On some alleged quantifier shift fallacies, Part I

If every reader of this blog owns a computer, it doesn’t follow that there is some one computer that every reader of this blog owns.  To think otherwise is to commit what is known as a quantifier shift fallacy.  A reader asks me to comment on the following passage from the second edition of Harry Gensler’s Introduction to Logic:  

Some great minds have committed this quantifier shift fallacy.  Aristotle argued, “Every agent acts for an end, so there must be some (one) end for which every agent acts.”  St Thomas Aquinas argued, “If everything at some time fails to exist, then there must be some (one) time at which everything fails to exist.”  And John Locke argued, “Everything is caused by something, so there must be some (one) thing that caused everything.”  (p. 220) 

Such claims about Aristotle, Aquinas, and Locke are often made.  Are they true?  The answer, in my view, is that they are not true – certainly not in the cases of Aristotle and Aquinas, and arguably not in the case of Locke either.

Let’s begin by reminding ourselves of some apposite remarks made by Christopher Martin, which I had reason to quote not too long ago: 

As [Peter] Geach points out, if we wish to show that an argument is invalid, it is not sufficient to show that it can be represented as instantiating an invalid form. It might instantiate an invalid form and at the same time instantiate a valid form: and for an argument to be valid it is sufficient that it should instantiate a valid form. The potentially vast numbers of invalid forms which it may instantiate are completely irrelevant.  (Thomas Aquinas: God and Explanations, p. 161) 

There is no doubt that Aristotle, Aquinas, and Locke could be read in the way Gensler and so many others suggest.  (Gensler is not actually quoting them, by the way, but paraphrasing what he is assumes is the gist of what they had to say.)  What is at issue is whether they should be read that way, whether it is plausible that they meant to say what Gensler thinks they did.  And in fact there are other plausible readings of the relevant texts that do not involve any quantifier shift fallacy.  Given that these readings are available, and that the writers in question are, as Gensler says, “great minds” who would surely be unlikely to commit so blatant a fallacy, the reasonable conclusion to draw is that they did not in fact commit it. 

Consider first the case of Aquinas.  The fallacy in question is allegedly committed in the last sentence of this passage from the Third Way: 

We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be.  But it is impossible for these always to exist, for that which is possible not to be at some time is not.  Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. 

Now since I dealt with the present objection in my book Aquinas, I have the luxury of quoting the relevant material here.  What I have to say is best understood in the context of what I say about another objection sometimes raised against this passage (in particular, against the claim made in its second sentence), so the paragraphs that follow (from pp. 91-95) address that separate objection first: 

One common objection to the Third Way… is the suggestion that Aquinas commits an obvious fallacy when he claims that “that which is possible not to be at some time is not,” for even if it is possible for something to go out of existence, it simply doesn’t follow that it will actually do so.  This objection would clearly be correct if by “possible not to be” Aquinas meant “non-existent in some possible world” or “the non-existence of which is logically possible,” for it is obvious that neither the fact that there is a possible world in which something doesn’t exist nor the fact that there is no self-contradiction involved in denying its existence entails anything about its longevity in the actual world.  Similarly, it is sometimes claimed against cosmological arguments that only propositions can be necessary, and not things.  This too might be a good objection to Aquinas if by “necessary” he meant “logically necessary.”  But again, Aquinas does not in fact mean “possible” or “necessary” in any of these modern senses, so these objections are irrelevant.  

What Aquinas does mean is indicated by the reason he gives for saying that some things are possibly either existent or non-existent, namely that we observe them to be generated and corrupted.  Now as we saw in chapter 2, for Aquinas generation and corruption, coming into being and passing away, characterize the things of our experience because they are composites of form and matter.  Their coming to be is just the acquisition by a certain parcel of matter of a certain form, and their passing away is just the loss by a certain parcel of matter of a certain form.  Hence it is ultimately this composite, hylemorphic nature that makes it the case that they are “possible to be and not to be” (ST I.2.3); it has nothing to do with possible worlds, with there being no self-contradiction involved in denying their existence, or any other such thing.  The “possibility” in question is not some abstract logical possibility but rather something “inherent,” a tendency “to be corrupted” rooted “in the nature of those things… whose matter is subject to contrariety of forms” (QDP 5.3).  In other words, given that the matter out of which the things of our experience is composed is always inherently capable of taking on forms different from the ones it happens currently to instantiate, these things have a kind of inherent metaphysical instability that guarantees that they will at some point fail to exist.  They have no potency or potential for changeless, indefinite existence; hence they cannot exist indefinitely. 

By “possible not to be,” then, what Aquinas means is something like “having a tendency to stop existing,”  “inherently transitory,” or “impermanent”; and by “necessary” he just means something that is not like this, something that is everlasting, permanent, or non-transitory.  Thus there is no fallacy in his inference from “such-and-such is possible not to be” to “such-and-such at some time is not,” for this would follow given an Aristotelian understanding of the nature of material substances.  Given enough time, such a substance would, if left to itself, have to go out of existence eventually.  There is no sense to be made of the idea that it might be “possible” for it not to exist and yet that it never in fact goes out of existence no matter how much time passes and even if nothing acts to frustrate its tendency toward corruption, for in that case the claim that it has an inherent tendency toward corruption would be unintelligible.  Something that always exists would by that very fact show that it is something whose nature does not include any inherent tendency toward corruption, and thus that it is necessary (In DC I.29). 

However, this still leaves untouched an apparently more serious difficulty with the Third Way.  Even if it is granted that Aquinas is justified in holding that whatever is “possible not to be” will at some time go out of existence, it is widely held that his further inference to the effect that if everything were “possible not to be” or contingent, then at one time nothing would have existed, is clearly fallacious.  Specifically, it is claimed that he is guilty here of a “quantifier shift” fallacy, of inferring from “Everything has some time at which it does not exist” to “There is some time at which everything does not exist.”  This is called a “quantifier shift” fallacy because the quantifying expression “everything” shifts position from the first statement to the second.  That it is a fallacy can be seen by comparing the argument above with parallel arguments that are clearly fallacious.  If every student in the room owns a pencil, it does not follow that there is a certain pencil that every student in the room owns; if every human being has someone as a mother, it does not follow that there is someone who is the mother of every human being; and so forth.  Similarly, even if every contingent thing goes out of existence at some time, it does not follow that there is some time when they all go out of existence together.  An alternative possibility is that even though every contingent thing goes out of existence at some point, there is always at least one other contingent thing that continues to exist in the meantime, and this overlapping series of contingent things could continue on infinitely.  (Certainly Aquinas could not rule such an infinite regress out, since it would involve a causal series ordered per accidens extending backward in time, and as we have seen, Aquinas concedes for the sake of argument that such a series might not have a first member.)  In this case, though, Aquinas’s conclusion to the effect that if everything were contingent than nothing would exist now would be blocked, and the Third Way would fail. 

But common though this objection is, it is not in fact fatal to Aquinas’s argument, for he need not be interpreted as arguing in the fallacious manner described.  As several commentators have suggested, what Aquinas really seems to be getting at is the idea that given an infinite stretch of time, and given also the Aristotelian conception of necessity and possibility described above, then if it is even possible for every contingent thing to go out of existence together (which even Aquinas’s critic must concede), this possibility must actually come about.  For (again, at least given an Aristotelian conception of possibility) it would be absurd to suggest both that it is possible for every contingent thing to go out of existence together, and yet that over even an infinite amount of time this will never in fact occur.  “Possibility” here entails an inherent tendency, which must manifest itself given sufficient time, and an infinite amount of time is obviously more than sufficient.  Hence if everything really were contingent, there would have been some time in the past at which nothing existed, in which case nothing would exist now, which is absurd, etc., and Aquinas’s argument would (up to this stage in the proof at least) be vindicated.  (Note that it would not help the critic to suggest that the series of contingent things had a beginning in time after all rather than being infinite, for in that case Aquinas could simply say that given the principle of causality this beginning must then have had a cause and that this cause would have to be something non-contingent, i.e. necessary, which is of course what he has been trying to prove the existence of all along.) 

Obviously there are other questions that might be raised about the Third Way and its Aristotelian metaphysical background, and I address them in the book.  For example (to quote now from pp. 95-96): 

[A] critic might… suggest (as J. L. Mackie does) that even if individual contingent things all go out of existence, there might still be some underlying stuff out of which they are made (a “permanent stock of matter,” in Mackie’s words) which persists throughout every generation and corruption.  Now if this were so, then what would follow, given the Aristotelian conception of necessity we’ve been describing, is that this stock of material stuff would itself count as a necessary being.  But (so the suggestion continues) the critic could happily accept this (as Mackie does) given that such a “necessary being” would, in view of its material nature, clearly not be divine.  

The trouble with this reply, though, is that it falsely purports to be asserting something that Aquinas would deny.  In fact, surprising as it might seem, Aquinas would be quite happy, at least for the sake of argument, to concede that the material world as a whole might be a kind of necessary being, in the relevant sense of being everlasting or non-transitory.  After all, as we have repeated many times, Aquinas does not think that proving the existence of God requires showing that the material world had a beginning.  Moreover, as we noted in our discussion of hylemorphism in chapter 2, Aquinas himself insists that while individual material things are generated and corrupted, matter and form themselves are (apart from special divine creation, to which he would not appeal for the purposes of the argument at hand lest he argue in a circle) not susceptible of generation and corruption.  Far from regarding the notion of the material world as necessary as a blow to the project of the Third Way, Aquinas would in fact regard it as a vindication of his claim that there must be a necessary being.  Indeed, he recognizes the existence of other non-divine necessary beings as well, such as angels and even heavenly bodies (which, given the astronomical knowledge then available, the medievals mistakenly regarded as not undergoing corruption). 

That this should not be surprising, and in particular that it should not be regarded as damaging to the aim of proving the existence of God specifically, should be evident when we remember that proving the existence of a necessary being is only one component of the overall argumentative strategy of the Third Way.  For recall that at this stage of the argument Aquinas immediately goes on to say that “every necessary thing either has its necessity caused by another, or not” and then argues that a series of necessary beings cannot go on to infinity… 

In particular (as I go on to explain), given a hylemorphic analysis of material objects, neither matter nor form nor a composite of matter and form could have its necessity in itself (if it has any necessity at all), but would have to derive it from something else.  Only that which is pure actuality could even in principle have its necessity of itself.  But as they say, read the whole thing.  What has been said here suffices to show that there is no good reason to think Aquinas guilty of a quantifier shift fallacy. 

We’ll look at Locke and Aristotle in two further posts.
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