tag:blogger.com,1999:blog-48565961941068205492024-02-20T19:10:24.526-06:00Ben Wallis’s counter-apologetics blogA blog for philosophy, maths, and religionBen Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.comBlogger55125tag:blogger.com,1999:blog-4856596194106820549.post-67189458206493099352020-08-15T08:48:00.006-05:002020-08-15T08:48:58.710-05:00podcast - The Empty Tomb<p> In this podcast, I discuss the historicity of the empty tomb narratives, in the context of Christian apologetics. Link below.</p><p><a href="https://ia801500.us.archive.org/33/items/2020-07-13-podcast-empty-tomb-lib_202007/2020-07-13-podcast-empty-tomb-LIB.mp3">https://ia801500.us.archive.org/33/items/2020-07-13-podcast-empty-tomb-lib_202007/2020-07-13-podcast-empty-tomb-LIB.mp3</a></p>Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com1tag:blogger.com,1999:blog-4856596194106820549.post-14549076728576649232020-05-28T09:51:00.000-05:002020-05-28T09:51:13.473-05:00podcast 5/27/2020 - Resurrection appearances<br /><a href="https://archive.org/download/benwallis_podcast_2020-05-27_LIB/benwallis_podcast_2020-05-27_LIB.mp3">https://archive.org/download/benwallis_podcast_2020-05-27_LIB/benwallis_podcast_2020-05-27_LIB.mp3</a><br />
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<span style="background-color: white; color: #1a1a1b; font-family: "Noto Sans", Arial, sans-serif; font-size: 14px;">I discuss why I don't believe in the vision or hallucination hypotheses to explain the reports of post-mortem appearances of Jesus to his disciples.</span>Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-22218223802427307742020-05-20T13:23:00.000-05:002020-05-20T13:23:14.418-05:00podcast 5/20/2020 - The Kalam cosmological argument, part IIn this podcast, I discuss my criticisms of Craig's defenses for the Kalam's first premise.<br />
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<a href="https://archive.org/download/podcast2020-05-20-LIB/podcast2020-05-20-LIB.mp3">https://archive.org/download/podcast2020-05-20-LIB/podcast2020-05-20-LIB.mp3</a>Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-23930028306319772092020-05-07T13:51:00.003-05:002020-05-09T06:49:35.412-05:00Plantinga's "victorious" modal ontological argumentWith fresh eyes, I revisited Plantinga's "victorious" modal ontological argument (hereafter, VMOA) yesterday. Some summaries of the argument, including the one at IEP, has Plantinga <i>defining</i> the term 'maximally great being' (hereafter, MGB) to be such that if it's possible an MGB exists, then an MGB <i>actually</i> exists, and has the properties of omnipotence, omniscience, and moral perfection. On the IEP's account, Plantinga's argument really only has one premise, and the conclusion follows immediately.<br />
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It turns out that IEP's summary is incorrect. Plantinga's argument has a number of different premises, and he doesn't ever explicitly define anything. His approach, instead, is to let the reader supply their own intuitive understandings of a given concept. Sometimes he'll help this process along by giving examples, or brief conceptual sketches. In one case (as we shall see momentarily) he actually gives an analysis---although that's still not quite a definition.<br />
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For his VMOA, he introduces the concepts of 'greatness' and 'excellence'. As usual, Plantinga declines to give explicit definitions, and instead expects us to have a kind of intuitive understanding of greatness. And I suppose we do, although I'm not at all certain our intuitions here are sufficiently refined to be pressed into service in the way that he wants. At any rate, he does have this to say about greatness and excellence:<br />
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<i>"We might make a distinction here between greatness and excellence; we might say that the excellence of a being in a given world W depends only upon its (non world-indexed) properties in W, while its greatness in W depends not merely upon its excellence in W, but also upon its excellence in other worlds."</i><br />
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I think I can follow him here. For instance, a person's greatness lies in part in his abilities, but then it also lies in part in the actions he actually performs. I suppose it's vaguely intuitive to isolate, so to speak, the second component as a separate concept. And I don't mind temporarily re-purposing the word 'excellence' to refer to it.<br />
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Before turning to Plantinga's VMOA, we also need the concept of an 'essence'. Roughly, he takes this to be a property, or group of properties, that an object has essentially, and that is unique to that object.<br />
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Now Plantinga states his argument:<br />
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<b>(1)</b> <i>The property 'has maximal greatness' entails the property 'has maximal excellence in every possible world'.</i><br />
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<b>(2)</b> <i>'Maximal excellence' entails omniscience, omnipotence, and moral perfection.</i><br />
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<b>(3)</b> <i>'Maximal greatness' is possibly exemplified.</i><br />
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<b>(4)</b> <i>For any property P, if P is possibly exemplified, then there is a world W and an essence E such that E is exemplified [by an object existing] in W, and E entails 'has P in W'.</i><br />
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<b>(5)</b> <i>Every world-indexed property of an object is entailed by its essence.</i><br />
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<b>(6)</b> <i>A being [or object] has a property in a world W only if it exists in that world.</i><br />
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Therefore, Plantinga claims:<br />
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<b>(7) </b> <i>There actually exists a being that is omniscient, omnipotent, and morally perfect; and that exists and has these properties in every possible world.</i><br />
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In reasoning from premises (1)-(6) to the conclusion (7), Plantinga considers a possible world W and a proposition p, and decides that, were W actual, p would be necessarily true. He then concludes that p is <i>in fact</i> necessarily true. These moves seem relatively safe, but they require two additional, unstated premises:<div><br /></div><div><b>(8)</b> <i>For any proposition p and possible world W, if p is true in W, then, were W actual, p would be true.<br /></i>
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<b>(9)</b> <i>For any proposition p, if there's a possible world W such that, were W actual, p would be necessarily true, then p is in fact necessarily true.</i><br />
<br />Is there a way to avoid these premises? Let's walk through Plantinga's reasoning and see if we can adjust it to make (8) and (9) unnecessary.</div><div><br /></div><div>From (3) and (4), there is a world W* and an essence E* such that E* is exemplified by an object existing in W*, and such that E* entails 'has maximal greatness in W*'. At this point, Plantinga invokes (8), and then a little later he invokes (9), too. Can we avoid it?</div><div><br /></div><div>By definition of 'essence,' there is an object x* that has essence E*. Now, x* therefore has the property 'has maximal greatness in W*'. This we shall take to mean simply that, at W*, the object x* has the property of 'maximal greatness'. Does that interpretation count as an additional premise? Let us suppose not. By (1), the property 'maximal greatness' entails 'has maximal excellence in every possible world', which again we shall simply take to mean that, for any world W, x* has 'maximal excellence' at W. In particular, x* has maximal excellence at the actual world. By (6), x* exists in the actual world, which is just to say that x* exists simpliciter. By (2), x* has the properties of omniscience, omnipotence, and moral perfection in every possible world.</div><div><br /></div><div>So, not only have we avoided (8) and (9), we've also avoided (5). But this comes at the cost of imposing a certain interpretation on the world-indexed properties mentioned above.</div>Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-10180121984433449892020-05-02T12:54:00.005-05:002020-05-02T14:14:22.835-05:00An invalid contingency argument on SEPBruce Reichenbach wrote the SEP article on cosmological arguments. SEP articles are, I believe, peer-reviewed, and so we shouldn't expect them to contain invalid arguments. This one does, however. Here it is:<br />
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<b>(1)</b> <i>A contingent being (a being such that if it exists, it could have not-existed or could cease to exist) exists.</i><br />
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<b>(2)</b> <i>This contingent being has a cause of or explanation for its existence.</i><br />
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<b>(3)</b> <i>The cause of or explanation for its existence is something other than the contingent being itself.</i><br />
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<b>(4)</b> <i>What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.</i><br />
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<b>(5)</b> <i>Contingent beings alone cannot provide a completely adequate causal account or explanation for the existence of a contingent being.</i><br />
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<b>(6)</b> <i>Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.</i><br />
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<b>(7)</b> <i>Therefore, a necessary being (a being such that if it exists, it cannot not-exist) exists.</i><br />
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<b>(8)</b> <i>The universe is contingent.</i><br />
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<b>(9)</b> <i>Therefore, the necessary being is something other than the universe.</i><br />
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What makes this argument invalid is pretty easy to see: In step (5), there is talk of a "completely adequate" account or explanation, but never in previous steps. So it can't be used to infer (6) as intended. This can be easily fixed by changing step (2), but I'm still alarmed by the fact that a peer-reviewed article on SEP is invalid.<br />
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There are a couple of other anomalies which also trouble me. For instance, step (3) is actually superfluous to the argument. And step (4) is pretty close to being superfluous too, not required so long as (5) is suitably adjusted. Finally, steps (1) and (8) could be combined for brevity.<br />
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The resulting argument would go something like this:<br />
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<b>(10)</b> <i>The universe exists and is a contingent being.</i> [Replaces (1) and (8).]<br />
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<b>(11)</b> <i> Its existence has a completely adequate </i><i>explanation or </i><i>causal account. </i> [Replaces (2).]<br />
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<b>(12)</b> <i>An </i><i>explanation or</i><i> causal account of the existence of a contingent being, such that all the existing beings involved are likewise contingent, isn't completely adequate. </i> [Replaces (5).]<br />
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<b>(13)</b> <i>Therefore, a necessary being, which is not itself the universe, exists, and is involved in a completely adequate </i><i>explanation or</i><i> causal account of the universe's existence.</i> [Replaces (6), (7), and (9).]<br />
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The above argument has the virtues of being shorter, clearer, and---most importantly---<i>valid</i>.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-64777686858611576302020-04-27T05:37:00.002-05:002020-04-27T05:37:32.305-05:00Podcast 4/26/2020 - Hume, Craig, and Miracles<a href="https://archive.org/download/podcast2020-04-26/podcast2020-04-26.mp3">Ben Wallis podcast 4/26/2020 - Hume, Craig, and Miracles</a>
<br><br>In this podcast, I discuss a common criticism of Hume.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-76789840111935008192020-04-22T09:01:00.001-05:002020-04-24T08:26:51.212-05:00Podcast 3/30/2020 - A skeptic's response to the Kalam cosmological argument<a href="https://archive.org/download/benwallis-podcast-2020-03-30/benwallis-podcast-2020-03-30.mp3">Ben Wallis podcast 3/30/2020 - A skeptic's response to the Kalam cosmological argument</a>
<br><br>In this podcast, I discuss how I think skeptics should respond to the Kalam Cosmological Argument.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-55691677247413240312020-03-08T11:06:00.000-05:002020-04-24T08:25:58.001-05:00Tim Stratton's freethinking argument against naturalismLast week I started reading about free will. That's right---last <i>week</i>! I've been studying philosophy in my spare time for the last fifteen years; why did it take me so long to finally broach what is considered one of its most fundamentally important topics?
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Well first of all, it's perhaps not as important as it might seem; for instance the late Buddhist philosopher Michael Dorfman once called the free will problem "much ado about nothing." Meanwhile, none of the discussion about free will whose snippets I encountered seemed very intriguing to myself, whose chief areas of interest lie in epistemology, mind, and the nonexistence of God. Finally, the very concept of free will just seemed unnecessarily obscurist, whereas I desire clarity. So, if I could just get by without ever having to discuss free will, that would be extremely gratifying.
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So, what changed? Well, to put it simply, I encountered Tim Stratton's "freethinking argument against naturalism," whose central premises deal with libertarian free will (hereafter, LFW). Stratton is an ex-pastor and current adjunct faculty teaching Christian Apologetics at Nebraska Christian College. He runs an online ministry which seems to be focused in large part if not entirely on Christian apologetics, and which he advertises as an affiliate of William Lane Craig's ministry <i>Reasonable Faith</i>. Although not a philosopher himself, he reports to be nearing completion of a Ph.D. in analytic theology from North-West University, a Christian school in South Africa which apparently offers such correspondence degrees.
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Stratton's argument runs as follows:
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<b>(1)</b> <i>If naturalism is true, the immaterial human soul does not exist.</i>
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<b>(2)</b> <i>If the soul does not exist, LFW does not exist.</i>
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<b>(3)</b> <i>If LFW does not exist, rationality and knowledge do not exist.</i>
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<b>(4)</b> <i>Rationality and knowledge exist.</i> Therefore,
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<b>(5)</b> <i>LFW exists.</i> Therefore,
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<b>(6)</b> <i>The soul exists.</i> Therefore,
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<b>(7)</b> <i>Naturalism is false.</i>
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<b>(8)</b> <i>The best explanation for the existence of the soul is God.</i>
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Personally I already affirm the existence of an immaterial mind, which doesn't seem at all at odds with naturalism. But I think by "the soul" Stratton means something more robust than just a mind---namely, something capable of existing independently of the physical world, and influencing rather than being influenced by the brain and other physical systems. Such a view, of course, has no basis in evidence, and in fact there seems to be a good deal of empirical evidence to contradict it. So, arguing against (1) seems to be a nonstarter.
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Premise (4) also seems fairly certain. As long as we don't import too much baggage with our notions of knowledge and rationality, it would seem obvious that we really do have the capacity for such things.
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That leaves us with denying that (2) and (3) can both be true; but which one is the most likely candidate? (They can't <i>both</i> be false, at least not on the material conditional interpretation.) Since we know the soul doesn't exist, and yet rationality and knowledge do exist, the only way to decide between (2) and (3) is to figure out whether LFW exists.
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LFW is just the conjunction of two simply-stated positions: human beings have free will, and free will is incompatible with determinism. Not surprisingly, there doesn't seem to be anything approaching a consensus on either one of those claims. So, here I am, one week into my reading, ready to make some pronouncements on a subject whose discussion goes back at least to Plato, and yet which has not been resolved more than two millennia later? I had better be very cautious!
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My first surprise was to learn that free will isn't about the will <i>per se</i>, at least not directly; rather, it's about our capacity for choosing and decision-making. So, the term "free will" strikes me as something of a misnomer; perhaps "freedom of choice" is a more apt label.
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My second surprise was to find that free will is supposed to be something distinguishing human beings from animals, or at least the lower animals. But surely animals are capable of choices and even rational deliberation. It's almost comical when, for instance, my cat stares at the bed for a full minute or more, unable to make up her mind whether to jump up onto it, or to go do something else. Is she really not deliberating in those instances? Is she just distracted and staring blankly while daydreaming?
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Some birds exhibit exceptional problem-solving abilities. For example, there's a TED talk available online which shows a video of a crow bending a wire into a hook, which she then uses to obtain food which was otherwise out of reach; her solution was spontaneous, not taught to her by the researchers. And of course it goes without saying that chimpanzees are able to solve problems too. In one infamous video clip, a chimp obtains a peanut from the bottom of a narrow glass by urinating into it so that it floats to the top---and I'm quite sure that idea was never suggested to the chimp by the researchers!
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Are these cases of problem-solving in the animal kingdom not the results of creative rational processes and deliberation? Are they really just some kind of blind and unconscious responses to stimuli? Surely not. And while it may take my cat a long time to decide whether to hop on the bed due to her comparatively primitive consciousness---that's what makes it kinda funny, after all---surely she is in fact deliberating, right? I mean, I can't <i>prove</i> that she's deliberating, but it certainly <i>seems</i> that's what's going on.
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So, whatever the kind of freedom of choice is imagined for proponents of LFW, it can't be mere deliberation between alternatives.
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Nevertheless, humans seem to be reflective about their choices in a way that nonhuman animals aren't. For instance, we have what Harry Frankfurt calls second-order volitions. Alan may want to eat donuts for breakfast. Recognizing healthy eating to be better for him in the long run, Alan has a second-order desire that the first-order desire for donuts should fail to move him. He may end up eating the donut after all, but if so then it's not an exercise in free will. After all, his <i>true</i> desire is to resist eating the donut, but he cannot resist; so he lacks freedom of choice in this instance, according to Frankfurt. If on the other hand his second-order volition wins out, then Alan has chosen freely by resisting the temptation for donuts.
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Of course, this is just one philosopher's (Frankfurt) stab at distinguishing the human capacity for choice from that of nonhumans; no doubt other philosophers would disagree. The point is, whatever freedom we have in mind for our choices, to the extent we want to distinguish it from the freedom had by nonhuman animals, it must be more than just rational deliberation, of which many species are evidently quite capable---or at least not obviously <i>in</i>capable.
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The other prong of LFW is to deny that free will is compatible with determinism, and indeed there does seem to be something initially plausible about that suggestion. However this initial plausibility quickly erodes when considering the alternatives. In particular, it's also initially intuitive that the only alternative to determinism is an element of randomness; and yet randomness seems just as anathema to freedom as determinism.
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The problem here is that the move from indeterminism to randomness isn't quite as straightforward as it first appears---perhaps there is a middle road. And that's exactly what libertarians argue.
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The standard move for libertarians is to invoke "agent causation" as something distinct from "event causation." So, the mental events might be undetermined by laws of nature, but they're still caused by the agent himself for reasons had by said agent. And if an agent acts rationally on the basis of reasons, that's not randomness.
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But isn't it? John Thorp, himself a libertarian, outlines the obvious concern:
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<i>"Agent causality was to save us from the embarrassment of event causality; but it is a kind of fool's gold: agents, on analysis, turn out to be just a cluster of events and states... agent causality turns out to be just a special case of event causality after all."</i>
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His answer is to claim that the causal connection between neurology and mental events is sometimes reversed:
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<i>"It is plausible to suggest that when, for example, we walk in the country and allow our thoughts free reign, it is the neurology beneath them that, according to its own laws, directs their course. On the other hand when we force our thought onto some track...the stream of mental events is directed by some mental (logical) laws, and the mental descriptive level is hegemonic: here the mental descriptions drag the neural descriptions about according to the laws of sequence which belong to the mental..."</i>
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Aside from the fact that we seem to have no good evidence for this reversal of causation (not to mention some very good empirical evidence against it), even if it were true it seems to be irrelevant to the randomness concern. One kind of determinism (whether or not it's the only kind) is that of <i>order</i>. That is to say, if events occur in the context of a sufficiently ordered system, then they will be deterministic. If true (and it certainly does seem to be true) then it means libertarians are committed to denying that the mental events such as our choices occur in a sufficiently ordered context. But that's just to say that the context must have a significant element of <i>disorder</i>. But why? How does disorder make us any more free than orderliness would allow? If agent causation is to answer this question, it can only be because it's impossible without disorder. But why think that?
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I think it's appropriate to call that kind of disorder <i>randomness</i>, even if it's being caused by the choices of a rational agent armed with reasons. And it seems far more implausible to me that such randomness should be some essential ingredient to our human capacity for deliberation, choice, self-reflection, and so on. Then again, I've only been thinking about it for a week, so who knows? But as of the present time at least, that's what my intuitions tell me.
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In light of all this, it looks to me like LFW isn't very promising. However, the compatibilist view has many proponents, including Frankfurt for example. If free will is really just about the ability for second-order desires to override first-order ones, then perhaps compatibilism is workable. But is that really the kind of freedom imagined when we throw around the term "free will"?
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Presumably not. Sam Harris once sarcastically summarized Frankfurt's position: <i>"A puppet is free as long as he loves his strings."</i> Sarcasm aside though, his point is well taken. Regardless of whether determinism is true (Harris thinks it is, but that's not necessary to make his point), it's hard to see how we could possibly be responsible for who we are. This point is expanded by Galen Strawson in his so-called "basic argument" against moral responsibility (as summarized by Gregg Caruso):
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<i>"Nothing can be causa sui---nothing can be the cause of itself. [But] in order to be truly or ultimately morally responsible for one's actions one would have to be causa sui, at least in certain crucial mental respects."</i>
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Strawson here is technically arguing against moral responsibility, but he might as well be speaking of free will.
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With all of this in mind, let's return to Stratton's argument. How does he defend (2) and (3)?
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Well, his defense of (2) is almost self-consciously nonexistent. He even admits outright, <i>"This premise actually does not need much defending as far as I am concerned"</i>. And he feels comfortable leaving (2) undefended because he thinks certain atheists---namely, Harris, Richard Dawkins, and Stephen Hawking---have already made the case for him. Harris and Hawking are both incompatibilists and determinists who therefore believe free will is an illusion; and maybe Dawkins believes the same. Stratton gives quotations from all three to this effect. But finding three naturalists who deny the existence of LFW doesn't constitute a defense of (2).
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For example, note that Thorp's position, and indeterministic agent causation in general, are completely consistent with naturalism and the nonexistence of a supernatural soul. Instead, all it requires is that mental events can sometimes cause physical events rather than just vice versa. And while there seems to be a great deal of empirical evidence against Thorp's view, that has nothing to do with whether or not a supernatural soul exists. So, while I'm inclined to believe that (2) is true, it's not for the reasons Stratton gives. And it's only an inclination anyway, not something I'm especially committed to right now.
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Stratton's defense of (3) is summed up in the following quotation:
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<i>"The process of rationality leading to warranted or justified true belief (knowledge) entails the properties of being able to think of and about competing hypotheses, deliberate between them, and the ability to infer and affirm the best explanation via the laws of logic. Therefore, a rational entity must also possess at least two other attributes: intentionality and libertarian free will."</i>
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But we have already seen from the examples of nonhuman animals that this is not the case. Cats may not be very smart, but they're still quite capable of knowledge, deliberation, and rational choice. Crows and chimpanzees are even more obviously rational, as evidenced by their strikingly creative problem-solving abilities.
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So on one hand we have LFW looking very implausible, while on the other hand, knowledge and rationality apart from free will (whether libertarian or not) looks to be not only possible but actually realized in nonhuman animals. We had previously decided that, on a plain reading of Stratton's argument, either (2) or (3) must be false; and these latest considerations make (3) the most likely culprit.
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Even so, we shouldn't rule out (1) and (4) as being problematic. It could be that by "soul" Stratton means nothing more than an immaterial mind; on that reading, (1) is plainly false. Additionally, Stratton might have an idiosyncratic view of rationality and knowledge, which might leave (4) in doubt too, as he intends it anyway. With Christian apologists, you just never can tell.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-17681960696590026652019-12-24T16:45:00.001-06:002019-12-25T13:52:28.666-06:00Robin Collins' argument in Blackwell is invalid on two countsI want to post this more or less for reference, because even though it's just a simple observation, it has serious implications for the argument of Robin Collins. Usually, when a professional philosopher publishes an argument in a peer-reviewed journal or book, certain things are taken for granted, like the validity of any deductive arguments given in it. So it's a pretty straightforward matter to make sure that one's central argument, if it's intended to be deductively valid, is *in fact* deductively valid. But Robin Collins' argument is not.
Here's an excerpt from the book:<br />
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<i>"(1) Given the fine-tuning evidence, LPU is very, very epistemically unlikely under NSU: that is, P(LPU|NSU & k') << 1, where k' represents some appropriately chosen background information, and << represents much, much less than (thus making P(LPU|NSU & k') close to zero).</i><br />
<i>(2) Given the fine-tuning evidence, LPU is not unlikely under T: that is, ~P(LPU|T & k') << 1.</i><br />
<i>(3) T was advocated prior to the fine-tuning evidence (and has independent motivation).</i><br />
<i>(4) Therefore, by the restricted version of the Likelihood Principle, LPU strongly supports T over NSU."</i><br />
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<a name='more'></a> Now, by the "Likelihood Principle" (hereafter, LP) he means this (again, quoting directly):<br />
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<i>"Let h1 and h2 be two competing hypotheses. According to the Likelihood Principle, an observation e counts as evidence in favor of hypothesis h1 over h2 if the observation is more probable under h1 than h2. Put symbolically, e counts in favor of h1 over h2 if P(e|h1) > P(e|h2), where P(e|h1) and P(e|h2) represent the conditional probability of e on h1 and h2, respectively. Moreover, the degree to which the evidence counts in favor of one hypothesis over another is proportional to the degree to which e is more probable under h1 than h2; specifically, it is proportional to P(e|h1)/P(e|h2)."</i><br />
<br />
He goes on to hedge this principle, thusly:<br />
<br />
<i>"The restricted version limits the applicability of the Likelihood Principle to cases in which the hypothesis being confirmed is non-ad hoc. A sufficient condition for a hypothesis being non-ad hoc (in the sense used here) is that there are independent motivations for believing the hypothesis apart from the confirming data e, or for the hypothesis to have been widely advocated prior to the confirming evidence."</i><br />
<br />
This argument is invalid on two counts.<br />
<br />
COUNT #1: Collin mixes up the roles of LPU and the fine-tuning evidence (call it FT) in his application of the restricted likelihood principle (call it RLP). Indeed, we read in premise (3) that it's FT from which T has independent motivation, where in RLP it's e from which h1 has independent motivation. So in order to apply RLP we need e=FT and h1=T. However, FT is not mentioned anywhere else in the argument. Instead, he concludes that LPU, not e, strongly supports T over NSU. That is to say, in the conclusion (4) he wants e=LPU, h1=T and h2=NSU. By mixing up the roles of LPU and FT in his argument, he leaves his conclusion as a nonsequitur.<br />
<br />
Luckily for Collins, the Likelihood Principle is true regardless of whether it is restricted or not. Indeed, it's just a consequence of Bayes' Theorem, together with some mild assumptions about the probabilities involved being nonzero. Recall that on Bayes' Theorem (with nonzero probabilities) we have<br />
<br />
P(h1|e) / P(h2|e) = [P(h1) / P(h2)] * [P(e|h1) / P(e|h2)].<br />
<br />
So the invalidity in count #1 has a more or less easy fix. Or at least it would, were it not for this next bit: <br />
<br />
COUNT #2: Unfortunately, the "strong support" in the conclusion (4) is not guaranteed by either LP or RLP. Instead, the strength of the evidence depends on the prior probabilities P(h1) and P(h2). Namely, if the prior probability P(T) of theism is too small relative to the other probabilities, then the evidence will be far too weak to matter. So, it's actually false that the strength of the evidence is proportional to the quantity [P(e|h1) / P(e|h2)], as Collins mistakenly claims, because the would-be constant of proportionality is actually the function [P(h1) / P(h2)].<br />
<br />
The invalidity in count #2 has no easy fix, and in fact it seems to doom the argument from the outset.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-43801899888011566572014-10-03T07:19:00.000-05:002014-10-03T07:19:20.702-05:00debate in Hickory Hills, IL (west suburb of Chicago), with Dr. Kirk MacGregor<p><b>When?</b> Friday, Oct 24, 7-9:30pm
<p><b>Where?</b> <a href="http://www.hickoryhillspres.org/" target="_blank">Hickory Hills Presbyterian Church</a>, 8426 W 95th St, Hickory Hills, IL 60457 (<a href="https://www.google.com/maps/place/8426+W+95th+St,+Illinois+and+Michigan+Canal,+Hickory+Hills,+IL+60457" target="_blank">map</a>)
<p><b>What?</b> The debate topic is: <i>Does God exist?</i>
<p><b>Who?</b> I will be debating <a href="http://www.kirkmacgregor.org/" target="_blank">Dr. Kirk MacGregor</a>.
<p><b>About the Debaters</b>
<p><i>Kirk MacGregor</i> (Ph.D. in religious studies, University of Iowa) teaches religion and philosophy at Carthage College and the College of DuPage. He is the Director of the Chicago Chapter of Reasonable Faith. His research has been published in the Harvard Theological Review and Philosophia Christi.
<p><i>Ben Wallis</i> (M.S. in pure mathematics, Northern Illinois University) teaches mathematics at Northern Illinois University and Kishwaukee College. With interests in philosophy of religion, he co-hosted the podcast Goodness Over God from 2011 to 2012. His research has been published in the Journal of Functional Analysis.
<p><a href="https://www.facebook.com/events/518713271598652" target="_blank">Debate website (facebook)</a>Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-63713448231187004272012-07-10T20:51:00.000-05:002012-07-13T15:24:02.864-05:00Sungyak Kim on faith and reasonSeminary student Sungyak Kim <a href="http://www.relevantmagazine.com/god/worldview/christianitys-new-f-word" target="_blank">has an unusual vision</a> of Christian apologetics. Quoting Soren Kierkegaard, he laments the existence of that apparently typical apologist who naively attempts to "deal with every accusation, every falsification, every unfair statement, and in this way is occupied early and late in counterattacking the attack." And who exactly does he have in mind, here? Well, it's hard to say exactly, but at the beginning of his piece he drops the names of William Lane Craig and Alvin Plantinga.
<p><a name='more'></a>I think it's clear that Craig and Plantinga are guilty of no such thing. But perhaps that was just Kim's attention-getting introduction. Before long he moves on to his real thesis: Christians should live by faith, without having to "surrender" to culturally-defined notions of rationality, reasonableness and justification.
<p>And yet surely that can't be right. Who wouldn't value rationality and reasonableness? Kim himself reminds us that Paul "reasoned" with the non-Christians of his day; and he also praises his presuppositionalist heroes Bahnsen and Van Til for being, according to Kim, "great Christian thinkers." Yet throughout his essay he makes constant jabs at the idea of respecting reason. So when he says things like, "Our faith in Christ has to be greater than our faith in wisdom and reason," it's hard to see what else he could mean but that we ought to discard reason whenever it happens to conflict with his favorite religious beliefs.
<p>He is free to do that, of course. Nobody is going to twist his arm or put a gun to his head to get him to see reason (although given his closing comments about "persecutions," perhaps that really is what he thinks will happen). But---call me crazy---it just seems like being reasonable is a worthwhile goal. One would think he would agree, Christian or not.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com2tag:blogger.com,1999:blog-4856596194106820549.post-72386092389531369122012-05-28T08:19:00.000-05:002012-07-13T11:04:04.104-05:00C-objectivity and Craig's moral argumentChristian philosopher William Lane Craig has developed and defended an increasingly popular forumlation of the moral argument for the existence of God:
<blockquote>(1) If God does not exist, objective moral values and duties do not exist.
<br>(2) Objective moral values and duties do exist.
<br>(3) Therefore, God exists. (<i>Reasonable Faith</i>, p172.)</blockquote>
His principal defense for premise (2) consists in pointing to our moral experience, where he thinks we apprehend the objectivity of morality. However I will argue that while there may be a semantic sense in which our moral experience does offer evidence for the objectivity of morality, nevertheless Craig has in mind a different, specialized sense of objectivity which involves the existence of a concrete exemplar, and which is unsupported by experience.
<p><a name='more'></a>Craig offers at least two defenses for premise (2), but here we shall only focus on one of them. According to Craig:
<blockquote>I take it that in moral experience we do apprehend a realm of objective moral values and duties, just as in sensory experience we apprehend a realm of objectively existing physical objects... Actions like rape, torture, child abuse, and brutality aren't just socially unacceptable behavior---they're moral abominations. By the same token, love, generosity, equality, and self-sacrifice are really good. People who fail to see this are just morally handicapped, and there is no reason to allow their impaired vision to call into question what we see clearly. (<i>Reasonable Faith</i>, pp179,81)</blockquote>
On the face of it, this appears quite plausible. It seems ludicrous to deny the objectivity of truths such as that, say, child abuse is morally wrong, or that love is morally good. The skeptic need not deny that we really do apprehend this objectivity of moral semantics. However, when Craig argues for the existence of "objective" moral values, he has something in mind other than the ordinary semantic objectivity we so often take for granted. He writes:
<blockquote>Our concern is with moral ontology, that is to say, the foundation in reality of moral values. Our concern is not with moral semantics, that is to say, the meaning of moral terms. (<a href="http://www.reasonablefaith.org/euthyphro-dilemma" target="_blank">ReasonableFaith.org Q&A #44, "Euthyphro Dilemma."</a>)</blockquote>
So we must carefully distinguish between moral semantics and Craig's notion of moral ontology if we are to evaluate his moral argument. Indeed, Craig seems not to challenge the notion that moral truths can be objective in a semantic sense apart from the existence of God. So for instance, if we have a semantic standard of goodness independent of God, then we can objectively evaluate thoughts, behaviors and so forth as being good or not against that standard. To be sure, this semantic objectivity is a different kind of objectivity than what Craig has in mind. Yet it is important to note that semantic objectivity really does stand independent of the existence of God. Even Craig seems to acknowledge this, as he continues:
<blockquote>The theist is quite ready to say that we have a clear understanding of moral vocabulary like "good," "evil," "right," and so on, without reference to God. Thus, it is informative to learn that "God is essentially good." (<a href="http://www.reasonablefaith.org/euthyphro-dilemma" target="_blank">ReasonableFaith.org Q&A #44, "Euthyphro Dilemma."</a>)</blockquote>
So even if God does not exist, moral language still has meaning, and hence moral statements can be objectively evaluated for truth or falsity against that meaning. So it really is the case, regardless of whether God exists, that sentences like "murder is wrong" and "love is good" can express objectively true statements, so long as we understand wrongness and goodness to be characterized by those semantics which are independent of God.
<p>The only catch is that this notion of objectivity is a semantic one, and Craig wants to talk about a different kind of objectivity. Let's call Craig's concept <i>C-objectivity</i> ("C" for Craig), to distinguish it from the semantic objectivity described above.
<p>So, just what is C-objectivity, then? Craig explains:
<blockquote>To say that something is objective is to say that it is independent of what people think or perceive. By contrast, to say that something is subjective is just to say that it is not objective; that is to say, it is dependent on what human persons think or perceive. So, for example, the distinction between being on Mars and not being on Mars is an objective distinction; a particular rock's being on Mars is in no way dependent upon our beliefs. By contrast, the distinction between "here" and "there" is not objective: whether a particular event at a certain spatial location occurs here or occurs there depends upon a person’s point of view. (<i>Reasonable Faith</i>, p173.)</blockquote>
Unfortunately, this is more confusing than helpful. For notice that even though the property of <i>being here</i> is said to be C-nonobjective, nevertheless it is objectively true (perhaps only in a semantic sense) that <i>I am sitting in my living room, and my cat is here too</i>. It really is the case that my cat <i>is here</i>, given what we mean by the term. Such statements are true independent of human values and opinions, yet Craig seems to want to deny that they are C-objectively true.
<p>To get a better handle on what we should take C-objectivity to be, I think the following quotation from Craig is instructive:
<blockquote>Just as a meter was once defined paradigmatically as the length of an iridium bar housed in the Bureau des Poids et des Mesures in Paris, so moral values are determined by the paradigm of God's holy and loving character. (Craig, "The Most Gruesome of Guests," <i>Is Goodness Without God
Enough: A Debate on Faith, Secularism, and Ethics</i>, pp169-70, as quoted in <a href="http://spot.colorado.edu/~morristo/DoesGodGround.pdf" target="_blank">Wes Morriston, "God and the ontological foundation of morality."</a>)</blockquote>
This is also problematic. What exactly does Craig mean by saying that the bar "paradigmatically" embodied the property of being a meter long? After all, I think most folks agree that meter bar project was misguided; we don't need a concrete exemplar of the property of <i>being one meter long</i> in order to have an objective semantic standard for that property. It is quite enough that we understand the ideal of meter length. Similarly, we don't need a concrete exemplar of perfect goodness in order to understand what it means to be good. Even Craig seems to acknowledge that much.
<p>Yet Craig appears resistant to the suggestion that having an abstract ideal counts as C-objectivity. For instance, in opposing the social contract theory offered by atheist philosopher Shelley Kagan, where morals are said to be grounded in the ideal of a perfectly rational committee of moral agents, Craig wrote:
<blockquote>Indeed, given that perfectly rational people do not exist, how can his pretended account actually ground moral values and duties? There is no such ideal committee; it does not exist and has never considered or decided anything. So how can actual objective moral values and duties be grounded in such a non-reality? (<a href="http://www.reasonablefaith.org/contemporary-moral-arguments" target="_blank">ReasonableFaith.org Q&A #44, "Contemporary Moral Arguments."</a>)</blockquote>
So it is not enough for Craig that we should have an abstract ideal; rather, we must have some concrete exemplar, akin to the Parisian meter bar. Only then can goodness and morals be rightly judged as C-objective.
<p>Unfortunately, when it comes time to look at our moral experience to assess whether or not moral properties and truths are C-objective, we immediately encounter problems. For whatever objectivity we perceive in our experience seems to be <i>semantic</I>, and fails to indicate the existence of a concrete exemplar of perfect goodness. Craig defends premise (2) of his moral argument by insisting that we apprehend objectivity in our moral experience. I think that is probably correct, except that the objectivity we apprehend is not the sort of objectivity Craig needs for his argument. In particular, we apprehend semantic objectivity; but we do not experience anything to justify inferring a concrete exemplar of perfect goodness any more than encountering an imperfect meter stick justifies inferring the existence of a perfect iridium meter bar.
<p>So I don't think that denying C-objectivity runs counter to our experience at all. Rather, it seems to me that when most people speak of "objectivity" they refer to semantic objectivity, i.e. whether or not it really is the case given what we mean by some property that an object possesses it. This kind of objectivity for morality stands quite independent from the existence of God, as Craig himself seems to recognize. In contrast, I don't think many folks have much of an eye for the alleged C-objectivity of moral values and duties, which is what Craig needs to show exists for his argument. That's not a part of my moral experience, and I see no reason to infer it from anything I really do experience.
<p>The skeptic, then, need not reject the objectivity of moral values and duties; nor need he reject the notion that we reliably apprehend a realm of objective moral values and duties in our day-to-day moral experience. Indeed both of these suggestions seem quite plausible. Instead, the problem with Craig's premise is that he posits the wrong kind of objectivity. We apprehend <i>semantic</i> objectivity, and not the external concrete exemplar required for C-objectivity. So by pointing to moral experience, Craig hasn't actually offered any evidence for premise (2) of his moral argument.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com7tag:blogger.com,1999:blog-4856596194106820549.post-23294641898853626252012-05-01T06:43:00.001-05:002012-07-13T10:53:02.607-05:00More on Rasmussen's New ArgumentRecall that Joshua Rasmussen in his <a href="http://www.nd.edu/~jrasmus1/docs/philrel/NecBeingAJP.pdf" target="_blank">"New Argument for a Necessary Being"</a> (2011), argues that
<blockquote><b>(1)</b> Normally, for any intrinsic property p that <b>(i)</b> can begin to be exemplified and <b>(ii)</b> can be exemplified by something that has a cause, there can be a cause of p's beginning to be exemplified. (p1)</blockquote>
When I expressed concerns with his published defense of (1), he (first privately, and later <a href="http://goodnessovergod.blogspot.com/2012/03/episode-15-joshua-rasmussens-argument.html" target="_blank">publicly</a>) offered the following supplement (my paraphrase): Consider mundane intrinsic properties of the form <i>being an apple</i>, or <i>being aluminum</i>, etc., which can begin to be exemplified. Clearly such properties possibly have a cause for their exemplification, and so inductively we infer (1).
<p><a name='more'></a>On the face of it, the argument appears structurally satisfactory. In order to affirm a statement of the form (*) "normally, for all x, if x is F then x is G," he appeals to the fact that in all observed cases, of which there are many, we find that if x is F then x is G. Meanwhile, we have no independent reason to suppose that (*) is false. Divorced of content, then, the inference to (*) appears appropriate. So what has gone wrong?
<p>The answer, I think, lies in the fact that, at least in my own intuitive judgment, his argument fails to cut up the world in a natural way. To use Rasmussen's term, it seems <i>gerrymandered</i> in the sense that his choices for properties F and G are too unusual.
<p>In contrast, the way I interpret the observations to which he appeals is that physical objects like chairs, apples, computers, etc., have physical causes which bring them into existence. Indeed for any such type, we can imagine a <i>first</i> instance of this type of object, and these will, like their successor instances, have physical causes bring about their existence. This is the backdrop against which Rasmussen wants to infer (1). According to him, a property like <i>being of type A</i> is intrinsic, and a cause of the existence of a first object of type A, at least in each of these cases which we have considered, also doubles as a cause of the property <I>being of type A</I> beginning to be exemplified. In this way, he extracts from a natural telling of the story the artificial elements which he needs to construct his inductive argument. In so doing, I find that he leaves behind any persuasive force the argument might otherwise have had, at least for me.
<p>This all reminds me of Goodman's paradox. To recap the famous example, Goodman proposes that all emeralds observed up to time t happen to be green, but that all other emeralds (notably those observed after time t) happen to be blue. This induces the predicate "x is grue," where <i>grue</i> denotes the property of <i>either being green and being observed before t, or else being blue and not being observed before t</I>. For a suitable choice of t, we find that all observed (so far) emeralds are grue. Inductively we infer that all emeralds are grue, which is to say that we should expect that any emerald discovered after t will be blue.
<p>Clearly, though, this is an unnatural way to cut up the world. Though we might not be able to explain why apart from appealing to intuition, emeralds ought not be classed as <i>grue</i> or <i>not grue</i>, but rather as <i>green</i> or <i>not green</i>. Once we leave behind the natural generalization of our observations, the inductive argument loses all its force, even though it has appropriate formal structure. In the same way, Rasmussen's argument does not seem to me the least bit compelling, despite its otherwise satisfactory structure.
<p>Now, he might object that I have not properly characterized the situation in question, that is, the situation of having intrinsic properties of the form <i>being of type A</i> caused to begin to be exemplified. In particular, I have assumed that if there is a first object of type A, and that object has a cause B of its existence, then B caused the property <i>being of type A</I> to begin to be exemplified. Perhaps this is not always the case, though. Consider the property of <i>being a rock with seven points</i>, i.e. a rock having a mostly round shape interrupted by seven sharp points. The first object bearing this property undoubtedly had a cause of its existence, but the property itself was not caused to begin to be exemplified in the sense that the cause of the existence of the rock was perhaps causally indifferent to whether or not it should have seven points. In that case we would have to re-cast the general story, but not in any way that I find would improve our confidence in Rasmussen's inference. For the only means I have of interpreting such properties to have a cause of their beginning of exemplification is to imagine them to have resulted from a physical process which tends to produce new properties of that sort. So for instance a cause of the property <i>being an apple</i> beginning to exemplified might consist in the running of a physical system (natural selection) which tends to produce new types of things.
<p>This is a more complicated story, but the result is the same: it seems unnatural and counter-intuitive to make the leap from physical systems generating diversity to the conclusion that the beginning of the exemplification of an abstract property like <i>being a contingent concrete particular</i> possibly has some kind of inscrutable cause. Structuring it as an inductive argument doesn't improve our situation any more than it did for blue emeralds.
<p>However the above objection is based primarily on intuition. I have made some pretty bold assertions as to what is natural versus what is not, and although I'm confident in these assertions, I don't have much support for them other than intuition. In effect, I'm gambling that most others share my intuition in this matter, and are able to see Rasmussen's argument as I do---gerrymandered to the point of being too unnatural to have any persuasive value. Perhaps I am mistaken about that, however; maybe some folks have differing intuitions which favor Rasmussen's argument. If so, I still have to go with my own best judgment, and this leads me to reject the inference as unwarranted.
<p><center>+ + +</center>
<p><b>Note:</b> I wrote the above over a month ago, before speaking with Rasmussen about it directly on <a href="http://goodnessovergod.blogspot.com/2012/03/episode-15-joshua-rasmussens-argument.html" target="_blank">the Goodness Over God podcast</a> last March. Unfortunately the conversation splintered a bit with other topics, and we didn't spend a lot of time discussing this particular objection. Perhaps we can hash it out another time. Meanwhile, enjoy the post!Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-5215551617541763792012-04-08T06:16:00.006-05:002012-07-13T15:25:00.506-05:00Why did God want Jesus to suffer?Christians face an interesting theological challenge regarding the crucifixion of Jesus, insofar as we want to know why Jesus had to suffer in order to save the faithful. God, being omnipotent, appears to have the power to save the faithful, regardless of whether he also sent Jesus to suffer on the cross. In order to explain why it was better for him to do so, we might be tempted to invoke the notion of justice. However, if we want to appeal to God's favorite system of justice to explain why Jesus had to suffer, then we must know why that system is ultimately good for us. Since we do not in fact know how God's rules of cosmic justice are ultimately good for us, then no appeal to those rules will serve as a satisfactory explanation.<br /><br /><a name='more'></a>In the actual world (per Christianity), we have the following scenario:<br /><br /><blockquote><b>(A)</b> God sends the faithful to Heaven instead of Hell, and he also sends Jesus to die on the cross.</blockquote><br /><br />Consider the following hypothetical variation on this:<br /><br /><blockquote><b>(H)</b> God sends the faithful to Heaven instead of Hell, but he does <i>not</i> send Jesus to suffer on the cross.</blockquote><br /><br />In (H), everyone has (as far as we know) the same amount of joy and suffering except Jesus, who has at least the same amount of joy but is spared a great deal of suffering, when compared to (A). So on (A), there appears to be an equal or lesser amount of total joy but greater total suffering than on (H).<br /><br />If we take for granted that (H) is coherent, which certainly appears to be the case, then God, being omnipotent, has the power to instantiate (H). Instead, though, he chose to instantiate (A), thereby expressing his preference for it. So the Christian here faces a pretty steep challenge, to answer the following question:<br /><br /><blockquote><b>(C)</b> Why does God prefer (A) to (H)?</blockquote><br /><br />Now, we need to make the move from talking about the total balance of suffering and joy to speaking in terms of <i>well-being</i>, i.e. what is good <i>for</i> a person. It is not immediately clear how to connect the two, but it seems to me quite intuitive to suppose that, at least on the surface, (H) appears better <i>for Jesus</i>, and not any worse for anyone else. Maybe this is not the case, but it seems a reasonable <i>initial</i> assumption given the way (H) is constructed. In other words, at first blush, the following appears to be true:<br /><br /><blockquote><b>(1)</b> Everyone in scenario (H) has the same well-being as in scenario (A), except for Jesus, whose well-being is greater in (H) than in (A).</blockquote><br /><br />However it turns out that, despite appearances, (1) must be false, for the following reason: By hypothesis, God is omnibenevolent, which we shall take to mean (among other things) that he is principally concerned with the well-being of other conscious creatures. If (1) were true, then given this guiding principle, God would instantiate (H) instead of (A). However God has instantiated (A); so, by contrapositive, (1) is false.<br /><br />These considerations set the context for evaluating the following possible answer to (C):<br /><br /><blockquote><b>(2)</b> God prefers (A) to (H) because (A) respects God's justice system whereas (H) does not.</blockquote><br /><br />Unfortunately, this answer is problematic. It's not that (2) is false; however it doesn't really <i>explain</i> very much, because it leaves a mystery why God should care about his justice system. It cannot be that God just really loves his favorite justice system for its own sake, since part of what it means to be omnibenevolent is to care principally for the well-being of others. Rather, God must love his justice system at least in part because it somehow results in (not necessarily strictly) greater well-being overall. So anyone using (2) as an answer to (C) therefore faces the following additional challenge:<br /><br /><blockquote><b>(C')</b> How is it that God's justice system results in a better total balance of well-being?</blockquote><br /><br />I submit that nobody has an answer for (C'). Furthermore, it seems clear that anyone using (2) to answer (C) hasn't provided a satisfactory explanation so long as (C') remains unanswered.<br /><br />To see what we mean by "satisfactory," consider the following analogy: Suppose John asks Mary, "why did you go to college?" and Mary responds, "I went to college in order to obtain my college degree." Now, Mary's answer doesn't have to be false, exactly; indeed it seems quite natural to suppose that she went to college for the purpose of obtaining her college degree. Yet clearly she has not actually provided a satisfactory response in stating this fact. For John quite obviously wants to know <i>why</i> Mary cares about having a college degree, and in her answer she completely avoided dealing with that issue.<br /><br />Similarly, (2) is not a satisfying answer to (C) unless we have an answer to (C'). Since we do not in fact have an answer to (C'), the Christian has not by offering (2) provided a satisfactory explanation for God's preference of (A) over (H).<br /><br />In short, appealing to a system of rules to explain Jesus' suffering on the cross isn't helpful unless we understand how that system of rules improves our overall well-being. So, since we don't know how God's favorite system of rules of cosmic justice improves our overall well-being, it cannot adequately explain Jesus' suffering.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com24tag:blogger.com,1999:blog-4856596194106820549.post-17555687409279420932012-03-17T10:53:00.002-05:002012-07-13T10:56:57.332-05:00two objections to Plantinga's evolutionary argument against naturalismThe complexity of philosopher Alvin Plantinga's well-known evolutionary argument against naturalism (hereafter EAAN) affords the skeptic a variety of avenues for criticism. Of these, I prefer to focus on the objections that, first, we cannot be rationally obligated to stop depending on our cognitive faculties since it is quite impossible for us to rationally do so, and second, the sort of skepticism which Plantinga describes, if indeed it poses any danger at all, applies as well to the theist as it does the naturalist unless we already have reason to suppose that theism is true.<br /><br /><a name='more'></a>It seems to me that, at least in a certain sense, we must take ourselves to have reliable cognitive faculties since we simply have no rational choice but to do so. Even to entertain the question we must rely on our own judgment. This is not, of course, to say that we must take our cognitive faculties to be reliable in the broadest sense, as if we should place as much confidence in our judgment on matters of metaphysics as we do in our judgment of whether or not the front door is closed. However we must be able to trust at least some significant subset of our beliefs if we are to at all aspire to rational thought. This is what I mean by having <i>reliable</i> cognitive faculties, and I think it's what Plantinga means as well when he discusses the proposition he labels <i>R</i>. So, while it is true in another sense that we might have unreliable faculties---that event R might be false---if it turns out that they really are unreliable, we cannot ever hope to know it. All we can do is be humble about our unusual situation, and acknowledge that we can be mistaken even about that which seems to us obviously true.<br /><br />Now, Plantinga argues that P(R/N&E), where N and E are, respectively, the events that naturalism and biological evolution are true, is low, and that, since naturalists are bound by the evidence to accept E, this constitutes a <i>defeater</i> for R. However he admits that his arguments for taking P(R/N&E) to be low are rather weak, and so we might instead take the value to be <i>inscrutable</i>. According to Plantinga, either conclusion gives the naturalist a defeater for R, and he supports this claim with the following argument: Let F denote a conjunction of "the relevant facts about their origin, purpose, and provenance," that is, the origin, purpose and provenance of our cognitive faculties (WCB, p224). If P(R/F) is low, he argues---or even just inscrutable---then believers in F should come to doubt that R is true.<br /><br />To support the step from concluding P(R/F) is low or inscrutable to doubting R, Plantinga offers two kinds of analogy. Both of these, I think, fail. In the first place, he suggests that if we consider not ourselves but rather a hypothetical alien race, then learning that P(R/F) is low or inscrutable should give us to doubt R as applied to those creatures. Similarly, if we discover that P(R/F) is low or inscrutable when applied to ourselves, then we should likewise come to doubt our own cognitive faculties.<br /><br />In a second type of analogy, Plantinga describes particular situations where he thinks we would be inclined to doubt R. For instance, if we believe that we have been created by a malevolent intelligence which aims to trick us into having mostly false beliefs, say a Cartesian demon or Alpha-Centaurian mad scientist, then we have a defeater for R. He elaborates:<br /><br /><blockquote>But to have a defeater for R it isn't necessary that I believe that in fact I have been created by a Cartesian demon or been captured by those Alpha-Centaurian superscientists. It suffices for me to have such a defeater if I have considered those scenarios, and the probability that one of those scenarios is true, is inscrutable for me---if I can't make any estimate of it, do not have an opinion as to what that probability is. It suffices if I have considered those scenarios, and <i>for all I know or believe</i> one of them is true. In these cases too I have a reason for doubting, a reason for withholding my natural belief that my cognitive faculties are in fact reliable. ("<a href="http://www.calvin.edu/academic/philosophy/virtual_library/articles/plantinga_alvin/naturalism_defeated.pdf" target="_blank">Naturalism Defeated</a>," 1994, p12)</blockquote><br /><br />At least in the first analogy, I think he's quite right that we should doubt R <i>as applied to the hypothetical alien population</i>. However, the fact that we are doubting the cognitive faculties of some <i>other</i> collection of creatures is key to the analogy. When we turn our attention to ourselves, we find that we believe R in a basic way. Moreover, we hold this belief before ever forming any other beliefs about the origin of our cognitive faculties. So any story we tell about the origin of those faculties will always be incomplete so long as we neglect to stipulate that it ends with R being true. In other words, if we run into a situation where P(R/F) is low or inscrutable (or indeed anything other than exactly 1), then we can be assured F does not contain all the relevant information about the origin of our cognitive faculties. In that case, we ought not be bothered that P(R/F) is low or inscrutable.<br /><br />In the case of the second analogy, we can offer essentially the same objection as described above. Since to begin with we all believe R in a basic way, then I have no business saying that, "for all I know, it could be the case that a malevolent intelligence has ensured that R is false"---at least not without some significant qualification.<br /><br />Nevertheless, this approach may seem too cheap to satisfy. As Plantinga points out, we ought to be able to defeat even basic beliefs. Personally, I don't think that's true in this case---I cannot imagine a situation where R could ever be defeated. We could lose confidence in ourselves, and be persuaded to minimize our trust in our own judgment, but we can never escape our own point of view. As much as we might try to outsource rational judgment, our decisions ultimately remain our own. So to suggest that we ought to stop trusting our cognitive faculties is about as realistic as suggesting that we should stop being nonomniscient. However suppose for the sake of argument that we <i>could</i> have some kind of rational obligation to stop trusting our own beliefs. Then the question is, have Plantinga's analogies demonstrated that in fact we <i>do</i> have such obligation?<br /><br />The answer appears to me a firm <i>no</i>. Consider that by a <i>defeater</i> for R, Plantinga evidently means a rational obligation to stop believing R. We can interpret this unusual situation in one of two ways: First, we can take unbelief in R to rationally obligate us to stop trusting our cognitive faculties. However, to the extent that it is not in our power to do this, we cannot ever be rationally obligated any more than we are rationally obligated to become omniscient. Second, we can take unbelief in R leave us free to rationally trust our cognitive faculties. In that case, we face no dire consequences in rejecting belief in R---no radical skepticism endangers us.<br /><br />However Plantinga faces a second problem: Suppose his argument against naturalism goes through, and this throws naturalists into an irreconcilable skeptical trap. As far as I can see, this is no epistemic advantage for the theist. We have two cases to consider why this is so: First, suppose that theism has warrant independent of the EAAN. In that case we have no need of additional warrant through the EAAN. And especially given that the EAAN is designed to undermine the confidence of naturalists instead of directly strengthening the confidence of theists, I don't see how it lends any additional warrant to theism. Yet even if the EAAN really is found to strengthen a pre-existing, independent warrant for theism, the fact remains that we will first need to stake out that independent warrant.<br /><br />Consider instead the case where theism is not warranted independent of the EAAN. Then since the EAAN does not directly argue for the existence of God, how else might it serve as justification for theism? One obvious possibility is that it offers us a pragmatic justification to that effect. In other words, it's not that we have a reason to think that God really does exist; but rather---on this view---we find that if we fail to assume in advance that God exists, then we fall victim to a self-defeating skeptical trap. At least, I can see no other plausible way to argue for theism based on Plantinga's conclusions about naturalism. On this view, the apologist ends up not concluding that theism is probably true, but rather he finds---or so he thinks---that theism is an inescapable pragmatic assumption.<br /><br />Whether we should actually <i>believe</i> our pragmatic assumptions is an open concern, but suppose for a moment that indeed we ought to do so. Even then, though, the apologist encounters a serious difficulty: It is simply not true that theism is the only alternative to naturalism which avoids the skeptical trap of doubting our cognitive faculties. In fact theism by itself is insufficient for this. Instead we require theism "plus a little something extra" (<I>Naturalism Defeated</i>, p46). In particular, Plantinga needs to presuppose a certain variety of theism whereby God creates us with reliable cognitive faculties. We might call this epistemically <i>good</i> theism (Plantinga calls it "theism simpliciter," in contrast to ordinary, or "austere," theism). So given this observation, it's easy to see how naturalists can make a similar move---instead of simply accepting a basic, stripped-down naturalism, we can assume (again motivated by pragmatic concerns) that if naturalism is true then it must be a kind of epistemically <i>good</i> naturalism. In other words, we can assume R itself, as originally suggested, and take a naturalist position only under the umbrella of that crucial assumption.<br /><br />A variation of this approach seems to have been first suggested by Carl Ginet in 1993-4 (though I cannot find it published until 1995), whereby he advises the naturalist to assume R in the same way that the good theist assumes his good theism. In response, Plantinga objects by claiming that<br /><br /><blockquote>the warrant austere theism has for the [good] theist is derivative from the warrant [good] theism has for her... (<I>Naturalism Defeated</i>, p47)</blockquote><br /><br />In other words, Plantinga thinks that good theism has warrant independent of the EAAN. However, remember that we are considering the case where theism has no such independent warrant. So Plantinga's response to Ginet cannot be adapted as a response to my objection here. Thus it seems his only recourse is to take the EAAN to drive us to a pragmatic assumption which entails R; yet in that case, why not simply assume R itself? After all, we appear to have independent motivation to do so, and even if we hadn't any such motivation, it seems less arbitrary to assume R than to assume something unnecessarily complicated (good theism) for the sole purpose of entailing R. At the very least, the EAAN itself offers us no reason to prefer good theism to good naturalism.<br /><br />Indeed Plantinga seems only to have added to his burden. For when he depends on the fact that his warrant for ordinary, "austere" theism is derivative of his warrant for good theism, he cuts off those avenues to theism which are unspecific to good theism. So, for instance (and for the present purpose), he couldn't use the William Lane Craig's Kalam cosmological argument, nor James Anderson's and Greg Welty's presuppositionalist argument from laws of logic, since these do not move us specifically to an epistemically good God.<br /><br />In sum, it seems that Plantinga needs to argue more persuasively that, first, we really can be rationally obligated to reject belief in R in such a way as to produce a skeptical trap, and second, such skepticism moves us towards theism and away from good naturalism. As things stand, I can find no reason at all to embrace radical skepticism, reject good naturalism, or accept theism.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-39585569658820373982012-03-04T09:02:00.008-06:002012-07-13T10:58:29.077-05:00premise (1) of Rasmussen's new argument for a necessary beingJoshua Rasmussen in his <a href="http://www.nd.edu/~jrasmus1/docs/philrel/NecBeingAJP.pdf" target="_blank">"New Argument for a Necessary Being"</a> (2011), argues that<br /><br /><blockquote><b>(1)</b> Normally, for any intrinsic property p that <b>(i)</b> can begin to be exemplified and <b>(ii)</b> can be exemplified by something that has a cause, there can be a cause of p's beginning to be exemplified. (p1)</blockquote><a name='more'></a><br /><br />Rasmussen takes care to add the "normally" operator since he views (1) as a general "rule of thumb," and not a hard and fast principle which can never admit counter-examples. In particular he believes that<br /><br /><blockquote>for any given property we consider, we have a reason to think (1) applies to it, unless we have reason to think that the property in question is an exception to the general rule. (p2)</blockquote><br /><br />His evidence for (1) takes two forms: First, he argues that (1) is supported by intuition. In particular he asks us to imagine an individual instance of (1), whereby some arbitrary property p begins to be exemplified. Quite naturally, we should wonder if this event had a cause, which inclines us towards thinking that it at least <i>can</i> have a cause. Second, he suggests the following abductive argument: when we imagine various examples of intrinsic properties beginning to be exemplified, especially those involving the appearance of new kinds of objects, we find that we can coherently imagine them to have a cause, and infer (1) as the best explanation for this power of our imagination. I regard both of these arguments as inadequate for supporting (1).<br /><br />The first is an argument from intuition. As with all such arguments, they will only have force insofar as we have reason to trust the underlying intuitions. So for instance if I intuit that my wife's body language indicates unhappiness, this holds inductive support based on my experience with her, and also my previous success in thusly gauging her mood. More broadly, it has support from my experience with other people in general. The further removed my intuition from supporting experience, the less bearing it has on what I should believe. So I'm less inclined to trust my intuition regarding the mood of, say, an orangutan, and still less so of a hypothetical extraterrestrial being. If I realize that I have no experience at all to guide me in an intuition, and I have no other reason to trust it, then the rational position in that case should be skepticism.<br /><br />Now when Rasmussen asks us to imagine our reaction to the instantiation of an arbitrary intrinsic property, we do indeed look to experience to judge our reaction. He is quite correct that we would naturally be inclined to think that such an event <i>can</i> have a cause. However the sense in which this is true is not the sense in which he needs it to be true for his argument. For Rasmussen is discussing broad logical possibility, but our inclinations in this matter involve only epistemic possibility (or something like it). That is to say, usually we should not be surprised to learn that some observed event has a cause. However this does not require us to suppose in advance that it is logically possible. To illustrate, suppose we are given a large odd natural number, say 3559. In that case we might not be surprised to learn that it is prime, or alternatively that it is not prime. However clearly each option is either broadly logically necessary or impossible. The open-ended possibility we detect for 3559 to be prime versus not prime is based on our own epistemic situation. In other words, for all we know, 3559 is prime, and for all we know it is not. Similarly, for all we know, the beginning of the exemplification of an arbitrary intrinsic property had a cause. This is all I take Rasmussen's thought experiment to show, but it does not follow from this that such beginnings are broadly logically possible.<br /><br />Regarding his second argument, I don't typically regard purely logical truths as helping to <i>explain</i> actual states of affairs. So for example, if we wish to explain why a piece of plastic has four corners, we might suggest that it is because the manufacturer's mold had four corners, and that in the manufacturing process the plastic must take the shape of the mold. However if you asked me why it was four corners and I replied, "because it is rectangular, and rectangles always have four corners," then you would rightly complain that I had not properly answered your question. So if Rasmussen wonders why we should be able to coherently imagine certain events having causes, a purely logical statement like (1) will not provide the sort of explanation we ordinarily would seek.<br /><br />Meanwhile, explanations of the other sort, that is, purely logical explanations, seem incompatible with abductive inference. For example, recall the following abductive argument from Aristotle's <i><a href="http://classics.mit.edu/Aristotle/heavens.2.ii.html" target="_blank">On The Heavens</a></i><br /><br /><blockquote>Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. (2.14)</blockquote><br /><br />In a physical context, where certain shapes like spheres are evidently more common than others, this is a more or less reasonable inference. The same sort of argument will not do in a purely logical context, however, where we have no means of assigning a high likelihood to the occurrence of a sphere over that of other three-dimensional objects which would result in the same difference of perspectives along their surfaces. In the same way, we have no means of assigning an a priori likelihood to (1) over competing explanations (or nonexplanations), which prevents us from running a successful abductive argument.<br /><br />Adding further difficulty, Rasmussen provides a counter-example to the imaginative procedure he asks us to perform. For the ultimate aim of his argument is to plug in property c for p in (1), where c is the property of <i>being a contingent concrete particular</i> (p1). However I cannot imagine in any robust sense property c beginning to be exemplified, and even if I could, I would not know how to proceed to imagine it to be caused. For I do not know what could constitute a context of entirely necessary affairs in which to frame such a cause. This consideration, then, casts doubt on the truth of (1) as applied to the case of property c.<br /><br />As an analogy, suppose we observe that f(x)=x<sup>2</sup> is uniformly continuous on any bounded interval. We might be tempted to think that a good explanation for this is that it is uniformly continuous on R (the whole real line). Of course in this case the suggested explanation is quite false. Indeed we might be moved to doubt our explanation if we realize that the usual method of showing that a function continuous on R is uniformly continuous on such intervals appeals explicitly to boundedness. Since R is unbounded, this would leave us without any reason to suppose f is uniformly continuous on R, even if we didn't already have reasons to think it false.<br /><br />Finally, the second argument only tracks if we take our imagination to be a reliable guide to broad logical possibility. For without that supposition, then even if we can imagine an event having a cause it will not follow that we have imagined something broadly logically possible, and hence we will have no basis to apply an abductive argument. On the other hand, if we do take our imagination to be a reliable guide to broad logical possibility, then since can imagine the nonexistence of a necessary being, we have as much reason to think it broadly logically possible as we would to abductively infer (1). In this way, Rasmussen's second argument for (1) comes at the cost of undermining the conclusion he ultimately wishes to draw, namely the existence of a necessary being.<br /><br />So I can find no good support for Rasmussen's premise (1), despite the arguments he suggests. Indeed for the reasons outlined here I think Rasmussen himself should give up his belief in (1), unless he can produce a satisfactory replacement argument for its truth.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-14870178016430306332012-02-27T05:55:00.005-06:002012-07-13T11:00:00.505-05:00Reasonable Doubtcasters on Van Tilian presuppositionalismThe Reasonable Doubtcasters have produced two marvelous episodes critiquing Van Tilian presuppositionalism: <a href="http://freethoughtblogs.com/reasonabledoubts/2012/02/09/episode-97-presuppositional-apologetics-part-1" target="_blank">episode one</a> and <a href="http://freethoughtblogs.com/reasonabledoubts/2012/02/22/episode-98-presuppositional-apologetics-part-2" target="_blank">episode two</a>.<br /><br /><a name='more'></a>To be honest, since atheists on the internet (also in philosophy, IMO) tend to tout some very bad criticisms of theism, I wasn't holding my breath in this case. However I was extremely and pleasantly surprised at what I heard! I must say, the folks at Reasonable Doubts really came through. Although there are spots where I have minor quibbles, in sum they present quite nicely the presuppositionalist case, and zoom in on two of its most serious and immediate problems. In addition, the tone of the podcasts are humorous and friendly, and in each case makes for an extremely entertaining listen. I highly recommend them!<br /><br />Recall that the general strategy of Van Tilian presuppositionalists is to raise a philosophical problem which they claim is unique to non-Christians, and complain that it is only solvable with Christian presuppositions. (This one-sentence summary of presuppositionalism will have to do for our purposes here.)<br /><br />The folks at Reasonable Doubts identify two key flaws in this strategy: First, quoting Gene Witmer's lamentably little-known <a href="http://web.archive.org/web/20100929040144/http://gatorfreethought.org/witmer%20talk%201.pdf" target="_blank">talk on the subject</a>, they point out that presuppositionalists simply presuppose their most basic religious views, and that if this is an appropriate move for the presuppositionalist then the non-presuppositionalist can do the same with the philosophical positions, only without also presupposing anything religious. I would add that far from being a mere hypothetical exercise, indeed this is exactly what we should do in most contexts, as long as we're honest and humble about what we're doing. Second, presuppositionalists do not, in fact, offer any solution to the philosophical problems which they claim plague unbelievers. Rather, we're all in exactly the same proverbial boat, and no appeal to God has yet changed that. So their criticisms, to the extent we might want to take them as being effective, apply to themselves as much as unbelievers.<br /><br />In addition to these two observations mentioned by the Reasonable Doubtcasters, I also like to stress a third important criticisms of Van Tilian presuppositionalism, which is that they often don't offer any valid or cogent <i>argument</i> for their central views, namely the truth of Christianity or the existence of God, instead relying on a rhetorical <i>strategy</i> for use in debates, dialogs, etc., aimed at making non-presuppositionalism look silly. You won't find, for instance, any clear-cut argument in <a href="http://www.bellevuechristian.org/faculty/dribera/htdocs/PDFs/Apol_Bahnsen_Stein_Debate_Transcript.pdf" target="_blank">Greg Bahnsen's debate with Gordon Stein</a>. Instead he talks <i>around</i> his supposed argument, referring to it from time to time without actually stating it in clear terms. Especially consider the last segment of Bahnsen's opening statement:<br /><br /><blockquote>When we go to look at the different world views that atheists and theists have, I suggest we can prove the existence of God from the impossibility of the contrary. The transcendental proof for God's existence is that without Him it is impossible to prove anything. The atheist world view is irrational and cannot consistently provide the preconditions of intelligible experience, science, logic, or morality. The atheist world view cannot allow for laws of logic, the uniformity of nature, the ability for the mind to understand the world, and moral absolutes. In that sense the atheist world view cannot account for our debate tonight.</blockquote><br /><br />Certainly that paragraph itself does not contain any argument for the existence of God, much less Christianity as a whole. Instead, Bahnsen devoted his opening statement to criticizing Stein's particular anti-religious views. So even if his critique was entirely justified (which is hardly the case, but let's assume for the sake of argument that Bahnsen was uniformly correct in that regard), it would not follow that Christianity is the one true religion, nor would even just the more modest claim that God exists. All Bahnsen did in his debate was employ the same strategy of criticism and ridicule of <i>particular</i> non-presuppositionalist positions.<br /><br />This is a typical example of Van Tilian presuppositionalism in action. A similar example can be found in my debate with <a href="http://www.pdf-archive.com/2011/01/17/hubner-wallis-debate-transcript-1" target="_blank">Jamin Hubner</a> (I recommend the transcript of this rather than the audio, since I'm not really a great speaker).<br /><br />On the other hand, some Van Tilians genuinely attempt to construct actual arguments for their beliefs. Sometimes these depart from the strategy mentioned above, as was the case for example in the recent paper "<a href="http://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf" target="_blank">Lord of Non-Contradiction</a>" by James Anderson and Greg Welty (2011, <i>Philosophia Christi</i>), and hence require their own responses. (However such arguments, to the extent that they depart from the Van Tilian strategy, cannot rightly be called <i>Van Tilian</I>.) In other cases the argument reflects a deeply Van Tilian apologetic, e.g. in my debate with <a href="http://www.pdf-archive.com/2011/03/01/bolt-wallis-transcript" target="_blank">Chris Bolt</a> (again, I recommend the transcript over the audio), or <a href="http://www.tsm.edu/sites/default/files/Faculty%20Writings/Collett%20-%20Van%20Til%20and%20Transcendental%20Argument%20Revisited.pdf" target="_blank">Don Collett's brief argument</a> based on Bas Van Fraassen's supervaluations.<br /><br />Anyway, I was very pleased in all with the Reasonable Doubtcasters these past couple of weeks. Go check them out!<br /><br />Also, feel free to read/listen to some of my own critiques of Van Tilian presuppositionalism in the links below:<br /><br /><a href="http://goodnessovergod.blogspot.com/2011/11/episode-11-special-guests-sye-ten.html" target="_blank">Goodness Over God podcast with guests Sye Ten Bruggencate and Pastor Dustin Segers</a><br /><br /><a href="http://benwallis.blogspot.com/2011/11/clarification-on-mixing-models_21.html" target="_blank">more on Pastor Segers' argument</a><br /><br /><a href="http://benwallis.blogspot.com/2011/11/clarification-on-mixing-models.html" target="_blank">more on Sye Ten Bruggencate's criticisms</a><br /><br /><a href="http://goodnessovergod.blogspot.com/2011/09/episode-10-special-guest-brian-knapp.html" target="_blank">Goodness Over God podcast with guest Brian Knapp</a><br /><br /><a href="http://benwallis.blogspot.com/2011/07/some-comments-on-brian-knapps-post.html" target="_blank">Brian Knapp and the atheist's burden of proof</a><br /><br /><a href="http://benwallis.blogspot.com/2011/11/more-on-burden-of-proof-for-gods.html" target="_blank">more on the atheist's burden of proof</a><br /><br /><a href="http://benwallis.blogspot.com/2010/12/colletts-transcendental-argument.html" target="_blank">response to Don Collett's argument</a><br /><br /><a href="http://benwallis.blogspot.com/2011/01/debate-with-jamin-hubner-on-existence.html" target="_blank">my debate with Jamin Hubner</a> (I recommend the <a href="http://www.pdf-archive.com/2011/01/17/hubner-wallis-debate-transcript-1" target="_blank">transcript</a> rather than the audio)<br /><br /><a href="http://benwallis.blogspot.com/2010/08/debate-on-existence-of-god-thursday-aug.html" target="_blank">my debate with Chris Bolt</a> (I recommend the <a href="http://www.pdf-archive.com/2011/03/01/bolt-wallis-transcript" target="_blank">transcript</a> rather than the audio)<br /><br /><a href="http://benwallis.blogspot.com/2010/10/recap-of-debate-with-chris-bolt.html" target="_blank">more on my debate with Chris Bolt</a><br /><br /><a href="http://benwallis.blogspot.com/2011/02/inductive-standards-and-calvinism.html" target="_blank">inductive standards (last response to Chris Bolt)</a>Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com13tag:blogger.com,1999:blog-4856596194106820549.post-80833301325010879202012-01-28T12:19:00.002-06:002012-07-13T11:01:36.291-05:00Craig and actual infinitesWilliam 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.<br /><br /><a name='more'></a><b>Metaphysical and logical possibility.</b><br /><br />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), <i>broad logical possibility</i>, which he laments must follow from the relatively weak force of "intuitions and conceivability arguments" (<i>Blackwell Companion to Natural Theology</i>, 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 <i>an omnipotent God can create a stone so heavy he cannot lift it.</i> 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 <i>make sense</i> 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.<br /><br />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.<br /><br />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 <i>absurdity</i> 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.<br /><br />Does the actual existence of the hotel, then, involve a logical contradiction? Craig argues that yes, it does, pointing to two distinct cases.<br /><br /><b>The first alleged contradiction.</b><br /><br />Craig seems to affirm both that<br /><br /><b>(i)</b> "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<br /><br /><b>(ii)</b> "there are more things in M than there are in M' if M' is a proper submultitude of M;"<br /><br />whereas these are, at least according to Craig, inconsistent with the idea that<br /><br /><b>(iii)</b> "an infinite multitude exists" (p110).<br /><br />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).<br /><br />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 <i>first</i> 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.<br /><br /><b>The second alleged contradiction.</b><br /><br />Craig writes:<br /><br /><blockquote>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).</blockquote><br /><br />What is, after all, the result of infinity <i>minus</i> 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 <i>subtraction</i> has a purely mathematical meaning in any case. Arithmetic, whether finite or transfinite, we apply to <i>quantities</i>, 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<br /><br /><b>(iv)</b> 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 <i>minus</i> Q'.<br /><br />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).<br /><br /><b>From the hotel to the general case.</b><br /><br />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, <i>Philosophical Perspectives on Infinity</i>, 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.<br /><br />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 <i>physical</i> 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.<br /><br />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 <i>fullness</i> 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.<br /><br />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 <i>existing</I> 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.<br /><br /><b>Conclusion.</b><br /><br />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 <i>first</i> 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.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com2tag:blogger.com,1999:blog-4856596194106820549.post-8732011253665127192012-01-01T08:34:00.000-06:002012-07-13T11:56:57.675-05:00an observation on William Lane Craig's divine command theoryWLC 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" (<i>On Guard</i>, 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.<br /><br /><a name='more'></a>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 <i>independent of DCT</i>. 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.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com21tag:blogger.com,1999:blog-4856596194106820549.post-28994553162124066382011-12-28T11:14:00.004-06:002012-07-13T11:44:40.385-05:00James Anderson and non-contradictionDr. James Anderson has recently completed, with Greg Welty, the forthcoming paper <a href="http://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf" target="_blank">"The Lord of Non-Contradiction,"</a> 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:<br /><br />"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).<br /><br />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.<br /><br /><a name='more'></a>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 <i>at</i> a world w, whereby it appears in the set associated with w, and being true <i>in</i> 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).<br /><br />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 <i>true at</i> w. Once we change "truths" to "true" and "in" to "at," the modified sentence no longer sounds inappropriate: <i>The laws of logic are true at w, but there are no laws of logic in w.</i><br /><br />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, <i>Warrant and Proper Function</i>, 1993, p119). To rebut the Adams objection, then, Anderson in <a href="http://proginosko.wordpress.com/2011/12/20/the-lord-of-non-contradiction" target="_blank">a blog post</a> appealed to an argument from Thomas Crisp in his paper "Presentism" (2005, <i>The Oxford Handbook of Metaphysics</i>). 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 <i>at</i> w. Thus we have no concept of a <i>description</i> of w compatible with the in/at distinction, and hence the distinction is not meaningful.<br /><br />It seems to me, however, that Crisp's key premise that <i>p describes w iff, were w actual, p would be true</i> 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 <i>the case</i>. Thus we have satisfied Crisp's demand for an account of descriptions compatible with Adams' in/at distinction.<br /><br />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 <i>in</i> each possible world, which given Adams' distinction is not evidently the case. Instead we can only say that propositions are true <i>at</i> each possible world, and we have no means of deducing from this that propositions have properties <i>in</i> each world.<br /><br />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.<br /><br />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?<br /><br />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):<br /><br /><b>(1)</b> "thoughts belong essentially to the minds which produce them;"<br /><b>(2)</b> "consequently, the thoughts of contingent minds must be themselves contingent."<br /><br />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:<br /><br /><b>(3)</b> if a proposition p exists in world w and essentially belongs to a mind m, then m exists in w.<br /><br />At least, without supposing something like (3), I don't see how to obtain (2) from (1).<br /><br />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?<br /><br />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.<br /><br />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.<br /><br />On his blog, Anderson denies that we need to attribute truth <i>directly</i> to human thoughts. So a human can instead <i>represent</i> 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 <i>Anderson</i>-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."<br /><br />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.<br /><br />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.<br /><br />EDIT: Prof. Anderson has responded to this blog post <a href="http://www.proginosko.com/2012/01/could-propositions-exist-contingently-a-response-to-ben-wallis" target="_blank">here</a>. You can also check out my counter-responses in the comments on that page.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com39tag:blogger.com,1999:blog-4856596194106820549.post-40760467338235289352011-12-16T08:32:00.003-06:002012-07-16T06:39:54.939-05:00a contextualist solution to skeptical problemsConsider 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 DeRose (1995, "Solving the Skeptical Problem," <i>The Philosophical Review</i> 104.1), we may claim the following:<br /><br /><b>(1)</b> I don't know that ~H;<br /><br /><b>(2)</b> If I know that O, then I know that ~H;<br /><br /><b>(3)</b> I know that O.<br /><br />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." DeRose's solution is to appeal to <i>epistemic contextualism</i>, 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:<br /><br /><b>(4)</b> I don't know/C1 that ~H.<br /><br /><b>(5)</b> If I know/C1 (know/C2) that O, then I know/C1 (know/C2) that ~H;<br /><br /><b>(6)</b> I know/C2 that O.<br /><br /><a name='more'></a>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.<br /><br /><b>Is the contextualist interpretation of the skeptical problem correct?</b><br /><br />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," <i>Philosophy and Phenomenological Research</i> 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 <i>sometimes</i> what counts as knowledge can vary from context to context doesn't mean <i>all</i> 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).<br /><br />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.<br /><br />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.<br /><br /><b>Do any further skeptical problems remain on the contextualist solution?</b><br /><br />Philosopher John Koethe remarks of this contextualist interpretation that "as a response to scepticism it strikes me as a nonstarter" (2005, <i>Scepticism, Knowledge, and Forms of Reasoning</i>, 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).<br /><br />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.<br /><br />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.<br /><br />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,<br /><br /><b>(7)</b> If it is not likely/D that P, then I do not know/E that P.<br /><br />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:<br /><br /><b>(8)</b> It is not likely/D that ~H,<br /><br />and given probabilistic closure we also have<br /><br /><b>(9)</b> If it is likely/D that O then it is likely/D that ~H.<br /><br />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.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com0tag:blogger.com,1999:blog-4856596194106820549.post-48790289056766230832011-11-24T08:48:00.003-06:002012-07-13T11:12:39.801-05:00Robin Collins' restricted principle of indifferenceIn <i>The Blackwell Companion to Natural Theology</i> (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 <i>Blackwell</i> his own "restricted" version of the principle (hereafter RPOI):<br /><br /><a name='more'></a><blockquote>...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.]</blockquote><br /><br />To support the validity of the RPOI, Collins appeals to two lines of evidence:<br /><br /><blockquote>(1) it has a "wide range of applicability" (p235); and<br /><br />(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.</blockquote><br /><br />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 <i>justified</i> 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.<br /><br />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.<br /><br /><b>The Zero Paradox:</b> Consider a situation similar to the one Collins discusses in <i>Blackwell</I>, 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 <i>certainty</i> 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.<br /><br /><b>The Continuity Paradox:</b> (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.<br /><br />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.<br /><br />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 <i>Blackwell</i>, 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 <i>other than a previous application of the RPOI</i> 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.<br /><br />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 <i>actual</i> 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.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com8tag:blogger.com,1999:blog-4856596194106820549.post-15812156321592001802011-11-21T08:52:00.002-06:002012-07-13T11:14:09.698-05:00clarification on "mixing models"[NOTE: This is a post on Pastor Seger's argument. For the discussion with Sye Ten Bruggencate, go <a href="http://benwallis.blogspot.com/2011/11/clarification-on-mixing-models.html">here</a>.]<br /><br />This past Thursday Michael Long and I sat down to have a <a href="http://goodnessovergod.blogspot.com/2011/11/episode-11-special-guests-sye-ten.html" target="_blank">taped conversation (over Skype) with Sye Ten Bruggencate and Pastor Dustin Segers about the existence of God</a>. 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.<br /><br />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:<br /><br /><a name='more'></a><blockquote>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</blockquote><br />[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 <a href="http://benwallis.blogspot.com/2011/12/james-anderson-and-non-contradiction.html">here (on-site)</a>.]<br /><br />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:<br /><br /><blockquote>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</blockquote><br />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.)<br /><br />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.<br /><br />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.<br /><br />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.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com2tag:blogger.com,1999:blog-4856596194106820549.post-79646929350318975222011-11-19T08:28:00.001-06:002012-07-13T11:15:46.754-05:00a discussion with Sye Ten BruggencateThis 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 <a href="http://benwallis.blogspot.com/2011/11/clarification-on-mixing-models_21.html">here</a>, and leaving this post open for further discussion on Sye's view. It comes after we interviewed him on <a href="http://goodnessovergod.blogspot.com/2011/11/episode-11-special-guests-sye-ten.html" target="_blank">the Goodness Over God podcast</a> this past Thursday.<br /><br />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.<br /><br />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):<br /><br /><blockquote>SYE: We're saying that we have a justification---revelation from God.<br /><br />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?<br /><br />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.</blockquote><br /><br />So that's the background to the following discussion. Enjoy!Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com19tag:blogger.com,1999:blog-4856596194106820549.post-48787212874810632832011-11-13T04:45:00.001-06:002012-07-13T11:19:33.691-05:00an argument for agnosticismLet 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.<br /><br /><a name='more'></a>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.<br /><br />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).<br /><br />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.<br /><br />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.<br /><br />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.<br /><br />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.Ben Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.com1