Abstract
What are the ontological commitments of a sentence? In this paper I offer an answer from the perspective of the truthmaker theorist that contrasts with the familiar Quinean criterion. I detail some of the benefits of thinking of things this way: they include making the composition debate tractable without appealing to a neo-Carnapian metaontology, making sense of neo-Fregeanism, and dispensing with some otherwise recalcitrant necessary connections.
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Notes
This isn’t quite accurate. There is a genuine disagreement between the rival parties, according to Hirsch. But the disagreement isn’t over how the mind-independent world is, it’s simply over the meaning of the quantifiers in English. But while Hirsch thinks that there is a genuine question as to which of the many candidate quantifier meanings is had by the English expression ‘there is’, he must also hold that there could be rival theorists who speak different languages but whose languages differ only in the meanings of the quantifiers: these theorists can have many disagreements that will be genuine disagreements, but when it comes to SCQ, they will simply be talking past one another.
See Eklund (2006), Sider (2007a), and Hawley (2007). I should point out for the record that not all these authors defend neo-Carnapianism, or even offer it as the neo-Fregean’s best hope. Sider does indeed think that the neo-Fregean should be a neo-Carnapian, but Eklund and Hawley think that the best meta-ontological position for the neo-Fregean to adopt is Maximalism: the view that any object which could exist does exist. I won’t be discussing Maximalism in this paper. For a presentation of the neo-Fregean program see Hale and Wright (2001).
See, inter alia, Quine (1953).
More precisely, Armstrong says that x is always a truthmaker for 〈x exists〉. He could grant what I say below: that 〈the sum of a, b and c exists〉 is made true by a, b and c, but he would add that it is also made true by the sum. What I want to deny is that we’re always committed to admitting x as a truthmaker for 〈x exists〉.
Objection (due to Jonathan Schaffer): a, b, c and d make true ‘the sum of a, b and c exists’ just as much as a, b and c on their own do, yet we don’t want to say that ‘the sum of a, b and c exists’ is ontologically committing to a, b, c and d, because we don’t want it to be ontologically committing to d. The natural thought is to appeal to the notion of minimal truthmakers, and claim that the ontological commitments of a sentence are the minimal truthmakers of that sentence. But we have no guarantee that we will always be able to find a minimal truthmaker for a sentence; indeed, sometimes it looks impossible. Consider ‘there are denumerably many things’. In a world in which that is true, there will be infinitely many collections of things that make it true, and no smallest collection of things that makes it true, so there will be no minimal truthmaker.
Reply: I do indeed want to appeal to the notion of a minimal truthmaker to explain why d is not an ontological commitment of ‘the sum of a, b and c exists’. I accept that ‘there are denumerably many things’ has no minimal truthmaker and I hold therefore that there is no things that are its ontological commitments. I don’t see this as a bad result. Consider what the Quinean says about the simple theory consisting of just the logical consequences of the following set of sentences: {‘a exists’, ‘b exists or c exists’}. The ontological commitments of this theory, for the Quinean, are just a together with the pure sets and the impure sets constructible from a. ‘b exists or c exists’ has no ontological commitments, because there are no things that have to exist for it to be true. The moral is that we can’t just take all the ontological commitments of our theory and claim that this is our ontology. In the above example, to arrive at a satisfactory ontology we have to supplement the ontological commitments of the theory either by admitting the existence of b (and the impure sets constructible from b), or by admitting the existence of c (and the impure sets constructible from c), or by doing both. ‘There are denumerably many things’ doesn’t have any ontological commitments, on my view, because it has no minimal truthmaker; nevertheless, if it is true any satisfactory ontology will have to include denumerably many things.
I offer a different way of making sense of the claim that ‘a exists’ is true but that there is no element of our ontology that is a in Cameron (forthcoming).
See, inter alia, Armstrong (1997, p. 12).
There are exceptions of course. Some of them told us that what it meant was that complex objects are identical to their parts. But if many-one identity is the price to pay, then it really does seem that there’s no such thing as a free lunch. For a defence of composition as identity see in particular Baxter (1988a, b). The view is also discussed, but not quite endorsed, by Lewis (1991, p. 81) and Sider (2007b).
I argue this in detail in Cameron (2007).
While I hold that the simples a, b and c make it true that there is a sum of a, b and c—and hence hold that those simples couldn’t exist and there not be such a sum—I am in no way committed to the claim that the thing that is their sum in one world is identical to the thing that is their sum in another. Such questions concerning trans-world identity are simply tangential to the current debate concerning the truthmakers for claims concerning the existence of complex objects.
What of the pure sets? Pure sets don’t cause the same problems with respect to the denial of necessary connections because they are necessary existents (if they exist at all), and the injunction is only against necessary connections between distinct contingent existents. Of course if a and b necessarily exist, a can’t exist without b existing; that’s no problem.
Cameron (2008).
For a discussion of totality facts see Armstrong (1997, chapter 13).
Objection: “This only works because you are considering a simple, and indeed simplistic, case. You won’t be able to tell this story if we want a more sophisticated account of when composition occurs. Suppose we want to be organicists, for example. You can’t tell your story, because whether or not a collection of simples jointly constitute a life doesn’t supervene on the relations that hold between those simples.”
Reply: Maybe so. But if it is so, that just gives the organicist a reason to believe that the complex living objects are real existents. That’s exactly the kind of argument for the real existence of complex objects that I am sympathetic to, so I don’t see the objection as a problem.
See Lewis (1986, pp. 211–2) and Sider (2001, pp. 121–32).
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Acknowledgements
Many thanks to David Armstrong, Elizabeth Barnes, Matti Eklund, John Heil, Jonathan Schaffer and Robbie Williams for helpful discussion.
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Cameron, R.P. Truthmakers and ontological commitment: or how to deal with complex objects and mathematical ontology without getting into trouble. Philos Stud 140, 1–18 (2008). https://doi.org/10.1007/s11098-008-9223-3
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DOI: https://doi.org/10.1007/s11098-008-9223-3