Counter-apologist and valued commenter Ben Wallis has posted some criticisms of the argument for God from logic. (His post is basically a synthesis of the comments he posted here.) His approach is to attack the claim that if there are necessarily true propositions (i.e., necessary truths) then those propositions necessarily exist by appealing to the distinction between truth-in-w and truth-at-w (a distinction employed by Kit Fine and Robert Adams, albeit with different terminology). Drawing on this distinction, Ben proposes a view of propositions according to which necessary truths exist contingently. In this follow-up post, I explain why I believe Ben’s proposal isn’t viable.
Given what Ben writes in his post, it appears he is committed to all of the following claims:
- There are some necessary truths, i.e., some propositions that are necessarily true.
- Propositions exist contingently.
- Propositions are dependent on minds; in the absence of minds there can be no propositions.
- A proposition is not identical to any particular thought, but is instead a sort of “similarity class” of thoughts.
- A possible world is a maximally consistent set of propositions that describes a hypothetical state of affairs.
- We can meaningfully distinguish between truth-at-w and truth-in-w, where w is some possible world; only the latter entails the existence of a truth (a true proposition) in w. To say that some proposition p is true-at-w is only to say that p is a member of w; it is not to say that p exists in w and is true in w.
I assume that Ben is committed to (1) because he doesn’t contest it, because he’s a sensible level-headed fellow, and because he’s a mathematician (mathematical truths being paradigmatic necessary truths). But he’s also committed to (2) because he wants to argue against the claim that propositions exist necessarily so as to evade the theistic argument.
(3) follows from Ben’s assumption that “propositions exist in any world only insofar as beings with sufficiently-developed minds express them.” Indeed, he thinks that propositions exist contingently precisely because he thinks the only minds that exist are contingent minds (but not necessarily human minds; I’m guessing Ben is open to the possibility of non-human contingent minds, e.g., advanced alien life forms).
(4) is stated directly in his post:
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.
My impression is that Ben isn’t firmly committed to this account of propositions, but thinks that at least something close must be true. For now I’ll assume Ben is committed to (4) unless he expresses a different view. (In any case, what I argue below can be easily adapted to apply to similar views.)
As for (5) and (6), these are affirmed in the fourth paragraph of his post:
Regarding the first point of disagreement, we appeal to a distinction made by Robert Adams in his paper “Actualism and Thisness” (1981). Adams prefers to treat possible worlds as maximally-consistent sets of propositions which tell “world-stories,” that is, which describe hypothetical states of affairs imagined by us. We can then distinguish between a proposition p being true at a world w, whereby it appears in the set associated with w, and being true in w. The latter sort of truth involves the proposition not only existing here in the actual world where we can use it to describe a hypothetical state of affairs and assign it a truth value in that capacity, but also existence within w, where denizens of that world can express it and assign it a truth value from their own point of view. Given that propositions exist in any world only insofar as beings with sufficiently-developed minds express them, this distinction seems intuitive and meaningful, and hence required in order to avoiding conflating existence inside a non-actual world of some truth there with its existence here in the actual world. Indeed it appears to have been championed quite independently of Adams, including by myself before I read his paper, and by Kit Fine under the labels “inner” versus “outer” truth (cf. “Plantinga on the reduction of possibilist discourse,” 1985).
In response, I’m going to point out some problems for Ben’s proposal before focusing in on one significant issue he needs to address.
In the first place, his definition of possible worlds as maximally consistent sets of propositions is vulnerable to a Cantorian objection (put forth here by Bill Vallicella). That is one reason why Greg Welty and I used a different definition of possible world in our paper.
Second, Ben’s understanding of propositions seems to reverse the relationship between thoughts and their propositional content. Propositions are primary truth-bearers and possess original intentionality (i.e., they are intrinsically ‘about’ things; they are not ‘about’ things in virtue of something more fundamental). A thought such as my belief that squares have four sides is true in virtue of its propositional content; it is true because the proposition that squares have four sides is true. So in an important sense propositions are logically prior to thoughts.
According to Ben’s proposal, however, thoughts are prior to propositions, since propositions are a sort of “similarity class” of (human) thoughts. On this view propositions are true (or false) in virtue of the thoughts that constitute them. But this gets things back to front.
Third, it follows from (4) that if propositions exist they are abstract entities (thought-types rather than thought-tokens). As such, they’re at least partly external to any particular human mind, and they’re not identical to any human thoughts or parts of human thoughts. But elsewhere Ben has written:
Certainly you [Anderson] never say that propositions are conceptually out of reach. But you do seem to suggest that propositions are external to our thoughts, i.e. they are not themselves our thoughts or parts of our thoughts. To my reckoning, that puts them conceptually out of reach.
By Ben’s own reckoning then, propositions (as he construes them) are “conceptually out of reach.” (I don’t agree with his reckoning, but the point is that if it’s a problem for my position it’s equally a problem for his.)
Fourth, Ben’s proposal has the odd consequence that nothing was true before human minds (or any other sufficiently developed minds) came into existence and nothing would be true if all such minds were annihilated. Assuming for the sake of argument that the only sufficiently developed minds in the cosmos are human minds, if a nuclear holocaust were to wipe out the entire human race then it would no longer be true that 2+2=4, that the sun is more massive than the earth, and that E=mc2. Bizarrely, it wouldn’t even be true that a nuclear holocaust had wiped out the entire human race.
Fifth, there simply are too many propositions — too many truths — for them to depend on human minds in the way Ben suggests. For example, for every natural number N there is the truth that N is not a purple armadillo. But most of these propositions, even though we know they’re all true, have never been entertained by any human mind and were true well before they were entertained by any human mind. (The counter that they might have been entertained by superior alien minds doesn’t have much mileage to it, for reasons obvious enough.)
Moreover, Ben takes possible worlds to be maximally consistent sets of propositions. It’s widely accepted, I think, that sets are ontologically dependent on their members; so if these possible-world-sets exist then their member propositions must exist too. Yet surely no human being has entertained every proposition in the set that is the actual world, never mind all the other possible worlds. So whose minds furnish the metaphysical basis for all these (arguably innumerable) propositions?
Finally, there are difficulties in explicating the distinction between truth-at-w and truth-in-w. Ben suggests that p is true-at-w iff p correctly describes w (or more precisely, describes the state of affairs that would obtain if w were actual). Thomas Crisp has pointed out that it’s hard to see how p could be true-at-w without being true-in-w. Doesn’t it seem obvious that if p correctly describes w then p would be true if w were actual? But if that proposition were true then (as we argue in the paper) it would exist. Nevertheless, Ben has a response to Crisp’s objection:
It seems to me, however, that Crisp’s key premise that p describes w iff, were w actual, p would be true is false. Our intuitive understanding of what descriptions are informs our statements about descriptions — not the other way round. As long as we have such an understanding, we are not required, I don’t think, to explicate it in English, or to construct a definition in terms of possible worlds semantics. If this bothers Crisp (or Anderson), then we can do as well with the following: p describes w iff, were w actual, p would be the case.
The trouble with this response is that being the case isn’t a property of propositions, and even if it were, one would still be stuck with a property-bearing entity (bearing the property being the case instead of the property being true). So the existence of propositions in w still hasn’t been eliminated. Perhaps this problem can be patched up in some other way, but even then Ben hasn’t addressed the other “awkward consequences” of the truth-at-w/truth-in-w distinction. So the viability of this distinction remains in doubt.
A Challenge: Making Sense of Necessary Truths
I now want to focus on one particular challenge that Ben needs to address. Since he’s committed to (1) he owes us an account of what it means for a proposition to be necessarily true, and one that is consistent with his other commitments. Here I’ll consider four possible accounts and point out why each one is unsatisfying with respect to Ben’s position.
Account #1: p is necessarily true iff p is true in every possible world.
This is perhaps the most natural explication of necessary truth, but clearly it’s one Ben wants to avoid because (as I think he concedes) it entails the necessary existence of propositions.
Account #2: p is necessarily true iff p is true in every possible world in which p exists.
This account avoids the entailment of the previous one by employing a weaker conception of necessity. A proposition p is necessarily true if it cannot fail to be true; that is, there is no possible world in which p exists but is not true. The problem with this account (as we point out in our paper: fn. 30) is that it has some absurd entailments. For example, the proposition that propositions exist turns out to be necessarily true, despite the fact that (according to this view) propositions exist contingently.
Account #3: p is necessarily true iff p correctly describes every possible world.
This account would seem to be attractive for Ben, since it employs his idea of truth-at-w (as opposed to truth-in-w). It apparently avoids the entailment that propositions exist in every possible world, but the question is whether it’s consistent with his other commitments. Remember that on Ben’s view, propositions arise from, or are abstractions from, actual human thoughts. But how could actual human thoughts have enough content to support all necessary truths? How could the human minds that exist today (never mind in earlier generations) sufficiently represent every possible world so as to allow necessary truths to “come out right” (i.e., to actually have the modality we take them to have)?
Account #4: p is necessarily true iff p is a member of every possible world.
This account is similar to the last insofar as it also appeals to the notion of truth-at-w. Recall that Ben defines possible worlds as maximally consistent sets of propositions. Why not say then that a necessary truth is just a proposition which is a member of every one of these sets?
The problem here, once again, is that human minds simply aren’t numerous enough and complex enough to account for all the propositions that constitute all these possible worlds. The domain of possibilities is far, far greater than the domain of actual human thoughts. In mathematics alone, there are countless truths that have been, and never will be, entertained by human minds. So it seems clear to me that this fourth account, while it may avoid the unwelcome (to some) entailment that propositions necessarily exist, can’t be reconciled with the sort of conceptualism or quasi-conceptualism that Ben wants to endorse.
I’ve suggested four accounts of necessary truth, none of which seem viable for Ben in light of his modal and metaphysical commitments. I believe the burden lies with him to come up with a coherent alternative account that can be reconciled with (1)-(6).
The ball is in your court, Ben!