Vallicella on the Argument for God from Logic

Bill Vallicella recently posted some comments on the paper I co-authored with Greg Welty. He states that he’s very sympathetic to our project, but he finds a weak point in our argument that renders it “rationally acceptable, but not rationally compelling.” Here I respond to his concerns.

Before addressing his criticisms, I should say that an argument doesn’t have to be rationally compelling (i.e., such that one could only reject it on pain of irrationality) to be a good argument. We actually make this point toward the end of the paper. (I suspect Bill would agree with this point, but it’s worth repeating.)

Vallicella begins by presenting an accurate summary of the argument. He then states that the whole argument hinges on one “crucial sub-conclusion”:

11. Propositions are thoughts.

He’s correct that this step is essential to our argument, and that we appeal to the principle of parsimony (at least in part) to defend it. We argue that propositions are intrinsically intentional and that intentionality is the distinctive mark of the mental; it is that feature which distinguishes the mental from the non-mental. As we put it:

It is the mental—and only the mental—that exhibits intentionality intrinsically. It is the mental that confers intentionality on the non-mental.

Thoughts, then, are the paradigmatic category of intentional entities. And the existence of thoughts is uncontroversial. . . . The question then arises as to how propositions relate to thoughts, given that propositions also exist (as argued above) and exhibit intentionality. Where should propositions be located in our ontology? Are propositions simply thoughts of some kind? Are they essentially mental items? Or should we posit a separate ontological category for propositions as intentional-but-nonmental items?

Surely the first option is the simplest and least arbitrary of the two. Unless we have some good independent reason for insisting that propositions are not mental items, we should conclude (on the basis that they possess the distinctive mark of the mental) that propositions are indeed mental items, rather than positing a sui generis ontological category for them to occupy. One might go so far as to say that the principle of parsimony demands it. Propositions, then, are best construed as mental in nature.

As I will explain in a moment, our argument doesn’t rest entirely on the principle of parsimony, but I quote the above just to give some context.

By way of evaluation Vallicella observes that there are (at least) three views to consider:

A. There are propositions and there are thoughts and both are intrinsically intentional.

B. Propositions reduce to thoughts.

C. Thoughts reduce to propositions.

All three views accept the existence of propositions and thoughts; the latter two reduce one type of entity to the other, while the first rejects any reduction. In light of this taxonomy, Vallicella raises two criticisms, the first of which runs thus:

Now do considerations of parsimony speak against (A)? We are enjoined not to multiply entities (or rather types of entity) praeter necessitatem. That is, we ought not posit more types of entity than we need for explanatory purposes. This is not the same as saying that we ought to prefer ontologies with fewer categories. Suppose we are comparing an n category ontology with an n + 1 category ontology. Parsimony does not instruct us to take the n category ontology. It instructs us to take the n category ontology only if it is explanatorily adequate, only if it explains all the relevant data but without the additional posit. Well, do we need propositions in addition to thoughts for explanatory purposes? It is plausible to say yes because there are (infinitely) many propositions that no one has ever thought of or about. Arithmetic alone supplies plenty of examples. Of course, if God exists, there are no unthought propositions. But the existence of God is precisely what is at issue. So we cannot assume it. But if we don’t assume it, then we have a pretty good reason to distinguish propositions and thoughts as two different sorts of intrinsically intentional entity given that we already have reason to posit thoughts and propositions.

So my first critical point is that the principle of parsimony is too frail a reed with which to support the reduction of propositions to thoughts. Parsimony needs to be beefed-up with other considerations, e.g., an argument to show why an abstract object could not be intrinsically intentional.

I agree that parsimony requires us to take explanatory adequacy into account. Parsimony tells us that ontology X (in which propositions reduce to thoughts) should be favored over ontology Y (in which propositions do not reduce to thoughts) only if ontology X explains all the relevant data (and explains it as well as ontology Y).

At this point Vallicella suggests (in effect) that our argument begs the question in favor of its conclusion. Are there unthought propositions? If God exists, no. But there were no God, it seems there would be many unthought propositions (such as the arithmetical ones). So those who don’t already accept the existence of God thereby have good reason to think that propositions aren’t reducible to thoughts.

It seems to me, however, that it is the objector who begs the question here. At this point in the argument we’re only considering the relationship between propositions and thoughts: we aren’t yet considering the implications or entailments of that relationship for the question of God’s existence. So it’s illegitimate to bring in an objection that says, in effect, “If God doesn’t exist then we have good reason to think that propositions don’t reduce to thoughts.” That would be no better than an objection to the cosmological argument which amounted to, “If God doesn’t exist then we have good reason to think that something can come from nothing.”

Perhaps a better way to look at the issue would be to consider our metaphysical options with the question of God’s existence rendered explicit. (In what follows, the existence of thoughts and propositions is taken for granted, since we’re agreed with Vallicella on that point. We argued for the existence of propositions earlier in the paper.)

Atheistic Platonism (AP): God does not exist and propositions do not reduce to thoughts (human or divine).

Atheistic Conceptualism (AC): God does not exist and propositions reduce to thoughts (specifically, to human thoughts).

Theistic Platonism (TP): God exists and propositions do not reduce to thoughts (human or divine).

Theistic Conceptualism (TC): God exists and propositions reduce to thoughts (specifically, to divine thoughts).

[We actually prefer the label “Theistic Conceptual Realism” for our position, since it makes clear that it combines aspects of both realism and conceptualism, but I’m going to use “Theistic Conceptualism” here for reasons of symmetry.]

Now which of the four options above best satisfies the criteria of parsimony and explanatory power? Parsimony clearly favors TC over TP, since TC posits less entities for the same explanatory benefits. And we can eliminate AC from the running for precisely the reason Vallicella mentions (viz., not nearly enough thoughts; we might also add that propositions exist necessarily whereas human thoughts exist contingently). So the contest is really between AP and TC.

It won’t do to argue that since TC posits an additional entity (God) AP is preferable to TC on grounds of parsimony. After all, both AP and TC posit entities in addition to human minds and thoughts; in the case of AP, an infinite number of abstract entities (unthought propositions). Moreover, there are several reasons why TC has greater explanatory power than AP.

First, there is the prima facie oddness of unthought propositions. (It’s hard to be more precise about this ‘oddness’, but it’s something akin to what J.L. Mackie had in mind when he spoke about the oddness of objective moral values in an atheistic universe.) One might not think it so odd that certain arithmetical truths have not, and never will be, thought by human minds. But isn’t it strange to think that there are abstract propositions — perhaps an infinite number of them — that exist but could not in principle be thought by human minds (on account of their intricacy or complexity)?

As we argued in our paper, propositions exist necessarily if they exist at all, from which it follows that they exist eternally (i.e., there is no time at which they do not exist). But then according to AP, myriad propositions about (say) Lady Gaga must have existed before the human race ever came into being — and most of which will never be thought by anyone. Indeed, odder still, there exist myriad propositions about Lady Gaga even in possible worlds where there are no humans at all (nor any other thinkers).

Clearly TC is not afflicted with this oddness, because every proposition is thought by God, and in every possible world (assuming God’s necessary existence).

Secondly, TC has more explanatory power than AP because it allows for the causal relevance of propositions. According to AP, propositions are abstract entities that do not subsist in any mind. As such, they are causally inert. They don’t cause anything and they aren’t caused by anything. There is no causal connection between propositions and our universe (including our minds). One wonders then how our minds can attain any “ontological contact” with propositions so construed.

This problem doesn’t arise with TC, of course, because propositions, being divine thoughts, have a causal connection with the universe (including our minds) by virtue of the fact that God is a causal agent — indeed, the causal agent par excellence.

Thirdly, TC offers a ready explanation for why propositions exhibit intentionality. We alluded to this point in our paper (although admittedly we could have developed it in more detail):

The physical marks [on a page] exhibit intentionality only insofar as they express thoughts. Without minds conferring meaning upon them, no physical structures would ever be about anything else, for only a mind has the intrinsic power to direct thoughts. In a universe without minds and thoughts, no physical structures could be ascribed truth-values. It is the mental—and only the mental—that exhibits intentionality intrinsically. It is the mental that confers intentionality on the non-mental.

As we had observed earlier in the paper, intentionality has two distinctive characteristics:

The first characteristic is directedness: an intentional entity is directed toward something else, viz., whatever it is about. Thus the statement “Tokyo is the capital city of Japan” is directed toward Tokyo (and perhaps also toward Japan). The second characteristic is aspectual shape, which can be thought of as the particular way in which the object (i.e., that to which the intentional entity is directed) is apprehended. For example, the two statements “Mark Twain wrote The Adventures of Tom Sawyer” and “Samuel Clemens wrote The Adventures of Tom Sawyer” are both directed toward the same object: the man who was born “Samuel Clemens” but later adopted the pen name “Mark Twain”. However, the two statements exhibit different aspectual shapes in their intentionality; they are directed toward that one man in different ways. We might say that they reflect different perspectives on their object.

Both of these characteristics reflect what we know a priori to be powers of minds. In the first place, minds can be directed toward certain objects; particular entities can be deliberately “picked out” for contemplation. And secondly, minds can consider those objects from different perspectives; particular entities can be regarded in one way rather than another (e.g., as “the eldest son of John Adams” rather than as “the 6th President of the United States”). But if propositions have no intrinsic connection to any mind, what else could explain their directedness and aspectual shape? (I suppose one could insist that these are just brute features of propositions, but it remains that TC sheds more explanatory light, based on what we already know about minds, than AP does.)

So there are multiple explanatory advantages that TC holds over AP. And that gives us some resources to address Vallicella’s second critical point:

Why not countenance (C), the reduction of thoughts to propositions? It could be like this. There are all the (Fregean) propositions there might have been, hanging out in Frege’s Third Reich (Popper’s world 3). The thought that 7 + 5 = 12 is not a state of an individual thinker; there are no individual thinkers, so selves, no egos. The thought is just the Fregean proposition’s temporary and contingent exemplification of the monadic property, Pre-Personal Awareness or Bewusst-sein. Now I don’t have time to develop this suggestion which has elements of Natorp and Butchvarov, and in any case it is not my view.

All I am saying is that (C) needs excluding. Otherwise we don’t have a good reason to plump for (B).

One obvious response is to point out the oddity of thoughts without thinkers. Can there be thoughts without thinkers any more than there can be actions without agents? But even leaving that aside, I think it’s reasonably clear from what I’ve written above that an atheistic version of (C) will suffer from the same explanatory deficiencies as AP, while a theistic version of (C) will be less parsimonious than TC. So TC will be the most reasonable view to take.

In sum, our claim that propositions reduce to thoughts has more in its favor than merely ontological parsimony. There are several other good reasons for preferring it to the alternatives (i.e., that thoughts reduce to propositions or that thoughts and propositions are ontologically independent). I can see no overriding reasons for favoring AP over TC, unless one finds the existence of God objectionable; but as Vallicella notes, that’s precisely the issue in question.


Addendum: Comments from Greg Welty

I didn’t initially write a reply to that post, since Vallicella already concedes that our argument is “competently articulated,” is “rationally acceptable,” “the premises are plausible and the reasoning is correct.” What more could one want in a philosophical argument? :-) Seriously though, it seems to me his strongest point is in the following passage:

Of course, if God exists, there are no unthought propositions. But the existence of God is precisely what is at issue. So we cannot assume it. But if we don’t assume it, then we have a pretty good reason to distinguish propositions and thoughts as two different sorts of intrinsically intentional entity given that we already have reason to posit thoughts and propositions.

So my first critical point is that the principle of parsimony is too frail a reed with which to support the reduction of propositions to thoughts. Parsimony needs to be beefed-up with other considerations, e.g., an argument to show why an abstract object could not be intrinsically intentional.

He’s right that there are two criteria for proper application of Ockham’s Razor: ontological parsimony and explanatory adequacy. And the former should not be applied at the expense of the latter, but only in the presence of the latter. Without explanatory adequacy, we have no business trimming down our ontology.

But then given these two criteria to which he has rightly drawn our attention, what Vallicella has to show is not that an atheist alternative is as parsimonious as the theistic one, but that it is as explanatorily adequate. And that’s where your fourfold taxonomy enables us to assess the options in that respect. It’s all well and good to say that you won’t assume the existence of God. The question is whether the resulting ontology is as explanatorily adequate as the theistic alternative.

Our argument in no way assumes the existence of God at the outset (though of course we are committed to the existence of God). However, it does assume the relevance of the two criteria Vallicella has mentioned, and argues that theistic conceptual realism is preferable on those grounds. That doesn’t seem question begging to me. Atheistic platonism might be as parsimonious as theistic conceptual realism, but it is not as explanatorily adequate as TCR for the three reasons you give: (i) oddness of unthought propositions, (ii) the causal irrelevance of propositions, (iii) brute fact intentionality of propositions rather than explicable as the intentionality of thoughts. (Some of these same points can be made on behalf of TCR about possible worlds, BTW, which is a further consideration for anyone who wants to integrate a view of propositions and possible worlds into a broader, overall view.)

2 Responses to Vallicella on the Argument for God from Logic

  1. Great stuff Greg and James,

    Great paper too.
    Reminds me of the stuff from Gerstner in his book Theology in Dialogue.

    There Gerstner argues that “intellectual potentiality [thoughts] and intellectual actuality [propositions] are essentially the same thing”. That “intellectual potentiality is [merely] actuality at rest” and conversely “that actuality is [merely] potentiality being exercised”- pg.22

    Of course this begs the question, ‘where does this exercise come from’
    and ‘is this exercise intrinsically good or evil’?

    Thanks for expanding my vocabulary.

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