Molnar on Truthmakers for Negative Truths Nils Kürbis Published in Metaphysica 19/2 (2018): 251-257 https://doi.org/10.1515/mp-2018-0014 Abstract Molnar argues that the problem of truthmakers for negative truths arises because we tend to accept four metaphysical principles that entail that all negative truths have positive truthmakers. This conclusion, however, already follows from only three of Molnar's metaphysical principles. One purpose of this note is to set the record straight. I provide an alternative reading of two of Molnar's principles on which they are all needed to derive the desired conclusion. Furthermore, according to Molnar, the four principles may be inconsistent. By themselves, however, they are not. The other purpose of this note is to propose some plausible further principles that, when added to the four metaphysical theses, entail a contradiction. Keywords: Negation, Falsity, Truth, Truth makers, Correspondence In his classic paper 'Truthmakers for Negative Truths' (Molnar (2000)), George Molnar discussed the problem of how, if everything in the world is positive, there can be true negative statements1 about the world. Molnar examines and rejects five common answers to this question2 and concludes that 'we do not have a satisfactory theory of truthmakers for negative truths' (72). Molnar argues that the problem of negative truths arises because we are prone to accept metaphysical assumptions which, he proposes, 'can be summed up in four theses: (i) The world is everything that exists. (ii) Everything that exists is positive. (iii) Some negative claims about the world are true. (iv) Every true claim about the world is made true by something that exists. 1I follow Molnar, who phrases his discussion in terms of statements or claims. 2They are the following. One. If a statement such as 'The apple is not red' is true, then there is a is a positive fact, such as 'The apple is green', which excludes or is incompatible with what the statement states. Two. In addition to the positive fact that the apple is green, there are 'absences or other kinds of negative facts' (76) corresponding to the false statement about the apple. Three. The totality of the facts about the apple, which is a positive general fact, makes the negative true statements about it true. Four. 'Higher order negative states of affairs supervene on the first-order positive states of affairs' (82). Five. Relinquish the idea that the relation between a true statement and its truth maker holds necessarily. 1 (i)-(iv) jointly imply that all negative truths must have positive truthmakers.' (84f) According to Molnar's analysis, 'each of (i)-(iv) is individually plausible, but the quartet may not be co-tenable.' (72)3 Molnar's paper has been discussed widely.4 However, a puzzling aspect of Molnar's analysis appears to have gone unnoticed. Commentators appear to be in agreement with Molnar that all four propositions are required to infer the conclusion that all negative truths have positive truth makers or, worse, that the four principles are inconsistent. (i), however, is redundant to draw the first conclusion, and further principles are needed for Molnar's four to entail a contradiction. The following already follows from (ii) and (iv): (v) Every negative true claim about the world is made true by something that is positive. (iii) ensures that (v) is not merely vacuously true because there are no negative true claims about the world. If what makes a claim true is its truth maker, (v) can be rephrased as (MC) Every negative truth about the world has a positive truth maker. This is the conclusion – paradoxical or at least uncomfortable to him and others – that Molnar draws from (i) to (iv) in the passage quoted above. Formalisation helps clarifying what is at issue. Writing Ex for 'x exists', Px for 'x is positive', Ncx for 'x is a negative claim', Cx for 'x is a true claim about the world' and Txy for 'x is made true by y', we can formalise (ii)-(iv): (ii′) ∀x(Ex→ Px) (iii′) ∃x(Cx ∧Ncx) (iv′) ∀x(Cx→ ∃y(Txy ∧ Ey)) The inference from (ii′) and (iv′) to (v′) ∀x((Cx ∧Ncx→ ∃y(Txy ∧ Py)) is formally valid. Notice that the predicate Ex can be avoided. It has been added to reflect Molnar's wordings. Anyone unhappy with using 'exists' as a predicate can drop Ex from the formalisation without loss and formalise (ii) as ∀xPx and (iv) as ∀x(Cx→ ∃yTxy). 3As Russell observed, 'there is implanted in the human breast an almost unquenchable desire to find some way of avoiding the admission that negative facts are as ultimate as those that are positive.' (Russell, 1919, 4). Unquenchable, it would seem, as the thirst of Tantalos. A good way of bringing out the issues Molnar tackles is to compare his problem with Hochberg's arguments that 'some type of entity, in addition to atomic facts, is needed to ground true negative sentences' (Hochberg, 1969, 333): no matter how one might call them, they effectively are the negative facts. Hochberg, interestingly, appears to classify general facts amongst the positive ones (ibid. 336f), while Armstrong, aiming to avoid negative facts that are on a par with atomic facts, accepts that general facts are a species of negative fact, as they impose limits on what there is (Armstrong, 1997, 200). Irrespective of how valiant the attempt to avoid negative facts in some parts of a theory, they keep emerging in others. 4To refer to only seven authors, Armstrong (2004) (88ff), Cheyne and Pigden (2006), Kukso (2006), Mumford (2007), Veber (2008), Waechter (2017), Cameron (2018) quote Molnar's four theses. The list could be extended. 2 By (iii′), (v′) is not just vacuously true, and we have∃x(Cx∧Ncx∧∃y(Py∧Txy)). This is the consequence that Molnar and his commentators agree truth maker theory or the correspondence theory of truth needs to tackle: how can there be negative true statement about the world, if everything in that world is positive? Molnar attaches some importance to (i), so it should not be redundant. According to Molnar, Meinong and Russell at the time of The Principles of Mathematics solved the problem of negative truth by denying (i) and accepting that 'there is more to Being than existence' (85). They reject that everything in the world exists, because some things in the world do not exist. The option is then open that negative truths can be made true by things that do not exist. I suggest to render (i) as (i′) Everything in the world exists. If being and being in the world are the same, then (i′) is what Meinong and Russell at some point reject. Molnar's (i) reads as if the world is identical to that which is exists, so we could strengthen (i′) to a biconditional. I prefer the conditional, as a biconditional would make one of the two concepts in (i) redundant, and the weaker version is all that is needed for the purposes of this paper. It also has the advantage of allowing for an understanding of existence and being in the world on which the realm of existence is broader than the realm of being in the world. Molnar deplores that to solve the problem of negative truth, 'the most popular contemporary move, alas, is to reject all forms of the correspondence theory of truth, including the moderate version embodied in (iv)-Putnam, Rorty, P.F. Strawson, etc. etc.' (85) Rejecting (iv) is to admit 'truths without the benefit of truthmakers. This is the way of ontological frivolousness. It is a truly desperate resort but we may yet be forced to adopt it, if we are unlucky.' (85) The core idea of the correspondence theory of truth is that our claims are made true by something external to them, by what they are about, not, for instance, by their internal coherence, their usefulness in achieving our goals, their simplicity, beauty or their consolatory virtues. As (iv) is intended to capture this idea, I suggest that it should have asserted that it is the world that makes statements about the world true, not something else: (iv′′) Every true claim about the world is made true by something in the world. Now (i) is no longer redundant to drawing the conclusion (v). With (iv) interpreted as (iv′′), it is once more useful to keep the conditional in (i), as we may want to allow there to be also claims that are not about the world, but about existence more widely, and formalise principles corresponding to (iv) such as 'Every true claim about the numbers is made true by something in mathematical reality.', 'Every true claim about the Forms is made true by something in the Realm of the Forms', or 'Every true claim about a mind is made true by something in that mind.'. I propose to interpret Molnar's quartet as the following four claims: (i′) Everything in the world exists. (ii) Everything that exists is positive. (iii) Some negative claims about the world are true. 3 (iv′′) Every true claim about the world is made true by something in the world. Writing Wx for 'x is in the world': (i′′) ∀x(Wx→ Ex) (ii′) ∀x(Ex→ Px) (iii′) ∃x(Cx ∧Ncx) (iv′′′) ∀x(Cx→ ∃y(Txy ∧Wx)) Drawing the conclusion (v′) now requires (i′′), (ii′) and (iv′′′). As before, (iii′) ensures that the conclusion is not merely vacuously true. Those unhappy with using 'exists' as a predicate may contract (i′) and (ii) to 'Everything in the world is positive'. Molnar's conclusion still follows. What could we add to (i′), (ii), (iii) and (iv′′) to derive a contradiction? Something needs to be said about the relation between positive and negative true claims about the world and the things in the world they are about. To get his point off the the ground, Molnar does not need a general account of what distinguishes positive from negative statements: one example of a true negative statement suffices. Some statements containing negation certainly are of this kind. Molnar's discussion establishes something stronger, which brings out the problem more forcefully. If every negative statement about the world was equivalent to some positive statement, we could explain negative truth in terms of the truth of those positive statements any negative statement is equivalent to. Some such idea is the motivation behind some of the approaches to the problem of negative truth that Molnar rejects. There are what we might call essentially negative statements about the world: statements that are negative, but not equivalent to any positive statement. We can sharpen (iii): (iii′′) There are negative true claims about the world that are not equivalent to any positive claims about the world. Using Pcx for 'x is a positive claim' and writing ENcx for 'x is an essentially negative statement about the world' and y ≡ x for 'y is equivalent to x': (ENc) ENcx↔ Ncx ∧ ¬∃y(Pcy ∧ (y ≡ x)) (iii′′′) ∃x(Cx ∧ ENcx) (iii′′) is a reasonable assumption in itself. Molnar shows how difficult it is to reject it and that the burden of proof is on those who are tempted to do so. By (i′), (ii) and (iv′′), there are essentially negative claims about the world that are made true by something positive. But there is still no formal contradiction. It may be that our language does not allow us to draw a strict distinction between negative and positive claims. Each of 'a is opaque' and 'a is transparent' is equivalent to the other's negation, but which one is positive and which negative? Maybe both are both. Essentially negative statements, however, are not positive statements: (vi) No essentially negative claim is a positive claim. (vi′) ∀x(ENcx→ ¬Pcx) To derive a contradiction, we need to say something positive about positive 4 claims. We may not be able to say whether a claim is positive or negative merely by looking at the claim, but we should expect to be able to do so by looking at its subject matter. What suggests itself is that a claim is positive if it is about something positive. In particular, as we are here only concerned with true claims, if a claim has a positive truth make, then it is positive: (vii) Every true claim about the world that is made true by something positive is positive. (vii′) ∀x∀y((Cx ∧ Txy ∧ Py)→ Pcx) We can now derive a contradiction. By (iii′′′) there is an essentially negative true claim about the world. Call it a. By (i′), (ii) and (iv′′), a has a positive truth maker. But them by (vii) a is positive, contradicting (vi). One way of evading Molnar's conclusion that (i′), (ii), (iii) and (iv′′) are not co-tenable is of course to deny (vii). Notice however that we can weaken the consequent of (vii) to claim only that in such a case there is a positive statement equivalent to Cx: (viii) For every true claim about the world that is made true by something positive, there is an equivalent is positive claim. (viii′) ∀x∀y((Cx ∧ Txy ∧ Py)→ ∃y(Pcy ∧ (y ≡ x)) By (i′), (ii), (iii) and (iv′′), some essentially negative true claim a has a positive truth maker, so by (viii), there is a positive claim that is equivalent to a, contradicting the essential negativity of a. (viii) may be harder to deny than (vii). It would indeed be surprising if there are positive states of affairs that could only ever be described by statements that are not positive. Maybe negative theology can give some examples. Another principle that would do the trick is that essentially negative truths cannot have positive truth makers: (ix) No essentially negative true claim has positive truth makers (ix′) ∀x∀y((Cx ∧ ENcx ∧ Txy)→ ¬Py) Again, we derive a contradiction, using all of (i′), (ii), (iii) and (iv′′). My reconstruction of Molnar's line of thought has not yet appealed to one quite obvious principle. Whereas our language may not draw a strict distinction between negative and positive claims about the world, the metaphysics of the negative and the positive should exclude any overlap: (x) Nothing negative is positive. (x′) ∀x(Nx→ ¬Px) It follows that nothing negative exists and that nothing in the world is negative, which was to be expected. We could appeal to (x) in the derivation of an inconsistency if we strengthen the consequence of (ix) to Ny: (xi) Every essentially negative true claim has only negative truth makers. (xi′) ∀x∀y((Cx ∧ ENcx ∧ Txy)→ Ny) Both options are plausible enough. 5 Each option of a derivation a contradiction from (i′), (ii), (iii) and (iv′′) require all four of Molnar's thesis. Thus the additional principles proposed here – each of (vii), (viii) and (ix) individually and the pair (x) and (xi) – can be accepted as common ground by anyone wishing to address the problem of negative truth by rejecting one of Molnar's four theses. 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