Abstract
The aim of this paper is to motivate and then defend a restricted version of the truth-maker theory. In defending such a theory I hope to do away with the perceived need for ‘negative existents’ such as totality facts and the like.
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Notes
I follow convention in allowing that ‘<P> ‘stands for ‘the proposition that P’.
Notably, maximalism and necessitarianism about truth-making often go hand in hand. I will not discuss the latter, here. My concern is to determine, not what the nature of truth-making is, but in which instances truth-makers are to be sought.
See, also, Melia (2005, p. 69).
Dodd (2007) turns this into an argument against truth-maker. Since I defend a restriction to truth-maker, I shall not consider Dodd’s argument here since it turns on the claim that all truths need truth-makers.
And I am going to assume that my opponent, the maximalist, is not swayed by it.
Notice, too, that Armstrong appeals to the intuitions of philosophers of a realist inclination (2004, p. 5).
Cf. Mulligan et al. (1984, p. 289).
The content of the bracket is to rule propositions such as <there are trees and there are tall perennial woody plants having a main trunk and branches forming a distinct elevated crown> as non-threatening to the atomicity of <there are trees>.
In Sect. 7 of his ‘Why the Negations of False Atomic Propositions are True’, Peter Simons (2008) gives an account with a similar feel. The idea that Simons develops therein is that the atomic propositions are the ones that are in need of truth-makers, where a proposition is atomic if and only if it can be true in only one way and false in only one way. Although I think that this is in the right vein, there are problems. For instance, <there exists an electron> could surely be true in more than one way. Electron x might exist and make it true, but, equally, electron x could have failed to exist and electron y could have existed and thereby made the proposition true. Thus, there is more than one way for <there exists an electron> to be true and so it does not require a truth-maker—an odd result! I do not say that Simons’ account can not be patched to deal with this, but, clearly, the account proposed here can deal with this case. Since the proposition <there exists an electron> is atomic, it will need a truth-maker—though see fn. 18. It is up to Simons, then, to elaborate upon what is meant by, ‘can be true in only one way’.
I treat ‘negative existential’ as synonymous with ‘the negation of an atomic proposition’. Strictly speaking, then, <there are no trees and there are no cabbages> is not a negative existential. See below for discussion of what I take to be complex propositions.
I take what I believe to be a reasonable assumption of bivalence—at least for claims about the present, claims about the future might be more complex. See Tooley (1997, pp. 130–146) for discussion.
I set aside concerns about vagueness here. For instance, you might worry that if it is an ontologically vague matter whether <P> is true, then it’s an ontologically vague matter as to whether ¬<P> is true.
See Mulligan et al. (1984) for discussion of how to resolve some of the potential difficulties with this view concerning identity and existence. Neither problem is insurmountable.
Mumford (2005, pp. 266–268) offers a similar discussion. But what Mumford does not do is give us a regimented means by which we may tell whether or not a proposition is to count as ‘atomic’: see above for such an account.
The existentially quantified form of the proposition is particularly revealing.
See, inter alia, Mumford (2005, p. 268).
It may well turn out that, upon inspection, ‘there is a coin in my pocket’ requires further analysis. For instance, coins might turn out to be composed ultimately by electrons that have particular fundamental properties. In that case <there is a coin> would be a complex proposition; there is an electron x, and an electron y,…. and αx, and αy,…. and x & y &…. compose. To this end, then, only fundamental truths require truth-makers, though the truths of natural language will supervene on the truth of the fundamental truths.
Parts of this section lean on arguments in Tallant (forthcoming).
And notice we are giving up at the first hurdle and not even trying to provide such an account here.
For a sustained defence of this kind of view, see Melia (1995).
Borrowing from Melia (1995, p. fn. 2): ‘There are three blind mice’ may be rendered as ‘∃x∃y∃z(x is a blind mouse & y is a blind mouse & z is a blind mouse & ¬(x = y) & ¬(y = z) & ¬(x = z) & ∀w(w is a blind mouse → w = x v w = y v w = z))’.
The content of the squared brackets is mine.
If, for instance, a definition of truth required an infinite disjunction in order to define it, then we would have a case against the proponent of the restricted truth-maker theory.
Other choices available to the maximalist are ‘big facts’ (Cheyne and Pidgen 2006) and that the world has its properties essentially (Cameron, 2008b). Since both views commit us to controversial ontology and the current proposal only to theoretical complexity, so the current account is to be preferred. [Indeed, Cameron (2008b) acknowledges that his argument is supposed to be preferable to other accounts of negative existentials, but thinks that because truth-maker implies truth-maker maximalism this is foisted upon us. Dialectically, I think that move can be blocked by the above attempt to motivate a restricted version of the truth-maker principle].
Although he acknowledges that this is far from a ‘royal road’ this is the spirit in which Armstrong (2004, p. 4) views truth-maker maximalism.
See Mulligan et al. (1984).
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Tallant, J. There’s no existent like ‘no existence’ like no existent I know. Philos Stud 148, 387–400 (2010). https://doi.org/10.1007/s11098-008-9327-9
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DOI: https://doi.org/10.1007/s11098-008-9327-9