Epistemic Two-Dimensionalism and the Epistemic Argument

Abstract

One of Kripke's fundamental objections to descriptivism was that the theory misclassifies certain a posteriori propositions expressed by sentences involving names as a priori. Though nowadays very few philosophers would endorse a descriptivism of the sort that Kripke criticized, many find two-dimensional semantics attractive as a kind of successor theory. Because two-dimensionalism needn't be a form of descriptivism, it is not open to the epistemic argument as formulated by Kripke; but the most promising versions of two-dimensionalism are open to a close relative of that argument.

Notes

¹See, among many other places, McDowell [1977] and Evans [1981].

²For defence of the former, see Plantinga [1978]; for defence of the latter, see Dummett [1981]; Sosa [2001]. For criticism of these approaches, see Soames [1998, 2002]; Caplan [2005].

³And, obviously, we can extend the definition to the case of a pair of a particular object and a property. A particular n and property F are independent iff (1) n's existence is compossible both with F's being instantiated and with F's being uninstantiated, and (2) n's existence does not a priori entail either that F is instantiated, or that F is uninstantiated.

⁴This principle is perhaps a bit more controversial than the others, since some think that we can know a priori of our own existence. If this were right, the principle would be true but vacuous, since given the above definition of independence nothing would be (for me) independent of my existence, since every proposition would a priori entail that I exist. I assume in what follows that we can't know a priori of our own existence, though almost all of the argument would survive giving up this assumption.

⁵Here and in what follows, claims about a priori knowledge could be recast in terms of a priori justification without affecting the argument.

⁶Given, of course, the above provisos about independence.

⁷The primary/secondary proposition distinction lines up with the diagonal/horizontal proposition distinction of Stalnaker [1978], the distinction between deep and superficial necessity of Evans [1979], and the A-intension/C-intension distinction in Jackson [1998], though these authors differ as regards both the nature of primary intensions and their proper theoretical role.

This is also a good place to dispel confusion about an aspect of the terminology used in this paper: the talk about sentences being necessary and a priori. Many will be inclined to object that the proposition expressed by a sentence rather than the sentence itself is the fundamental bearer of necessity and a prioricity. The problem in the present context is that the nature of the fundamental bearers of these modal and epistemic properties is part of what is up for grabs in this debate, with two-dimensionalists wanting to replace talk about ‘the proposition expressed by a sentence’ with talk about the primary and secondary intensions of the sentence. But both two-dimensionalists and their opponents can agree that we can speak of sentences being a priori or necessary in a derivative sense, even if they disagree about how this is to be analysed. So the talk about sentences being a priori and necessary can be thought of as an attempt to find a non-prejudicial way to state the relevant issues.

⁸Here, as is standard, I am identifying the secondary intension of a sentence with either what Russellians would call the proposition semantically expressed by that sentence or the intension (structured or not) determined by that proposition.

⁹A relatively minor difference here stems from the fact that Kaplan's characters were functions from contexts to functions from circumstances of evaluation to extensions. Contextual intensions are functions from contexts to extensions—the extension that would be delivered by the value of a Kaplan character if the circumstance of evaluation is the context. I take it that this is the view Chalmers has in mind when he says ‘a primary intension is straightforwardly derivable from a character and vice versa’[Chalmers 1996: 356–6, n. 25]].

¹⁰This problem is discussed in §2 of Chalmers [2006a]; García-Carpintero [2006] argues that the problem is not fatal to contextual two-dimensionalism. This problem of overgeneration of a priori truths is, obviously, akin to the problem with descriptivism Kripke identified in his epistemic argument. Among the most difficult further problems faced by contextual two-dimensionalism is that in order to respect standard examples of the necessary a posteriori, the contextual two-dimensionalist must treat names and natural kind terms as indexical, rigidified descriptions. For an in-depth discussion of the problems with this view of names and kind terms, and critique of various versions of contextual two-dimensionalism, see Soames [2005]).

¹¹Chalmers [2002, 2004, 2006a, 2006b, ms.].

¹²Chalmers [2004: 177–8].

¹³See, for example, the discussion of Ramsey intensions in Chalmers [2006a: §3.3].

¹⁴Though not everyone; for a view which denies the transitivity of a priori entailment, see §V of Soames [2007].

¹⁵Schroeter [2005].

¹⁶As will become clear, there's also an interesting connection between the present argument and the argument that various forms of externalism entail that we have a priori knowledge of the existence of natural kinds like water. See, among other places, Boghossian [1997].

¹⁷This follows the discussion in Chalmers [2006a: §3.7].

¹⁸Could the two-dimensionalist let ‘Mick Jagger exists' lack a truth-value, rather than be false, at scenarios at which ‘Mick Jagger’ lacks a reference? This does not look like a promising reply, for two reasons. First, we want ‘Mick Jagger does not exist’ to be epistemically possible, which requires its being true in at least one scenario. But if this is true in at least one scenario, then presumably it is true at all scenarios at which the name lacks a reference. Second, as we'll see below, the relevant point can be made without using existential claims involving a name.

¹⁹Thanks to Ali Kazmi for pointing out that the example can be put in this way.

²⁰Thanks to David Chalmers for pointing this out.

²¹Another way to ‘stipulate away’ the possibility of divided reference is to conjoin (5) with the claim ‘There is at most one Mick Jagger’. The resultant conjunction still seems, contra the epistemic two-dimensionalist, to be epistemically possible.

²²Chalmers emphasizes that indexicals might be relevant to the assignment of reference to subsentential expressions with respect to a scenario in Chalmers [2006a: 93–4].

²³Here I'm assuming that I can't stand in relations to things without existing; this would be denied by someone who endorses presentism without ‘serious presentism’, or actualism without ‘serious actualism’. Thanks to Ben Caplan for pointing this out.

²⁴Recall when indexical properties were introduced above, I suggested two ways to modify the argument against the two-dimensionalist: split the relevant indexical properties, or stipulate that there are no relevant indexical properties in the scenarios in question. (17) presupposes the latter way of running the argument; but we could generate a similar example just as easily using the ‘split the indexical properties' form of argument. Suppose again that we split the relevant indexical properties of Mick Jagger into two equally weighted conjunctions of properties, I ₁ and I ₂. Then it looks like the two-dimensionalist must regard the following as a priori:

(Mick Jagger is F&I ₁) →  ((Keith Richards is G&I ₂∨ Keith Richards is H&I ₂) →  Keith Richards is H&I ₂)

This, like (17), is a violation of (D).

²⁵Chalmers [2006a].

²⁶It is worth noting in this connection that the condition on scenarios given by the consequent of (4) and its descendants is a sufficient condition for the name to lack a reference, and not a necessary and sufficient condition. If it were a necessary and sufficient condition, then one could use this condition to formulate a description which picked out the same object as the name with respect to every scenario; so the assumption that we can provide a necessary and sufficient condition would, in a way, build in the assumption that the epistemic intensions of names are equivalent to descriptions. But in giving merely sufficient conditions for the name to lack a reference we make no such assumption.

²⁷Further, the reply has no real plausibility. Normally, when we acquire knowledge that some object is F, this is a posteriori—we could not have discerned a priori from our previous knowledge of the object that it was, in addition, F—nor could we have known a priori, given the information that the object is F, that it also instantiated those other properties we know it to have. If so, then F is independent of those other properties. But given how commonplace this sort of property independence apparently is, could it really be impossible to split the properties of an object into two independent conjunctive properties which have equal weight in identifying the referent in various epistemic possibilities?

²⁸See Evans [1979].

²⁹See the discussion of deference in Chalmers [2002] and in §III of Schroeter [2005].

There is also a more radical strategy that the epistemic two-dimensionalist might pursue: he might simply give up the idea that names are barred from appearing in the canonical descriptions of scenarios. As noted above, this version of two-dimensionalist semantics will provide no help to those who would like the theory to underwrite inferences from certain sorts of epistemic possibility (conceivability) to metaphysical possibility. I think that there are further problems with this sort of view, but the issues are complex and deserve a fuller discussion than I can provide here.

³⁰I doubt that we get even this result, since I'm not convinced that I understand what I am supposed to be doing when I try to identify Mick Jagger in a scenario. But I grant the point for purposes of argument—and many people do seem to understand what we are supposed to be doing in this sort of case.

³¹Thanks for helpful comments and discussion to Laura Schroeter, Ben Caplan, David Chalmers, Ali Kazmi, Mike McGlone, Casey O'Callaghan, Colin Klein, Joe Levine, Michael Nelson, and the participants in my graduate seminar in the spring of 2007 at Notre Dame, as well as audiences at the Pacific APA of 2008 and at the University of Illinois at Chicago.