### 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?

## 7 Comments:

I also wonder about a better treatment of truthmakers for negative propositions, but I'm inclined towards particular absences as the means to make-true negative atomic propositions.

In other words, there is such a thing as the absence of Bertrand Russell, and that is what makes true the proposition that Russell does not exist.

Hi Chris,

A few 'from the hip' reactions:

First, it seems like there are two ways to interpret your view, though both interpretations seem problematic.

On one hand, I take it you're

notsaying that what makes "there are no hobbits" true is the gappy states-of-affairs [_,is a hobbit]. Rather, you take the sentence to be made true by a certainnegativestate-of-affairs: namely, the state-of-affairs [NEG, [[_,is a hobbit], obtains]]. But if that's supposed to be the truthmaker, then the appeal to gappy state-of-affairs does no meaningful work. For you could just ditch the gappy state-of-affairs and let the truthmaker for negative existentials be the negative state-of-affairs like [NEG, [is a hobbit, is instantiated]].Another way of reading you is saying that what makes "there are no hobbits" is made true by the negative state-of-affairs of that sentence's

not representing an obtaining state-of-affairs. (I won't attempt to symbolize this!) But not only does this suffer the same difficulty as with the strategy above; it also violates the 'aboutness' constraint. (I reject this constrain, but set that aside.) Presumably, "there are no hobbits" is not about what that sentence represents. It's abouthobbits.Second, what about sentences like "

ais a unicorn", where 'a' fails to refer to an individual. Singly gappy states-of-affairs seem bad enough. Butdoublygappy states-of-affairs like [_, _] seem just perverse.Dear Lewis:

"Pegasus-shaped holes"? You're fucking with me, right? :)

More seriously, I assume BR is one of absolutely everything. Hence he exists. This could be rejected though. But I'm not sure how to square up the proposed view without being Meinongian. BR does not exist

now(in the relevant sense) on the view I prefer because that filled proposition does not involve an entity that is among the present things.Dear Alex: I realize that gappy states of affairs are not immediately of use in non-singular true negative existentials. I was trying to give an account of what it was in virtue of which 'there are no hobbits' is true. (Provided that it is! I actually think it is false.) I agree with the property of being a hobbit not being instantiated account. I was suggesting this was so in virtue of certain states of affairs not obtaining. And even if we can eschew them in the non-singular case with "filled" properties (though I don't think we can!) we need them in the other cases.

I'm also cool with certain sorts of perversion. We'll need that in the proposition case if Kripke is right. And Kripke is almost always right.

Um, I meant "filled" propositions, not "filled" properties.

Hi Chris,

Also, and perhaps I'm just ignorant of all the relevant literature, but: doesn't virtually everyone that makes use of gappy propositions believe that none of them (nor their negations) bear truth values? (They explain away that impression otherwise, I take it, by whatever tricks they use to deal with Frege's Puzzle.)

That's my impression, at least. And why believe otherwise? But if that's the case, we really don't need gappy states-of-affairs at all: sentences with non-referring expressions (and the gappy propositions they express) would be neither true (nor false) if that were the case, and thus would need no truthmakers (nor falsemakers).

I realize you're assuming that gappy propositions are truth-evaluable. My point is that the proposal seems to lose its motivation if it's meant to do work in cases that (by the lights of many) are not possible.

Hi Alex,

It's true that a number of gappy proposition-ists think they lack truth value. I'm not aware of any very compelling argument for this conclusion however. A natural view for atomic propositions is that they are true if the relevant individual, if any, has the relevant property, if any. And false otherwise. And if they are false, their negations are true.

Braun (2005) argues that even if atomic gappy propositions are truth value-less there is good reason to take their negations to be true. Suppose p is an atomic gappy proposition and is neither true nor false. Then Not-p basically says that the proposition p is not true. But if p is truth value-less, then this claim is true. So arguably there are true negative gappy existentials even if atomic ones lack truth value.

The motivation for the view I have in mind has to do with some of the concerns raised in Merrick's book "Truth and Ontology". It appeared that apart from concerns about parsimony (which he claimed to be important because of the alleged innocence of Truthmaker) a trope-theoretic approach to defending Truth-Maker that posited privations would avoid all of Merricks' other worries about Truth-Maker.

Suppose I grant that Bertrand Russell exists-sub-tenseless or whichever way you want to say it where "Bertrand Russell does not exist" has a sense which comes out true. The easiest way to get a truth-maker for the proposition that Bertrand Russell does not exist (in the sense where it should be true) is to postulate a thing that exists everywhere and every time that he does not: his absence.

Here is one way that we might think about the benefits of positing "pegasus shaped holes" as you enjoy labeling them:

Suppose that we want to vindicate Truth-maker for propositional calculus (a modest goal that would be important to achieve before we could really hope to vindicate it for the range of propositions resulting from standard predicate calculus, or modal logic, or higher order modal logic, etc.)

For every object O, there is the proposition that O exists, and luckily, O can serve as the truth-maker for that proposition. However for every pair of propositions {P,Q} there is the proposition that P&Q, PvQ, and P>Q, and for every proposition P, there is the proposition that ~P. So, if we just had to worry about starting with atomic existential propositions, we'd have a great deal of work left to do. However, atomic existential propositions have the following nice feature: you can read their truthmaker straight off of their subject place. So, now, suppose we permit mereological fusion of objects, so that for every pair of objects O1 and O2, there is an object O1+O2. We now have the truth maker for the conjunction of P and Q where P is the proposition that O1 exists, and Q is the proposition that O2 exists. It is a well known fact that negation and conjunction are sufficient to get the full expressive power of propositional calculus, and so, if there were negative objects (individual absences or "pegasus shaped holes") we would be able to get a truth maker for disjunctions and material conditionals (as well as the negations of atomic existential propositions), provided the way to get from an object to the negative object could be applied recursively. As luck would have it "the absence of" does apply as needed, and, if reified, would produce an elegant solution to truth-maker for propositional calculus that treats objects as entering into relationships structurally isomorphic to those embodied in the propositional calculus.

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