Abstract
In this paper I argue against Armstrong’s recent truthmaking account of possibility. I show that the truthmaking account presupposes modality in a number of different ways, and consequently that it is incapable of underwriting a genuine reduction of modality. I also argue that Armstrong’s account faces serious difficulties irrespective of the question of reduction; in particular, I argue that his Entailment and Possibility Principles are both false.
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Notes
Combinatorialism ‘traces the very idea of possibility to the idea of the combinations – all the combinations – of given, actual elements’, namely universals and particulars (1989a: 37; see also, 1997). The theory is intended to be reductive of the notion of possibility, since the latter ‘is given an analysis, an analysis which uses the universal quantifier’ (1989: 47), i.e., which merely uses the universal quantifier.
I follow Armstrong (and others) in using ‘< >’ to pick out propositions.
For Armstrong’s truthmaking account of necessary truth, which will not concern us here, see Armstrong 2004: Ch. 8.
Like truthmaking, existence-making is not a causal making.
Armstrong thinks that a combinatorialist element is present in the provision of minimal truthmakers for possibilities concerning alien particulars and universals. We return to this in section 4 below.
Armstrong attempts to accommodate our modal intuitions by endorsing a highly deflationary form of Lewis’ counterpart theory. When we say, e.g., that the Eiffel Tower could have been 1 mm taller than it actually is, what we say is strictly speaking false. What is true, however, is that there could have been an object very much like the Eiffel Tower, which was 1 mm taller than the actual Eiffel Tower (2004: 47). We return to the topic of counterparts in section 4 below.
On p. 103 of Truth and Truthmakers Armstrong himself glosses partial identity in this way (see also, 1997: 17-8).
Could Armstrong now simply say that all particulars are thick ones? I do not think so, for he would then have to rethink his conception of states of affairs, and indeed his whole atomistic metaphysics. I assume that faced with this degree of revisionism, he would rather give up the view of instantiation that demands it.
Baxter, from whom Armstrong gets the idea of instantiation as partial identity, says that the partial identity of a universal with a particular is ‘the identity of an aspect of [the] universal with an aspect of [the] particular … The aspect is the part they have in common’ (Baxter 2001: 453). Aspects are meant to be real entities; we refer to them through phrases such as ‘insofar as’, ‘to the extent that’, and ‘qua’, e.g., ‘x insofar as it is F is H’. As far as I can tell, Armstrong does not endorse Baxter’s theory of aspects. And this is a wise decision. For, despite Baxter’s insistence to the contrary, the theory’s ‘underlying idea’ that an entity can differ from itself without contradiction, that ‘something can be true of one aspect of an entity that is false of another aspect of it, even though its aspects are numerically identical with it’ remains obscure (Baxter 2001: 449; see also Simons 2005: 258-9).
Distinguish the coherence of necessary existence from the coherence of God. Even if the latter is deemed incoherent, abstract objects are still plausible candidates for necessary beings.
Any non-minimal truthmaker for <T exists> must therefore have T as a part or constituent.
I thank the referee for this journal for raising this issue. It is actually questionable whether <Armstrong exists or Armstrong does not exist> is made true by Armstrong. For this proposition is not so much true in virtue of Armstrong’s existence or non-existence as true regardless of his existence or non-existence. In other words, <Armstrong exists or Armstrong does not exist> is arguably true in virtue of its logical form alone. <Armstrong exists or Armstrong does not exist> is an instance of the law of the excluded middle, and it is plausible to take instances of the law to inherit their truth from the truth of the law itself (what, in turn, makes the law true is another matter). But even if this correct, there are other necessary truths of a disjunctive form that are made true by Armstrong. The proposition <Armstrong exists or 2+2=4> is one such example. (This proposition is, of course, also made true by the truthmaker for the disjunct <2+2=4>).
Strictly speaking, not all contingent propositions are of the form <T exists>. But those contingent propositions that are not of this form must nevertheless themselves contain a proposition that is of that form, and from which they then derive their contingency. Thus, <x exists or y exists> is a contingent proposition because its disjuncts <x exists> and <y exists> are themselves of the form <T exists>, and as such are contingent. The same is true for the proposition <x exists and 2+2=4>. This proposition is contingent because one of its conjuncts, <x exists>, is a contingent proposition of the form <T exists>.
Again, this does not presuppose that existence is a genuine property of objects. If we take existence to be the second-order property of being instantiated instead, then the contingency of (say) Armstrong’s existence amounts to the conjunction of Armstrong’s properties having instances only contingently.
Rodriguez-Pereyra uses a different example.
This point is reminiscent of Kit Fine’s insight that essence is a more fine-grained notion than necessity. Socrates, for example, is necessarily a member of the singleton Socrates {Socrates}, since he could not exist without being member of that set. But he is not essentially a member of the singleton {Socrates}, since Socrates is not what he is in virtue of being a member of that set (see Fine 1994).
Armstrong himself makes this assumption in earlier work (cf. 1978).
As Rodriguez-Pereyra shows, the Entailment Principle cannot be saved by adopting a relevant notion of entailment. Systems T, R and E of relevant logic all validate the entailment ‘(P&Q) →P’. It is true that connexive logic does not validate that entailment, since it takes the relation of entailment to be determined by meanings rather than truth-values. But that notion of entailment is irrelevant to truthmaking theory, since truthmaking is an ontological rather than a semantic relation (for details, see Rodriguez-Pereyra 2006, sections 7 and 8).
References
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Rodriguez-Pereyra, G. (2006). Truthmaking, entailment, and the conjunction thesis. Mind, 115, 957–982.
Simons, P. (2005). Negatives, numbers, and necessity: Some worries about Armstrong’s version of truthmaking. Australasian Journal of Philosophy, 83, 253–261.
Acknowledgements
I wish to thank Hanjo Glock for comments on a previous draft of this paper.
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Kalhat, J. A Critique of Armstrong’s Truthmaking Account of Possibility. Acta Anal 23, 161–176 (2008). https://doi.org/10.1007/s12136-008-0027-z
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DOI: https://doi.org/10.1007/s12136-008-0027-z