalities, Ministers: Seraphim e 'the Cherubim; clarity and light, day and night, the winds , water and fire. He accomplished all this on the first day holy by his first words. The day (F. 3 r0 b) God created all this, the Holy Spirit made Vombre Waters. Waters were blessed and sanctified, and they multiplied, through procreation, all (things) with a living soul.

The second day, God created the water below, that man's eyes are clear. The sky was separated from the heavens above. Indeed, above the sky, called Falek, there is another heaven above this heaven there is another heaven called Dortiqon above this (last) there is the flame fire over the fire there is another sky. All the heavens are filled with clarity and (F. 3 v0 a) light that human eyes can not see. In this second day, God created (separation) between water which is above the sky, and water on earth. The rise of the water took place that day in the form of dense clouds. As the waters that remain, they remain in the air forever and will be tossed to and fro.

The third day, God commanded the waters which were under the sky, called Falek, to gather in one place so that the sec appeared. It was. Then (dry) appeared to be mud, (F. 3 v0 b) of the earth and water mixed. Water exists on (land) and under (ground). The winds themselves, rose from the bosom of the earth and breathed with measurement. It is through them that every creature lives on the type of sponge, who lives on the water. On this day, the Lord commanded (to ground) to produce green grass, trees, seeds, medicinal and other plants (plants).

The fourth day, God created the sun, moon and stars, so they fulfill a role (useful) for land. The sun (had the role of dry) the mud and harden the earth.

On the fifth day God commanded the waters to produce (F. 4 r0 a) the family of the various fish species. In addition, he created (birds) flying over water, and those that fly through the air, and the great sea monsters, whose appearance is amazing.

The sixth day, God created all land animals, beasts and worms. In addition, he created Adam our father land, and created our mother Eve of a rib (diAdam).

The seventh day, as he had done, he rested from all his work, and he called (so far) the Sabbath.

1.3.1. The Lord created Adam our father to three hours on Friday, the sixth day. But at the same time, (F. 4 r0 b) the jealousy pt pride entered Satan. The Lord sent down from heaven to earth. Before (God) create our father Adam, silence fell over all the powers of heaven. The Lord said to his Father Son and Holy Spirit: Come: rhomm.e do to our image and our likeness. When the angels had heard the word of the Lord Almighty, he came upon them a big fright and (much) fear. They conversed among themselves, saying, What is this great wonder, do we learn? How is it that (F. 4 v0 a) the image and likeness of our God and our Creator appear?

Then the angels saw the (main) right of the Lord (who) was extended over the whole earth. The world was in his hand. Here he took the whole ground a little dust, all the water a drop of water, air a bit (of air), the fire burning a little (of fire). All (these) were in his hand. The Lord created Adam our father of four (elements) low (and) without force, so that all creatures obey (to Adam. He created for) land, so that (F 4 \ ° b) any creature (which exists on earth) obey him; (water, so that any creature) generated in water (obeyed); air so he could feel it by lodorat breathe fire, so that his body became strong and heat he found (in it) a strong adjuvant. Thus that the Lord our Father created Adam in His own image and likeness, his holy hands. (11 created him) in his own likeness, so he received wisdom, the language, the ability to feel and all science.

1.3.2. When the angels had seen the majesty, honor and glory that were on Adam, they were afraid and they trembled because of the greatness of his majesty. (The Lord) had crowned. On his face was shining the light of divinity, which (F. 5 r0 a) was brighter and more intense than sunlight. His body shone like the morning star. ^ Hen I (the Lord) had finished cvéev Adam (Adam) was held in the face of any land, raised her feet on Golgotha, and extended his right hand and his left hand at 'where they planted the tree of the cross of our Lord. Then the Lord put on our father Adam a royal robes, put on her head a crown of glory, and (the student) to a great majesty. He put on his head a crown of glory, and instituted, thereby, priest, prophet and king.

1.3.3. The Lord made him sit on a throne of glory. (F. 5 r0 b) All animals, beasts, birds, all (the animated beings), that the Lord had created, assembled from (à'Adam) and stood before him. They bowed their heads and prostrated themselves before Adam. He called them all, each by name. They obeyed Adam and watched his words. So laparole heard the angels of the Lord Almighty, who said: Adam, here I have made you king, priest, prophet, prince and master of all creatures. They obey your word and be on hand for you alone! I give you the power and I'll let you do what you want with respect to all (F. 5 v0 a) creatures. When the angels had heard the word of the Lord Almighty, the majesty Adam was much greater before them.

1.3.4. When Satan had seen the greatness and glory that were given to Adam by the Lord, of jealousy from that hour, and began to think about it, to find against him the opportunity to seduce and was obeyed him. So, Satan became the rebel Lord's grace, which remained in him. At that time, the Lord (him) took off the garment of glory and majesty that was great about him, and he called the name of Satan. (F. 5 v0 b) It had become arrogant to the Lord, did not go in his ways, and had wanted the glory for himself.

1.3.5. While Adam had stood on Golgotha, here all the creatures had gathered around him to hear the word of the Lord, which he had been. Then came a cloud of light. She put Adam and led him into paradise. All the armies of the angels went with Adam, running hymns, songs and sweet melodies. The Cherubim blessed; Seraphim singing: Holy, Holy, Holy, before him. (Angels) led him to paradise. Adam went to heaven to three hours, (F. 6 r0 a) on Friday. The Lord meant all the commandments and commanded him specifically. do not eat (the fruit) of the tree that was in paradise.

1.3.6. Then the Lord Almighty sent sleep upon Adam, (who) slept in the paradise of a dreamland. The Lord took one of his left ribs, and created Eve. When Adam was awakened from his sleep, he saw Eve, welcomed and loved greatly. While they remained in YÉden, the paradise of happiness, the Lord clothed in the glory and majesty, and rejoices (F. 6 r0 b) much of the greatness of the glory that was upon them. The crown for the Lord (their) marriage, e 'are delighted about them (him) and all the angels. There was therefore a great joy, as there had not been since (the original) world, and such that there will not until hearing the word of joy from those who are right. Adam and Eve lived in paradise for three hours.

1.3.7. Paradise was high in the air, land (of paradise) was also heavenly rose fifteen cubits above it high mountains and hills. (The tree of forbidden fruit) was the symbol of the tree of the cross (F 6 v0 a), which (Jesus Christ) extended his hands, the tree of life and hi, ( tree) of the Holy Cross, which was planted in the ground.

Wandering Prophets in the Time of Mark

2010-01-31T08:50:00.000-06:00

Examining the Scriptures, we may notice a passage in Mark 6, with parallels in Mt 10:1-15 and Lk 9:1-6, 10:1-12, in which Jesus charges his disciples to go out and evangelize. Here I reproduce the ostensibly original Markan passage (ESV):

7 And he called the twelve and began to send them out two by two, and gave them authority over the unclean spirits. 8 He charged them to take nothing for their journey except a staff---no bread, no bag, no money in their belts---9 but to wear sandals and not put on two tunics. 10 And he said to them, "Whenever you enter a house, stay there until you depart from there. 11 And if any place will not receive you and they will not listen to you, when you leave, shake off the dust that is on your feet as a testimony against them." 12 So they went out and proclaimed that people should repent. 13 And they cast out many demons and anointed with oil many who were sick and healed them.

I have little doubt that many modern Christians identify the most important message in this passage, and also its Synoptic counterparts, as a reminder to distinguish between those who are receptive to the Gospel and those who are not, in order that evangelists not waste their efforts on the wicked opposition of skeptics. As Jesus said, "Do not give dogs what is holy, and do not throw your pearls before pigs, lest they trample them underfoot and turn to attack you" (Mt 7:6). Now, I agree that this seems to have been a key motivator for Mark, and more so for Matthew and Luke (or perhaps their source document Q), for whom Jesus adds, regarding each population which rejects his disciples, "Truly, I say to you, it will be more bearable on the day of judgment for the land of Sodom and Gomorrah than for that town" (Mt 10:15). So, clearly, these ancient Christian authors shared in some sense the modern concern for resistance to their religion.

However, this was by no means the only object of their attentions. Consider that they discussed a mode of operation for evangelists which appears to have continued well into the day of the authors. For, we must consider another passage from the Didache, a late-first-century or early-second-century Christian document which outlines a code of conduct for both wandering prophets as well as their hosts (chap. 12):^[1]

1 But let every one that cometh in the name of the Lord be received, and afterward ye shall prove and know him; for ye shall have understanding right and left. 2 If he who cometh is a wayfarer, assist him as far as ye are able; but he shall not remain with you, except for two or three days, if need be. 3 But if he willeth to abide with you, being an artisan, let him work and eat; but if he hath no trade, 4 according to your understanding see to it that, as a Christian, he shall not live with you idle. 5 But if he willeth not to do, he is a Christ-monger. Watch that ye keep aloof from such.

Thus we consider a particular perspective when reading the Synoptic Gospels, in light of the Didache.

It must have been tempting for Christians to adopt an occupation whereby they could expect their fellow believers to provide for them food and shelter, and where their duties might not far exceed simply preaching the Gospel with alacrity. That both Mark and the Didache are concerned with the conduct of such men seems fairly obvious; yet they address, I think, slightly different problems arising from that same issue.

Mark specifies that a prophet must not hop from dwelling to dwelling (6:10), and Luke, perhaps quoting Q, doubly so (9:4, 10:7). What might be their intent, then? Although I cannot appeal to hard evidence to answer that question, I suspect the following as an explanation: It could have been that evangelists unhappy with the hospitality of a particular host sought to be welcomed by more generous neighbors. In other words, they might have felt tempted to troll a Christian community for credulous or naive benefactors. They may not even have done so consciously; for it is not the case that an irresponsible person must always be aware of the insidious and resource-exhausting character of his own actions. Whether or not they recognized the cast of their hypothetical tactics, however, the consequences surely would have been clear to their victims' communities, prompting the sort of disapproval we see in Mark and Luke.

The Didache, on the other hand, demands an itinerant lifestyle for evangelists. While Mark seems to take for granted the homelessness of evangelists, the Didache makes it an explicit requirement, and sets strict limits on the time such men may stay in any one place. Again, I must admit we have no external indication of the author's motivation, but we may yet propose a plausible explanation, namely that evangelists in that day tended to settle wherever comforts abounded. That is, we have the same hypothetical situation I have suggested Mark was addressing, only on a larger scale: Instead of going from house to house, a Christian evangelist could travel from community to community, until such time that he discovered hosts who would treat him relatively richly. The Didache, then, we may interpret as abhorring that sort of opportunistic behavior.

With all of this in mind, we ask if it might be possible to use these interpretations to inform a date for any of Mark, the Didache or Q. To this end, we may construct an argument that all three compositions date from approximately the same time, since we may read them to reflect the same or quite similar historical circumstances, in which wandering prophets have become a public concern. In my judgment, we ought to hold onto the majority dating of Mark's Gospel, scholars usually placing it c. 65-70 AD. If Luke quotes Q in 10:7, then under the hypothesis presented here, Q and the Didache both fall in or about this same span.

Now, certainly this argument of mine hasn't the strength to settle any dating disputes with confidence. In fact, at the moment it amounts at most to a plausible suggestion, relying not on the texts themselves, but on particular exegeses thereof, which, although I find them quite natural and believable, remain highly interpretative nonetheless. We must, then, retains serious reservations while seeking corroborating evidence. Alternatively, we may attempt to overturn my relative dating hypothesis with a more attractive explanation.

Of course, one may point out that evangelists clearly had been active and highly mobile since the earliest days of the Christian movement, even to the 30s AD, just after Jesus' crucifixion. The Acts of the Apostles and other ancient sources record the names of several traveling preachers, including Barnabas, Apollos, Titus, Timothy, Peter and James, among others. We can reasonably expect imitators of these early Church founders and authorities to have arisen fairly quickly. Yet it is not the mere activity of such evangelists which I suspect had occasioned the stipulations elucidated in Mark and the Didache, but rather an ongoing and publicly-recognized problem with such men taking undue advantage of Church hospitality. The key element, then, is this identification of wandering prophets as undesirable characters who sap Church resources, a notion we may not see in writings from the 50s and earlier, nor after the late 70s. If we find this idea expressed in an ancient document, then by my hypothesis it dates from or near 65-70 AD, or else the supporting argument breaks down.

One might interpret 2 Thessalonians to meet this very criterion. In chap. 3, vv.7-8, Paul writes to those Christians of Thessalonica, "you yourselves know how you ought to imitate us, because we were not idle when we were with you, nor did we eat anyone’s bread without paying for it" (ESV). So, if we regard the epistle as genuine, which I for one am inclined to do, we have at least one instance of instruction regarding evangelists dating from the 50s or early 60s AD. However, it's quite possible that 2 Thessalonians is actually pseudepigraphical. In either case, we are free to place 2 Thessalonians in roughly the same proposed period as Mark, Q and the Didache, c.63-64 if it is genuine, and c.65-70 if not.

Dating issues aside, one other consequence of reading Mark as I have is that we best understand Jesus' words as somewhat anachronistic. For, he is speaking, we might think, to a situation not in his own day, but in Mark's. On the other hand, the assumption that the passage has heightened relevance to Mark's situation does not strictly imply the denial of its historicity; it could be, for instance, that Christians of the 60s and 70s appealed to Jesus' charge to evangelize in order to justify their opportunistic lifestyle, and that Mark and Q responded by pointing out that Jesus condemned such behavior in that very charge. So, it is their emphasis, and not their content, which I suggest relates to their motivation. Still, I do consider it simplier to posit that at least the words "whenever you enter a house, stay there until you depart from there" (Mk 6:10), are apocryphal. Moreover, we ought to notice that it undercuts my argument for relative dating to suppose they are genuine.

The approaches I've discussed may already have some precedent in the scholarly literature, either supported or opposed, although if so I am unaware of it at the present time. In any case, further exploration of the issues seems prudent. Meanwhile, I must remind my readers that these speculations of mine likely have little real use. I do not regard them as constituting some kind of essential insight; for they are surely nothing so grand. I only offer them up for whatever value, however minimal, they may happen to have.

Footnotes:

[1] Tr. Isaac H. Hall and Mr. John T. Napier, ed. Alexander Roberts and James Donaldson. http://www.ccel.org/ccel/schaff/anf07.viii.iii.xii.html

Slavery in Antiquity

2010-01-17T08:52:00.004-06:00

In my experience, skeptics of Christianity often have problems with the Bible's comments on slavery. The Old and New Testaments alike provide instructions on how God's people are to treat their slaves, not always palatable to their readers. Unbelievers have attempted to cast doubt on the divine origin of Scripture by pointing to the passages discussing slavery, and observing that they do not reflect our modern moral compass.

I must emphatically assure my own audience that I am unconvinced that this approach is viable. Although some passages in Leviticus could perhaps convict its author (e.g. Lv 25:44-46), I have never encountered a cohesive argument against Biblical inspiration which depends on modern moral condemnation of slavery. Since Scripture never explicitly denies the evils of slavery, we have some limited room for subjective interpretation. Acknowledging that fact constitutes the best defense I know from skeptics' criticisms, and indeed it may be adequate to the task. Christians themselves often contend that the Bible in no way implies God condones the institution of slavery.

That said, Christian apologists do sometimes take a different approach with which I have serious issues, claiming that the slavery of antiquity was not really so horrible, and that we should therefore not expect God to vehemently object to it. For example, Michael Marlowe, a Reformed theologian, Pittsburgh Theological Seminary alumnus, and editor of the website bible-researcher.com, describes ancient slavery thusly:^[1]

Those who have been in the military have experienced something like it---being legally bound to an employer and to a job that one cannot simply "quit" at will, not free to leave without permission, subject to discipline if one disobeys or is grossly negligent---all of this is familiar enough to those of us who have served in the military. And yet we know that the daily life of a good soldier is not especially hard. This is what it was like to be a slave.

Of course, this is patently false. Modern military service is not remotely similar to slavery in ancient cultures.

In order to justify my disagreement, I shall present evidence in the form of selected quotations of ancient literature on the subject of slavery. Please note that I do not indent to exhaustively catalog antiquated opinion, but rather provide a small sample for the reader of the much larger evidentiary case for our historical understanding of the institution as it was practiced so many years ago.

We may begin with Aristotle, who believed that some men were naturally slaves, and that the universality of slavery was therefore an inevitable feature of the natural order of things. He wrote at great length on this topic in his work Politics, of which I reproduce one particularly disturbing passage here:^[2]

Those men therefore who are as much inferior to others as the body is to the soul, are to be thus disposed of, as the proper use of them is their bodies, in which their excellence consists; and if what I have said be true, they are slaves by nature, and it is advantageous to them to be always under government. He then is by nature formed a slave who is qualified to become the chattel of another person, and on that account is so, and who has just reason enough to know that there is such a faculty, without being indued with the use of it; for other animals have no perception of reason, but are entirely guided by appetite, and indeed they vary very little in their use from each other...

If these sentiments were common, as is reasonable to suppose, then we gain insight into how we might expect free citizens to treat their nation's bonded population. In one account, for instance, recorded by Diogenes Laërtius, we hear that the philosopher Diogenes the Cynic (of no relation to his biographer) was enslaved by pirates and sold on the Cretan market, whereupon he insisted that he was skilled in "governing men." Accordingly, he was put to work tutoring the sons of one Xeniades, resident of Corinth.^[3] On this occasion, then, we observe that the ancients acted in concordance with the belief that some men were naturally predisposed to a particular service, in this case tutorage. Diogenes Laërtius also records that another fourth-century Greek philosopher, Phaedo of Elis (after whom Plato's famous dialog was named), was similarly captured and "compelled to submit to the vilest treatment" before he was freed by Socrates.^[4]

Aristotle's own tutor, Plato, likewise penned extensive thoughts on slavery, and described a great variance of treatment to which slaves in his day were subjected. Quoting an earlier poet, he writes:^[5]

Different persons have got these two different notions of slaves in their minds---some of them utterly distrust their servants, and, as if they were wild beasts, chastise them with goads and whips, and make their souls three times, or rather many times, as slavish as they were before;---and others do just the opposite.

So we see that the comparatively comfortable employment of Diogenes with respect to Phaedo's "vilest treatment" reflect typical snares of fortune in the ancient Greek slave industry.

Aristotle characterizes the "rule...of a master over slaves" as "despotic," further confirming our modern understanding of slavery as great evil, and suggests tantalizing slaves with the possibility of freedom, presumably in order to manage their behavior and compel them into docility.^[6] In the same book he quotes an earlier proverb, affirming that "there is no leisure for slaves."^[7] Indeed, prior to the sixth century B.C., loans in Athens had been "secured upon the debtor's person" by "custom," and if the debtors "failed to pay their rent they were liable to be haled into slavery, and their children with them."^[8] This evidently widespread problem persisted in Athens prior to the election of Solon as Archon c.594 B.C., and highlights the capriciousness of the Athenian slave industry.

Scripture itself affirms the evils of slavery in its depiction of Moses, Aaron and the plight of the Hebrews in Egypt. Consider the haunting passage from Exodus 1 (ESV), in which the Egyptian's treatment of the Hebrews is tersely stated:

13 So they ruthlessly made the people of Israel work as slaves 14 and made their lives bitter with hard service, in mortar and brick, and in all kinds of work in the field. In all their work they ruthlessly made them work as slaves.

In addition to all this, we may further recall that bondage passed from parent to child, such that children of slaves were themselves born into slavery. This practice is referenced in Lv 25:46, in which slave lineages are promised to Jewish generations "to inherit as a possession forever" (ESV); yet it was by no means confined to the near east. We may consider the Helots, an entire slave population in ancient Sparta, kept subdued up to at least the fifth century B.C., and whose mistreatment meets any modern horror. For example, Plutarch records an ordinance given by the eighth-century Spartan legislator Lycurgus, establishing the custom of indiscriminate murder of Helots by young Spartan men.^[9] So objectionable was the Spartan persecution of their Helot slaves---and other lower classes, for that matter---that we have preserved for us by Xenophon the observation that "whenever among these classes [Helots, freedmen, lesser Spartiatae, and Perioeci] any mention was made of Spartiatae, no one was able to conceal the fact that he would be glad to eat them raw."^[10]

As previously indicated, I am disinterested at this time in taking sides regarding the moral argument against Biblical discussions of slavery; rather, I aim only to address one particular apologetic claim. To this end, I have provided here a few scattered quotations in the ancient literature regarding the slave industry and the treatment of those bonded, not to paint a complete picture of the institution in antiquity, but rather to dispel the modern misconception among Christians that slavery was somehow humane in those days. I can find no basis whatsoever in the historical record to justify such a bizarre suggestion, which appears motivated by theology rather than a primary concern for historical accuracy.

Footnotes:

[1] Marlowe, Michael. "Some Observations on Biblical Interpretation and Slavery" (an internet essay). http://www.bible-researcher.com/slavery.html

[2] Aristotle, Politics: A Treatise On Government I.V, tr. William Ellis, A.M. http://www.gutenberg.org/files/6762/6762-h/6762-h.htm

[3] Diogenes Laërtius, Lives and Opinions of Eminent Philosophers VI.II.IX (Diogenes of Sinope), tr. Charles Duke Yonge. http://classicpersuasion.org/pw/diogenes/dldiogenes.htm

[4] Diogenes Laërtius II.IX.II (Phaedo). http://classicpersuasion.org/pw/diogenes/dlphaedo.htm

[5] Plato, Laws VI, tr. Benjamin Jowett. http://classics.mit.edu/Plato/laws.6.vi.html

[6] Aristotle, Politics VII.III,X, tr. Benjamin Jowett. http://classics.mit.edu/Aristotle/politics.7.seven.html

[7] Aristotle, Politics VII.III.XV.

[8] Aristotle, The Athenian Constitution I.II, tr. Sir Frederic G. Kenyon. http://classics.mit.edu/Aristotle/athenian_const.1.1.html

[9] "By this ordinance [the Cryptia], the magistrates despatched privately some of the ablest of the young men into the country, from time to time, armed only with their daggers, and taking a little necessary provision with them; in the daytime, they hid themselves in out-of-the-way places, and there lay close, but in the night issued out into the highways, and killed all the Helots they could light upon; sometimes they set upon them by day, as they were at work in the fields, and murdered them." Plutarch, Lycurgus, tr. John Dryden. http://classics.mit.edu/Plutarch/lycurgus.html

[10] Xenophon, Hellenica III.III.VI, tr. Carleton L. Brownson. http://old.perseus.tufts.edu/cgi-bin/ptext?lookup=Xen.+Hell.+3.3.1

A Colorful Re-interpretation of Paul and Polycarp

2010-01-10T06:10:00.000-06:00

In my recent exploration of the Apostolic Fathers, one passage from Polycarp caught my attention. He writes, in his epistle to the Philippians,^[1]

7:1 "For whosoever does not confess that Jesus Christ has come in the flesh, is antichrist;" and whosoever does not confess the testimony of the cross, is of the devil; and whosoever perverts the oracles of the Lord to his own lusts, and says that there is neither a resurrection nor a judgment, he is the first-born of Satan.

Paul records a similar phrase in 1 Corinthians 1 (ESV):

17 For Christ did not send me to baptize but to preach the gospel, and not with words of eloquent wisdom, lest the cross of Christ be emptied of its power. 18 For the word of the cross is folly to those who are perishing, but to us who are being saved it is the power of God.

With Paul, he speaks of "the word of the cross" ("ο λογος γαρ ο του σταυρου"), whereas Polycarp urges us to "confess the testimony of the cross" ("ομολογη το μαρτυριον του σταυρου"). I find it quite natural to interpret both expressions as referencing the Gospel message, with a particular emphasis on the atoning sacrifice of Jesus. In the case of Polycarp this is especially likely, considering that he seems intent on answering the Docetic heresy.

Nevertheless, I shall now offer an alternative interpretation. Suppose Paul and Polycarp understood the cross itself to have declared a testimony to the world. While certainly a strange notion, it is not without precedent in the ancient Christian literature. Indeed, the fragmentary Gospel of the Savior personifies the cross. Consider first vv73-77, in which Jesus and his disciples continue a discourse:^[2]

73 [He] said to us, "I am among you [as] a child." 74 He said, "Amen!" 75 "A little while I am among you." 76 [...] responded, "Amen!" 77 "[Those who] [to set (?) the world] against me [are] plotting against me because I am a stranger to it."^[3]

Thus is established a structural motif whereby Jesus (known only as "the Savior" in this Gospel) teaches a mystery, and some agent, unknown due to the missing text in v76, responds by speaking the word "Amen!" Now, we must observe that at least two of the scholars to translate this work, Hans-Martin Schenke and Stephen Emmel, believe that this agent is one or more of Jesus' disciples. Schenke suggests that v76 may read "We responded...", but Emmel declines to commit to the reading, noting that the reconstruction "He responded..." fits the text, with "he" possibly referring to the Apostle John, who also spoke in v68.^[4] I'm inclined to defer to their expert opinion, as I recommend others to do, as well. However, suppose we suspend our agreement momentarily for the purpose of considering a wilder hypothesis, that it is the cross which utters the word, "Amen!" While admittedly an unusual suggestion, consider that Jesus proceeds in later verses to speak directly to the cross. His address spans at least vv98-119, of which I provide the following excerpt:

101 "[For] those on the [right will] take shelter [under you, apart from] those on the [left, 102 O] cross, [...5 lines untranslatable...]. 103 O Cross, [...] you [...] height ... [...] for this is your desire. 104 O cross, do not be afraid! 105 I am rich. I will fill you with my wealth. 106 [I] will mount you, O cross. [I] will be [hung] upon you [...] ... [..."---"Amen!"] 107 "[...6 lines untranslatable...]. 108 [Do not] weep, O [cross], but rather [rejoice] and recognize [your] Lord as he [is coming toward you, 109 that he is [gentle] and [lowly]!"---"Amen!"

So we see that the cross is thusly personified, such that it might be said to offer its own testimony of agreement to Jesus' teachings in this Gospel.

A similar scenario is more explicitly articulated in the securer text of the Gospel of Peter, in which the author leaves no question that the cross really does speak. In the famous scene, it is very early on the morning of the Resurrection, still before dawn, and the stone has just been removed from Jesus' tomb in order to admit two young men. Frightened and disturbed, the Roman soldiers guarding the tomb run off to report the remarkable turn of events. Thus begins the following quotation:

39 And while they were relating what they had seen, again they see three males who have come out from they sepulcher, with the two supporting the other one, and a cross following them, 40 and the head of the two reaching unto heaven, but that of the one being led out by a hand by them going beyond the heavens. 41 And they were hearing a voice from the heavens saying, "Have you made proclamation to the fallen-asleep?" 42 And an obeisance was heard from the cross, "Yes."^[5]

If this account was widely known by the end of the first century, then we have a definite lead as to what specifically the cross conveyed, that Jesus preached the Gospel to the dead during the period between his own death and Resurrection. If that doctrine conflicted with Docetic theology, then Polycarp's intent is well-served by reminding his readers of it. Paul, also, in 1Co 1:18, may have wished to reference Jesus' role as an evangelist as testified by the cross.

Now, this literal interpretation of Paul's and Polycarp's "word (testimony) of the cross" is quite clearly tenuous in the extreme; I do not mean to suggest anyone take it too seriously. However, I find it to be an amusing spin on the words of Paul and Polycarp, and so I offer it up here for reflection.

Footnotes:

[1] Tr. Alexander Roberts and James Donaldson. http://www.earlychristianwritings.com/text/polycarp-roberts.html

[2] Emmel, Stephen. "The Recently Published 'Gospel of the Savior' ('Unbekanntes Berliner Evangelium'): Righting the Order of Pages and Events." The Harvard Theological Review, Vol. 95, No. 1 (Jan., 2002), pp45-72. The translation itself is also available online: http://books.google.com/books?id=e-13kf8OPqIC

[3] Emmel uses a system of notation here which is best described in his own words: "I have enclosed in square brackets much that is only slightly uncertain paleographically, preferring to give the impression that some portions of the text are less securely established than is in fact the case" (Emmel, p52).

[4] Emmel, p58.

[5] Tr. Raymond Brown. http://www.earlychristianwritings.com/text/gospelpeter-brown.html

Paul and Clement: Egalitarian Champions?

2010-01-03T11:03:00.002-06:00

Codex Boernerianus, also known as G, relocates 1Co 14:34-35, and in their place has a single word, διδασκω, a verb meaning "teach."

Reading 1 Clement for the first time, I ran across a passage which I find historically interesting. For those who may not know, tradition holds that Clement was Bishop of Rome c.92-c.99 AD, and wrote a letter to the Corinthians c.95, here denoted as 1 Clement. While scholars dispute its authenticity, the date is largely uncontested, making this text a very early witness for Church doctrine. I quote the surprising passage from chapter 21:

06 Let us reverence the Lord Jesus Christ, whose blood was given for us; let us esteem those who have the rule over us; let us honour the aged among us; let us train up the young men in the fear of God; let us direct our wives to that which is good. Let them exhibit the lovely habit of purity [in all their conduct]; 07 let them show forth the sincere disposition of meekness; let them make manifest the command which they have of their tongue, by their manner of speaking; let them display their love, not by preferring one to another, but by showing equal affection to all that piously fear God. Let your children be partakers of true Christian training;^[1]

Of course we can interpret this passage in several different ways. Should men also "show[] equal affection to all that piously fear God," or just women? What sort of discrimination is Clement condemning? Does he wish us to overlook classes and socio-political influence? Or is he merely referring to the preference of one doctrinal faction over another? However we read it, though, clearly the notion of a oneness in Christ has the potential to fuel an egalitarian spirit. Therefore we refer back to that famous passage of the New Testament, in Galatians 3 (ESV), where Paul articulates that very sentiment:

24 So then, the law was our guardian until Christ came, in order that we might be justified by faith. 25 But now that faith has come, we are no longer under a guardian, 26 for in Christ Jesus you are all sons of God, through faith. 27 For as many of you as were baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus. 29 And if you are Christ’s, then you are Abraham’s offspring, heirs according to promise.

Yet while Paul's most explicit endorsement of gender equality appeared as above in Galatians, we may glean additional insight from examining his epistle to the Romans.^[2] In chapter 16 of that letter, he extends greetings to a number of churchpersons, among them a woman called Phoebe, "a patron of many and of" Paul, that the Romans "may welcome her in the Lord in a way worthy of the saints." He thanks the couple "Prisca and Aquila," naming the woman Prisca before the man Aquila, and calling them both "fellow workers in Christ Jesus, who risked their necks" for Paul's life, and in whose house the Romans are expected to meet.^[3] Paul also mentions a certain Mary, "who has worked hard" for the Roman church, and Junia, his "kins[woman]" and "fellow prisoner[]," who was "well known to the apostles." He also gives the names Tryphaena, who may or may not have been the same as one Antonia Tryphaena, a Thracian princess from the first century, and Tryphosa, who he describes as "workers in the Lord." He further greets the mother of a Christian man named Rufus, the sister of another man Nereus, and a woman named Julia. So, we can see that whatever Paul's view of women in the church, he deems them honorable, worthy of respect, and valuable in their contributions to the community.

Sadly, this all stands in stark contrast to the demeaning comments of 2 Timothy chapter 2 (ESV):

8 I desire then that in every place the men should pray, lifting holy hands without anger or quarreling; 9 likewise also that women should adorn themselves in respectable apparel, with modesty and self-control, not with braided hair and gold or pearls or costly attire, 10 but with what is proper for women who profess godliness---with good works. 11 Let a woman learn quietly with all submissiveness. 12 I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet. 13 For Adam was formed first, then Eve; 14 and Adam was not deceived, but the woman was deceived and became a transgressor. 15 Yet she will be saved through childbearing---if they continue in faith and love and holiness, with self-control.

If we regard the Pastorals as authentic epistles of Paul, then this passage demands we temper our interpretations of Galatians 3 and Romans 16. If not, and if the Pastorals were written as might be supposed in the late first century, about the time of 1 Clement, then we see that egalitarianism could not have completely dominated the proto-orthodox movement. However, it is certainly possible that the Pastorals date from the early-to-mid-second century, in which case we would observe the beginnings of a framework of evidence showing that the beginnings of proto-orthodoxy began with the ingredients for an egalitarian movement, and then drifted later away from that laudable tradition, at least with respect to gender.

On the other hand, we must not overlook the infamous passage from 1 Corinthians 14 (ESV):

33 For God is not a God of confusion but of peace. As in all the churches of the saints, 34 the women should keep silent in the churches. For they are not permitted to speak, but should be in submission, as the Law also says. 35 If there is anything they desire to learn, let them ask their husbands at home. For it is shameful for a woman to speak in church. 36 Or was it from you that the word of God came? Or are you the only ones it has reached? 37 If anyone thinks that he is a prophet, or spiritual, he should acknowledge that the things I am writing to you are a command of the Lord. 38 If anyone does not recognize this, he is not recognized. 39 So, my brothers, earnestly desire to prophesy, and do not forbid speaking in tongues. 40 But all things should be done decently and in order.

One immediately notices the parallel to 2 Timothy 2. How can one argue that the Pastorals depart from the usual theology of Paul if it explicitly reflects his teachings from 1 Corinthians? Unfortunately, this matter is not quite as simple as we might like it to be; for as it happens, we have a textual problem in 1 Co 14:34-35 (the italicized words above). For while no manuscript actually omits the passage altogether, several Western text-type witnesses place it after v40.^[4] Thus our text is not perfectly stable, and given the disparity between this theology and Paul's opinions from Ga 3 and Ro 16, we may have reason to doubt its authenticity. Nevertheless, our doubt must not necessarily be so strong as to reject it outright. While scholars such as Gordon Fee regard it a later interpolation,^[5] others like Daniel B. Wallace accept it as authentic.^[6]

Furthermore, the theological problems with vv34-35 ought not be overstated. For in 1 Co 11:2-16 Paul relates his opinions that women must keep their heads covered while praying, emphasizing that "man was not made from woman, but woman from man" (11:8, ESV). While not as radical as demanding their silence in the church, it does demonstrate that Paul recognized distinct gender roles. I am therefore inclined towards the view of Wallace, which in turn undercuts any objection to the authenticity of the Pastorals on the grounds of theological disharmony between 2Ti 2 and Ga 3.

In sum, the author of 1 Clement almost certainly didn't have some grand egalitarian vision in mind when he wrote his offhand comment from 21:7, but his dedication to a unity in Christ may yet speak to an albeit limited spirit of equality among the earliest Christians. Whatever the truth of Paul's feelings, the opinions expressed in Galatians 3 and Romans 16 make it abundantly clear that he shared Clement's apparent predilection towards Christian unity. I expect this pleases Christians, as well as Western non-Christians such as myself, whose culture has roots in the Church.

Footnotes:

[1] Tr. John Keith. http://www.newadvent.org/fathers/1010.htm

[2] The ensuing quotations come from Ro 16:1-15, ESV.

[3] We find further discussion of this couple in Ac 18, 1Co 16:19 and 1Ti 4:19. For more information, cf. the wikipedia page Priscilla and Aquila. http://en.wikipedia.org/wiki/Priscilla_and_Aquila

[4] "Most MSS (including P⁴⁶ A B K Ψ 0243 33 81 1739 Maj) include these verses here; they are found after v. 40 in D F G 88* a b d f g Ambrosiaster Sedulius-Scotus, thus the entire Western tradition." Gordon Fee, The First Epistle To The Corinthians, p699 ISBN 0-8028-2507-9 (http://books.google.com/books?id=6K3KJR7fpcgC).

[5] Fee, p705: "On the whole, therefore, the case against these verses is so strong, and finding a viable solution to their meaning so difficult, that it seems best to view them as an interpolation."

[6] "We are thus compelled to regard the words as original, and as belonging where they are in the text above." Daniel B. Wallace, "The Textual Problem of 1 Corinthians 14:34-35" (http://bible.org/article/textual-problem-1-corinthians-1434-35).

Metaphysical Order

2009-10-25T08:20:00.000-05:00

It is certainly natural to perceive a physical order to the universe. Matter behaves in particular, predictable ways, and we have used mathematics to generalize those predictions with incredible, perhaps "unreasonable" success, to borrow Eugene Wigner's famous characterization.^[1] An associate of mine recently offered up an argument for the existence of God which alleged that this formal order strongly suggests the influence of a personal designer. He did not rely directly on any Platonic understanding of math, although I suspect he believes therein; however, one of his key premises assumed that the order itself possesses divine attributes. If not exactly on the same grounds as Platonism, I must vehemently disagree.

He described the physical world as "mathematical," and conforming to an order which is "omnipotent, omnipresent, and omniscient as can be demonstrated by a few quantum experiments."^[2] Yet to thusly imbue mathematical abstractions with anthropomorphic qualities is at best highly misleading. While we may sometimes decide to engage in such an exercise by constructing creative illustrations in order to aid human understanding (e.g. the concept of "happy" atoms in chemistry), we must never remove those models from proper context, nor misunderstand them to literally represent actual processes. Molecules do not really feel joy, and math is not an intelligent agent.

If we crop the argument somewhat, supposing our mathematical universe is unexpected apart from the design of a deity, on what do we justify even that more modest contention? One might argue that, without God, we have no reason to believe math will accurately describe the behavior of matter. Yet this constitutes evidence for God only if it is the sort of being who wishes math to model that behavior. Furthermore, it ignores the fact that we require no expectation of efficacy in order to hold to naturalistic assumptions. For an ordered, material world, free from supernatural influences is a perfectly consistent hypothesis, requiring no reconciliation through the invocation of God.

Even careful not to commit such errors, we might yet feel inclined to treat physical order as something quite special, and in need of a deeper explanation. Here too I must urge caution. Why is order so unusual or unexpected? One might answer that disorder is the natural state of physical systems. Yet this sort of entropic disorder is not at all similar to that so often postulated by the apologist, which supposedly stands in contrast to the mathematical order of the universe we occupy. Indeed, entropic disorder is itself described by its own family of equations,^[3] and thus is among the very phenomena which theists prefer to explain through divine will.

Provided we understand all this, I have no objection should we wish to seek an explanation regardless, and in fact I support any such pursuit of knowledge. If we have independent justification for belief in the existence of God, then we may perhaps incorporate that into an account of metaphysical order. If not, then we are nevertheless welcome to pursue God as an open hypothesis, developing possible leads which we can empirically investigate. Yet we obtain no license to advocate an unsupported explanation simply by our desire to avoid facing the unknown. I certainly look forward to that day, should it come, in which we are able to satisfy our curiosity through evidence and reason. Until then, we must content ourselves with the beauty of mystery.

Footnotes:

[1] Wigner, Eugene. "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960). New York: John Wiley and Sons, Inc. Link to article.

[2] The fellow in question I met on William Lane Craig's message board, and goes by the name harvey1. His argument, from which my quotations are drawn, can be found online, here.

[3] For example, one entropy equation defines dS=(δQ/T)_{int rev}, where dS and δQ are entropy and heat, respectively, expressed in differential form, T is a temperature variable, and "int rev" denotes an internally reversible process. Cf. Çengel, Yunus A., and Michael A. Boles. Thermodynamics, An Engineering Approach, 5th ed., 2005, ISBN 9780073107684, p333.

Richard Swinburne, and the Chalcedonian Divinity of Jesus

2009-09-06T19:11:00.001-05:00

According to amazon.com, it was 2003 Feb 20 when the venerable Christian philosopher Richard Swinburne published his book, The Resurrection of God Incarnate (hereafter simply Resurrection). Swinburne, 74 years old as of today (2009 Sep 06), holds an Emeritus professorship at Oxford University, and has spent his academic career arguing for the existence of the Christian God, among other philosophical pursuits. I borrowed Resurrection from my own university library over the summer (of 2009), and acquainted myself with Swinburne's formalized thesis therein.

In the book, Swinburne suggests to the reader four particular probability values. If we accept his choices, then we can plug them into a statistical equation called Bayes' theorem to show that the probability Jesus was God incarnate is about 97%.

This is quite a claim. If we accept probability theory--and most of us do accept it, for good reason--then we are invited to take the single question of Jesus' divinity, and parse it out into four separate issues which can be tied together by Bayes' theorem.

So, what exactly are the four ingredients in this mathematical recipe? First, Swinburne suggests that the probability that God exists, given the evidence from natural theology, is about 50% (p211). Second, he gives possible reasons for thinking that the probability of God choosing to become incarnate, should He actually exist, also approaches 50%. Thirdly, he contends that out of all the religious figures in history, only Jesus Christ is accompanied by a certain threshold of evidence indicating that he might be an incarnation of God; if God really did become incarnate, then Swinburne argues that the probability of exactly one human being satisfying this requirement is a "fairly low" 10% (p212). Fourth, and finally, he tells us that, assuming that God either did not become incarnate or does not exist at all, the probability that some prophet in history would satisfy the evidentiary requirements of the strength which Jesus allegedly satisfied is a distant 0.1% (p213).

Swinburne proceeds to take these four probability values and plug them into Bayes' theorem, ultimately producing a probability value of 97% that Jesus was God incarnate (p214). So goes his unifying argument.

As a fourth-year math major, myself, I can verify that Swinburne's use of Bayes' theorem is, strictly speaking, logically valid. If we accept Swinburne's four suggested probability values, along with a few relatively uncontroversial historical conclusions, then they do indeed show that there is a 97% probability Jesus was God incarnate. So, the spotlight shifts to the four values themselves. Are they accurate?

In selecting an appropriate probability that God exists given the evidence from "natural theology," Swinburne settled on the figure of 50%. Natural theology, for those who may not know, involves philosophical evidence such as the cosmological and teleological arguments for the existence of God. Apparently, Swinburne believes these are convincing enough to bring the otherwise distant probability of God's existence to that of a fair coin toss.

I find this somewhat strange. I get the impression that he believes the actual probability of God's existence given natural theology nears 100%, but he has reduced this value to 50% in order to avoid criticism from those who might not agree with his assessment. Yet why should anyone compromise on the results of these arguments? If at least one of them is acceptable, then the probability that God exists surely exceeds 50%. Conversely, if they are all dubious, then they have little or no significance to the question of God's existence or nonexistence. Which arguments for the existence of God does he suppose have sliding scales of success, whereby they can function just well enough to raise the probability of the existence of God to his preferred assignment?

I for one reject those natural theological arguments, of which I have encountered many. For example, I remain thoroughly unconvinced that God can be defined into existence, as the ontological argument attempts to do. Nor do I believe for a second that we can use our everyday intuition to accurately guess truths regarding causality and the big bang, as the cosmological argument often requires. For me, the probability that God exists after we consider natural theology is exactly the same as whatever it was before we did so.

In the second chapter of Resurrection, Swinburne relates an apparently novel argument, the conception of which may have served as the inspiration for the overall approach. Under the assumption that God exists, he claims a number of reasons, for example supplying atonement for moral infractions, which in good Christian form Swinburne calls "sin" (p38), that God has for choosing to take on human form. This he calls a "Chalcedonian" incarnation (p51), after the Council of Chalcedon by the Roman Catholic Church in AD 451. In his own words: "...his [God's] incarnation could not involve his ceasing to be divine. It must, rather, involve God taking on additionally a human body and a human nature understood as a human way of thinking and acting" (p51).

Swinburne clearly has orthodox Christian doctrine in mind when discussing the possibility that some God might choose to become incarnate in a human vessel. So, if you have problems with evangelical theology, then you may not find Swinburne's argument regarding the Chalcedonian incarnation all that convincing. Even for people like me, who acknowledge the coherency of such theology, we need some good reasons to suppose that God, if he exists, actually agrees. Otherwise Swinburne's claim that there is a 50% chance God would choose to take human form will ring hollow.

We may also ask, as Swinburne did, what is the probability that, if God did become incarnate, we should discover some particular strength of historical evidence to that effect? Swinburne apparently wished to err on the side of caution, choosing an artificially (in his opinion) low value. But is it really so low? Does a reasonable spectrum of probabilities extend below his 10% suggestion? In my opinion, a value close to 1% seems just as valid. Perhaps we could go even lower.

I regard the fourth probability value as the most wildly speculative of them all. Here we are to assess the probability that some unnamed prophet might satisfy the relevant evidentiary requirements of Jesus, despite the assumption that God chose not to take human form. How can we possibly hope to achieve accuracy with such an unintuitive question? Swinburne argues that it would be "immensely unlikely" to think God would "permit" a historical figure to uniquely satisfy evidentiary requirements similar to Jesus (p213), but of course I disagree. Moreover, since I deem the probability that God does not exist as rather high, I would be most concerned with that scenario. What, then, is an appropriate value, if not 0.1%? From my perspective, 10% seems incredibly more reasonable, although of course any value assigned to such an obscure variable will be necessarily dubious.

Suppose, now, that we alter some of the values in Swinburne's equation. Namely, let's say we agree that arguments from natural theology are consistently unsound. So, where Swinburne chose 50%, we might instead assign the probability of God's existence given natural theology a value of only 1%. In that case, the probability that Jesus was God incarnate drops from the 97% value Swinburne gave to a somewhat low 33%.

Suppose further that we reject Swinburne's 0.1% probability that a threshold of evidence exemplified by Jesus mistakenly points to the Chalcedonian divinity of some prophet in history (even Jesus himself), in favor of a more generous 10% value. Then the probability of Jesus being God incarnate drops from 33% to a dramatically lower 0.5%.

If we wished, we could adjust each of the remaining two input values similarly, to push the final probability value lower still. However, I will leave that exercise to my readers, if they are sufficiently interested to track down a copy of Resurrection and learn the formal framework of its central argument.

The aim of Swinburne's book is to use historical evidence and philosophical analysis to make a case that Jesus Christ really was God incarnate. The idea behind this approach is that one does not require religious faith to accept Christianity. Instead we deal only with historical evidence in the natural world, analyzed in light of general philosophical concepts. Similar approaches have quite popular in modern apologetic circles. Apologists Gary Habermas, William Lane Craig and Lydia McGrew, for example, all make arguments from historical evidence that Jesus' body was reanimated after death. Just like Swinburne, they wish to address religious questions with primarily secular tools.

While I laud their efforts, I invariably find them insufficient. Resurrection constitutes yet another albeit inventive attempt in an ostensibly doomed cause.

the voting paradox and god-belief

2009-08-23T09:00:00.000-05:00

One of the objections I have encountered to my unbelief is that religion, properly deployed, provides a basis for morality, which in turn is quite helpful to society. These objectors argue that if God doesn't exist, then god-belief is highly unique in that it is the only known false belief which is actually beneficial on a large scale. Therefore, they continue, god-belief is made more rational than it would otherwise be.

Two immediate problems stand out in this argument. First of all, it's not at all clear that people need a religious basis for morality. In fact, many unbelievers making their way in the world are living proof that, at the very least, not everyone requires such a basis. Secondly, the argument is invalid. Even if god-belief is unique as contended, that in no way suggests that some god exists.

Although I might be willing to grant for the sake of argument that religion is beneficial as described by Christians and other theists, I am quite satisfied to point out the invalidity of the argument. Indeed, religions are unique in many respects, both individually and as a category; yet it simply does not follow from observing that, say, Buddhism is highly unique, that therefore Buddhist beliefs are true. Still, god-believers often demand exemplary arguments. So, wouldn't it be great to respond by citing a demonstrably false belief which improves society in one way or another? If we can find such an example, we shall have yet a third objection to the afore-mentioned argument.

Watching a taped economics lecture a few days ago, I was reminded that self-interests often interfere with healthy social operation, and invite suppression from various agencies. While in most cases this takes the form of offering real incentives, thus creating a sort of artificial, indirect self-interest for individuals, at least one special case is addressed by false education.

That case is the voting paradox. In a democratic government, where officials are elected by citizens, and for districts in which voters number in the thousands or more, each individual voter has close to a zero probability of affecting the outcome of the election. So, unless he has some additional incentive to vote, a rational citizen will not expend his precious time and effort for an essentially non-existent payoff.

We should note that in many cases people do have additional incentives. For example, I consider it a fascinating experience to vote, and to know that I am just one tiny cog in an immense machine. So in my case, I just happen to enjoy the process. Yet I don't think everyone shares my abstract perspective. In most cases, I should think, people vote because they believe their vote actually makes a difference, when it clearly does not.

Numerous educational programs encourage this false belief. In October 2007, for example, Roy Hanson, Jr., the director of Private & Home Educators of California, an organization providing informational assistance to parents homeschooling their children, wrote, "Ignoring our responsibility to vote is, by default, to vote for tyranny" (source). His sentiments are shared by many across all kinds of demographics. Consider also Citizen Change's infamous "vote or die" slogan from the 2004 United States Presidential election, which falsely cautioned that declining to vote was fundamentally dangerous.

Those false messages, however, if believed, result in positive results for society. Democracy really does work better with higher voter turnout. In short, this is a great example of a false belief which benefits society, just as religion is claimed to do uniquely.

Any time we have a conflict between individual interests and social interests, false beliefs may potentially play some helpful role. However, they do not come without cost. For, on some level, we also value honesty, and false beliefs, no matter how helpful in other respects, will always conflict with truth.