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.