Abstract
The proper evaluation of a theory’s virtues seems to require taking into account what the theory is indirectly or implicitly committed to, in addition to what it explicitly says. Most extant proposals for criteria of theory choice in the literature spell out the relevant notion of implicit commitment via some notion of entailment. I show that such criteria behave implausibly in application to theories that differ over matters of entailment. A recent defence by Howard Peacock of such a criterion against this objection is examined and rejected. I go on to a develop a better proposal on which, roughly speaking, a theory is counted committed to a claim if and only if its best fully explicit extension is explicitly committed to the claim. Such extensions in turn are evaluated by ordinary standards of theory choice adapted to the case of theories assumed to articulate their intended content in a fully explicit fashion.
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Notes
The view is widely but of course not universally shared; alternative approaches to theory choice are possible, such as Popperian corroborationism, probabilism, or decision theory, on which putative theoretical virtues may have no obvious role to play. Thanks here to an anonymous referee.
A set of sentences is closed under logical consequence iff it includes every sentence logically entailed by it.
Appeals to Occam’s Razor are generally relative to some phenomena to be explained, or to some specific subject matter that the theories are supposed to be theories of. We shall usually leave the specification of subject matter or phenomena implicit. Thanks here to an anonymous referee.
It is worth emphasizing that the interest of the main points of my paper therefore does not depend on Occam’s Razor but only on the weaker claim that what a theory is committed to is relevant to theory choice.
In order to decide what a given theory is explicitly committed to, we need to know which of its expressions mean there is (in the ontologically important sense). I assume throughout the orthodox view that the ordinary first-order existential quantifier ‘\(\exists x\)’ does; nothing of substance hinges on that assumption. (For recent criticisms of the assumption, see e.g. Azzouni 2007 and Fine 2009.)
For related arguments for the same point, cp. e.g. (Peacock (2011), pp. 81ff.).
When in the sequel I speak of parsimony, unless otherwise noted, I mean ontological parsimony.
If T is necessarily false, whatever one puts for ‘\(F\)’, the right-hand side of (OCM) is vacuously satisfied since the antecedent ‘T is true (on its actual interpretation)’ of the embedded conditional is necessarily false. So if T is necessarily false, whatever one puts for ‘\(F\)’, (OCM) implies that T is committed to \(F\)s.
It is worth stressing that the point does not assume that the result that necessarily false theories are maximally committed is implausible; indeed, we could make essentially the same point without appeal to that result. For instance, we might add to \(\hbox {T}_{\mathrm{UM}}\) its standard modal logical consequence ‘necessarily, if no two objects compose, then any two objects compose’, which has to be assumed false if we are to maintain that \(\hbox {T}_{\mathrm{NM}}\) does not entail that any two objects compose and accordingly is not committed to composite objects. Then to decide whether \(\hbox {T}_{\mathrm{NM}}\) is committed to composite objects, we need to assume either the falsity of it, or the falsity of \(\hbox {T}_{\mathrm{UM}}\).
Thanks to an anonymous referee for pressing me on this.
One might wonder if the problem can be circumvented if one assumes that in order not to beg the question against a theory, it is sufficient to consider it an epistemic rather than a metaphysical possibility. (This idea was suggested to me by an anonymous referee.) Unfortunately, I do not think that this will ultimately help. In the case at hand, a full answer to what the theories are committed to must be based, among other things, on a premise that ascribes metaphysically necessary falsity to one of the theories—call that theory T. Now suppose T is an epistemic possibility for me, so that for all I know, T may be true. Then presumably for all I know, T may not be metaphysically impossible. But if nothing I know rules out the metaphysical possibility of T then I cannot appropriately determine T’s commitments by making use of the premise that T is metaphysically impossible.
As the subject matter of the toy theories here compared, we may take the question under what conditions some objects compose a further one; \(\hbox {T}_{\mathrm{NM}}\) offers the more parsimonious answer to that question.
See e.g. the explications of Quinean formulations offered in Cartwright (1954) and (Rayo (2007), §2.1), as well as the criterion in terms of a priori entailment in Michael (2008). As argued by e.g. Cartwright (1954) and Parsons (1967), Quine’s own insistence that ontological commitment is an extensional notion, belonging to what he termed the theory of reference (cf. Quine 1961, p. 130f), threatens to leave him with a criterion that fares even worse than (OCM). Here is one way to see the point. If commitment is extensional, then if a theory is committed to \(F\)s, and all and only \(F\)s are \(G\)s, then it is committed to \(G\)s. In particular, if there are no \(F\)s, it is committed to unicorns, sets that are not sets, and more generally self-distinct \(G\)s for arbitrary ‘\(G\)’. So if a theory says there are \(F\)s, then in order to work out what it is committed to, I need to decide whether there are indeed \(F\)s. If I am to choose between the theory in question and a competing one saying that there are no \(F\)s, I cannot do so in a non-question-begging way. In contrast to the case of (OCM), here it is not even required that the theories have their status as true or false as a matter of metaphysical necessity, but they may have it contingently.
Here and in what follows, I assume as correct the view that disagreements over matters of logic are not merely verbal disagreements, and that principled, rational debate about (theories employing) competing logics is possible. Thus, I assume, for instance, that when Graham Priest utters a sentence of the form ‘\( p \,\, \& \,\, \lnot p\)’ with sincere assertoric intent, he asserts the very claim that is rejected by a classical logician when he utters with sincere assertoric intent the corresponding sentence of the form ‘\( \lnot (p \,\, \& \,\, \lnot p)\)’. So on the view I assume to be correct, the theories \(\hbox {T}_{\mathrm{PARA}}\) and \(\hbox {T}_{\mathrm{CLASS}}\) really do employ different logics that are in competition with each other, and are not just addressing slightly different topics, talking past each other, as it were. For a detailed defence of that view, see e.g. (Williamson (2007), Chap. 4).
For instance, Priest (2006) advocates a paraconsistent set theory that includes supposedly true contradictions.
As the subject matter of the theories we may take the question what set-like objects there are, so our question is which offers the more parsimonious answer to that question.
Two exegetical remarks: Peacock sometimes seems to claim that (OCM) does not render choice between theories impossible in the cases at issue. Nothing he says seems apt to support this claim. The best interpretation of his view therefore seems to be the one assumed above, on which choice based on ontological commitment is conceded to be impossible, but in some sense choice based on ontology is nevertheless possible. Peacock also at times speaks of the commitments we would recognize were the theory true rather than the commitments we would recognize were we to think that the theory is true. I assume that the latter is intended. Generally speaking, whether a theory is true has no obvious implications for what we think about commitment, whereas what we take to be true does often have an impact on what we take theories to be committed to. Moreover, on standard accounts of counterfactuals, if a theory T is necessarily false, every instance of ‘we would recognize T as committed to \(F\)s if T were true’ is vacuously true. If so, determining what we would recognize a theory as committed to were it true turns out problematic in a similar way as determining what it metaphysically entails.
Although if T explicitly asserts a contradiction, and a rival T* explicitly asserts that one strictly cannot accept theories containing outright contradictions (and that counterpossibles are vacuously true), it might be that unless T* is false, every instance of ‘I would take T to entail the existence of \(F\)s, were I to accept T’ would be vacuously true, and many of these would thus probably be question-begging in the relevant context.
Thanks here to an anonymous referee.
Thus, Peacock—quite plausibly, it seems to me—considers it a desideratum on a criterion of ontological commitment that it reveal ‘what ontology we ought to adopt commensurate with some theory we do in fact accept’ (Peacock 2011, p. 81).
What if there is no such coherent understanding of the phrase? In that case, I think we may plausibly conclude that the theories in question actually are strictly incomparable. If so, it does not count against our proposal that it renders them incomparable.
Might it not be argued, however, that (OCL*) is entailment-based after all, because the notion expressed by ‘includes a logic L such that on L, it logically entails’ is itself a notion of entailment? Suppose this is so. What is important for my purposes is merely that the latter notion is different in kind from the notions of logical/analytical/metaphysical/... entailment, which seems undeniable. If nevertheless, all the notions are notions of entailment, I may simple use different terminology to draw the intended distinction. Thus, we may call a notion of entailment internal iff, for some notion of entailment we shall express by ‘entails*’, the notion is defined by: T entails sentence \(S\) iff T includes a theory of entailment* on which T entails* \(S\), and call a notion of entailment external iff it is not internal. Then the notion of entailment on which my (OCL*) is based is an internal notion of entailment, whereas the notions on which (OCL) et al are based are all external notions of entailment. My proposal, therefore, while entailment-based, is not external-entailment-based, and this feature of the proposal is essential for the solution to the problem of incomparability it provides. Readers wishing to count the notion of a theory’s including a logic on which it entails some sentence a notion of entailment may therefore simply qualify relevant occurrences of ‘entailment-based’ in the subsequent sections by ‘external’. Thanks to an anonymous referee for pressing me on this poin.
This stipulation has the admittedly odd-sounding consequence that {‘\(p\)’} does not quasi-explicitly answer the question whether \(p\), since it does not include an account of logical consequence. We could easily avoid this result by adding ‘it includes a sentence meaning \(p\) or meaning not-p’ as a second disjunct to the definiens. Since it is not my aim to capture or approximate any ordinary meaning of ‘quasi-explicit’, but use the term merely as a partly suggestive label for a purely technical notion, I shall stick to the definition above.
Strictly speaking, the left-hand side of the biconditional should be something like ‘a set of sentences T is ontologically committed to \(F\)s qua explicit theory’. I shall keep using the less cumbersome formulation above which may be read as shorthand for the more strictly adequate reformulation.
Note that the subject matter-relativity of (OCO) may even help explain some data concerning ascriptions of commitment. For instance, in most contexts, most philosophers will be happy to say that set theory is ontologically committed to abstract objects. Nevertheless, it also seems tempting to say that as a piece of pure mathematics, standard set theory does not carry any distinctive metaphysical commitments. (OCO) allows us to explain this kind of variation as a variation in what subject matter is at issue—pure mathematics in the one case, and a more comprehensive, partly metaphysical account of sets in the other.
Suppose that the relevant differences in commitment are as follows. The unique best extension of \(\hbox {T}_{1}\) is committed to \(F\)s, whereas one best extension of \(\hbox {T}_{2}\) is committed to \(G\)s, and the only other best extension of \(\hbox {T}_{2}\) is committed to \(H\)s. Then on the first condition, we have to ask whether a commitment to \(F\)s is more or less substantial than a commitment to \(G\)s-or-\(H\)s. (This assumes that both best extensions are committed to \(G\)s-or-\(H\)s, which is guaranteed if both include a logic validating or-introduction.) On the second condition, we have to ask how a commitment to \(F\)s compares to both a commitment to \(G\)s and a commitment to \(H\)s.
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Acknowledgments
The earliest predecessor to this paper was written just over five years ago. Very many people provided very valuable feedback, criticism, and encouragement over the various stages of development the paper has since undergone. I thank all of them, and especially John Divers, Joseph Melia, Howard Peacock, Benjamin Schnieder, Moritz Schulz, Jason Turner, Robbie Williams, as well as three anonymous referees.
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Krämer, S. Implicit commitment in theory choice. Synthese 191, 2147–2165 (2014). https://doi.org/10.1007/s11229-013-0388-8
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DOI: https://doi.org/10.1007/s11229-013-0388-8