### Truthmakers for Negative Existentials

Some assumptions:

- Atomic singular sentences of the form a is F encode atomic Russellian propositions.

- Atomic sentences that contain non-referring names encode atomic gappy propositions.

- Atomic sentences that contain a name for a property that does not exist encode atomic gappy propositions.

- Atomic sentences that include 'exists' or cognates encode the first-order property of existence.

- Non-singular existence statements encode a second-order property of existence.

- All atomic gappy propositions are false. All of their negations are true.

That a proposition is true or false is not a fundamental fact. Truthmaker theorists want to capture this nonfundamentality by holding that for every true proposition there is some state of affairs that makes it true. (I'm ignoring the trope option here. I'm also joining truthmakerists in ignoring the issue of falsemakers. After all, that something is false is no more fundamental than that something is true. But falsemakers never seem to come up. Maybe the assumption is that we could do falsemakers in terms of truthmakers if we could just nail truthmakers. I'm not sure this assumption is true, but I'll bracket it here.) True negative existentials are a major bugaboo for truthmaker theorists. Two main constraints on truthmakers is that they must necessitate the relevant truth and the truths must be about them. Another is that they are supposed to not be "suspicious". (This is related to the power of truthmakers to "catch cheaters".)

It is widely held that the best shot for being a truthmaker for a singular or non-singular true negative existential is something like the entire world plus the fact that there's nothing more. Opponents of truthmaker complain that this sort of truthmaker does bad on all counts. I wonder if there is not a better one to be had. (I don't know the truthmaker literature very well though.)

Here's the idea: the gappy proposition < __, smokes > is false and it represents nothing at all as smoking. This is to say that it represents the gappy state of affairs [ __, smoking ] as obtaining. Paradoxes aside, suppose a liberal account of states of affairs, including gappy ones. To be true is to represent a state of affairs that is among the states of affairs that obtain. To be false is to fail to do that.

So < NEG, < __, exists > > is true because [ __, exists ] is not among the states of affairs that obtain.

< NEG, < hobbits, exist > > is true because nothing has the property of being a hobbit. That is to say, [ __, is a hobbit ] is not among the states of affairs that obtain, and neither is any state of affairs [ o, is a hobbit ] for any o that exists.

Following Kripke, suppose 'is a unicorn' does not express a property. Then 'Unicorns don't exist' encodes something like < NEG, < __, exist > > where the existence property is second-order. This is true for reasons parallel to the first-order case.

This view seems to beat others in terms of necessitation and aboutness, though perhaps gappy states of affairs are suspicious. I don't know.

Perhaps the fact that the gappy states of affairs are not among those that obtain is not itself a fundamental fact. Maybe it holds in virtue of the totality of things plus the fact that there is nothing more. Maybe that eases suspicion while maintaining aboutness. But it does not merely collapse into the usual account. If I say that Joshua's life is longer than JonBenet Ramsey's, I am talking about their lives. But that is consistent with their lives being nonfundamental. So I think this is okay.

Perhaps one could object to the intrinsic weirdness of gappy states of affairs. But if one accepts gappy propositions, one should not have this problem with gappy states of affairs. Russellian propositions are so very states-of-affairs-like that I can't think of a principled reason for accepting one and not the other. The link is even tighter if we accept the identity theory of truth (I don't): the true propositions just are the states of affairs that obtain. Then gappy propositionists get gappy states of affairs "for free".

What's not to like?

- Atomic singular sentences of the form a is F encode atomic Russellian propositions.

- Atomic sentences that contain non-referring names encode atomic gappy propositions.

- Atomic sentences that contain a name for a property that does not exist encode atomic gappy propositions.

- Atomic sentences that include 'exists' or cognates encode the first-order property of existence.

- Non-singular existence statements encode a second-order property of existence.

- All atomic gappy propositions are false. All of their negations are true.

That a proposition is true or false is not a fundamental fact. Truthmaker theorists want to capture this nonfundamentality by holding that for every true proposition there is some state of affairs that makes it true. (I'm ignoring the trope option here. I'm also joining truthmakerists in ignoring the issue of falsemakers. After all, that something is false is no more fundamental than that something is true. But falsemakers never seem to come up. Maybe the assumption is that we could do falsemakers in terms of truthmakers if we could just nail truthmakers. I'm not sure this assumption is true, but I'll bracket it here.) True negative existentials are a major bugaboo for truthmaker theorists. Two main constraints on truthmakers is that they must necessitate the relevant truth and the truths must be about them. Another is that they are supposed to not be "suspicious". (This is related to the power of truthmakers to "catch cheaters".)

It is widely held that the best shot for being a truthmaker for a singular or non-singular true negative existential is something like the entire world plus the fact that there's nothing more. Opponents of truthmaker complain that this sort of truthmaker does bad on all counts. I wonder if there is not a better one to be had. (I don't know the truthmaker literature very well though.)

Here's the idea: the gappy proposition < __, smokes > is false and it represents nothing at all as smoking. This is to say that it represents the gappy state of affairs [ __, smoking ] as obtaining. Paradoxes aside, suppose a liberal account of states of affairs, including gappy ones. To be true is to represent a state of affairs that is among the states of affairs that obtain. To be false is to fail to do that.

So < NEG, < __, exists > > is true because [ __, exists ] is not among the states of affairs that obtain.

< NEG, < hobbits, exist > > is true because nothing has the property of being a hobbit. That is to say, [ __, is a hobbit ] is not among the states of affairs that obtain, and neither is any state of affairs [ o, is a hobbit ] for any o that exists.

Following Kripke, suppose 'is a unicorn' does not express a property. Then 'Unicorns don't exist' encodes something like < NEG, < __, exist > > where the existence property is second-order. This is true for reasons parallel to the first-order case.

This view seems to beat others in terms of necessitation and aboutness, though perhaps gappy states of affairs are suspicious. I don't know.

Perhaps the fact that the gappy states of affairs are not among those that obtain is not itself a fundamental fact. Maybe it holds in virtue of the totality of things plus the fact that there is nothing more. Maybe that eases suspicion while maintaining aboutness. But it does not merely collapse into the usual account. If I say that Joshua's life is longer than JonBenet Ramsey's, I am talking about their lives. But that is consistent with their lives being nonfundamental. So I think this is okay.

Perhaps one could object to the intrinsic weirdness of gappy states of affairs. But if one accepts gappy propositions, one should not have this problem with gappy states of affairs. Russellian propositions are so very states-of-affairs-like that I can't think of a principled reason for accepting one and not the other. The link is even tighter if we accept the identity theory of truth (I don't): the true propositions just are the states of affairs that obtain. Then gappy propositionists get gappy states of affairs "for free".

What's not to like?