Abstract
This paper argues for and explores the implications of the following epistemological principle for knowability a priori (with ‘\(\mathcal{K}_\mathcal{A}\)’ abbreviating ‘it is knowable a priori that’).
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(AK) For all ϕ, ψ such that ϕ semantically presupposes ψ: if \(\mathcal{K}_\mathcal{A}\phi, \,\mathcal{K}_\mathcal{A}\psi .\)
Well-known arguments for the contingent a priori and a priori knowledge of logical truth founder when the semantic presuppositions of the putative items of knowledge are made explicit. Likewise, certain kinds of analytic truth turn out to carry semantic presuppositions that make them ineligible as items of a priori knowledge. On a happier note, I argue that (AK) offers an appealing, theory-neutral explanation of the a posteriori character of certain necessary identities, as well as an interesting rationalization for a commonplace linguistic maneuver in philosophical work on the a priori.
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Notes
In the standard λ-notation, ‘:’ indicates partiality. For example, λ x:F(x)·x is a partial identity function, mapping all and only those x’s such that F(x) to themselves.
There may be cases where α and ψ meet condition (SP1) or (SP2) without α presupposing ψ. To pick something at random, perhaps it is a condition on a sentence ϕ being evaluable for truth that \([\![{\cdot} ]\!]\) is a compositional function from sentences to characters (in particular, that \([\![ {\phi} ]\!]\) is defined and computable compositionally). We would not generally want to say that ϕ presupposed that there is such a compositional interpretation function. Though such cases may be relevant to the possibility of a priori knowledge (indeed, I think they probably are), they are not really my focus here. My point in this paper is to make the case that much philosophical discussion of the a priori has failed to notice the epistemological significance of things that are accurately described as semantic presuppositions.
Except in cases of “local presupposition satisfaction.” See Sect. 4.3 below.
I think it is fairly clear they satisfy standard linguistic tests for presupposition (see, e.g., the data in Sect. 4.4). So I will here argue only that (SP2) holds for them.
This definition is revised slightly in Sect. 4.3.3.
Examples like this are, of course, not the most solid basis for establishing a general claim like (7). If the reader does not find the arguments given for the plausibility of (7) persuasive, I invite him or her to restrict the scope of the claim to cases where it seems to him or her to hold. Such a reader, if s/he is inclined to accept the possibility of a priori knowledge in any case, will, I expect, agree that the applications in this paper in which some sentence ϕ is seen to (SP1)-presuppose ψ are such that \(\mathcal{K}_\mathcal{A}\square(\phi \rightarrow \psi).\) This sort of reader will then be able to appreciate the uses to which (AK) is put here, even while suspending judgment about the extent of further applications of the principle in cases involving different kinds of (SP1)-presupposition. Similar remarks apply to my arguments for (11) below.
Compared to the rather direct argument that (AK) follows from (SP1), this is relatively convoluted. But the complications are necessary: although (5) (SP2) presupposes zip, it’s not knowable a priori that \(\square\) ((5) \(\rightarrow \hbox{\textsc{ZIP}}\)) (because it is false that \(\square\) ((5) \(\rightarrow \hbox{\textsc{ZIP}}\)), since there is a possible world where Julius, the actual inventor of the zip, is dead in 1909 and zips do not exist). It is, however, as I argue below, plausibly knowable a priori that, if Julius died in 1909, there must have been a unique inventor of the zip.
Although some deny that \(\{\phi, \, must\,(\phi \rightarrow \psi)\} \models \psi, \) there are good (ostensibly a priori) arguments in favor of it. For some of these, see von Fintel and Gillies (2012).
Swanson (2006) argues, contra Geurts (1997), that the fact that proper names bear descriptive presuppositions is compatible with a Kripkean semantics for proper names. For an argument in a similar spirit, see directly below. I note in passing that we might also wish to encode the presupposition at the hyperintensional level, so that \([\![{\epsilon}]\!]\) would be defined at c only when \(\epsilon\) designated a unique individual at \(\langle c, w_c\rangle. \) That seems plausible to me, but I will pass over this issue here.
A residual puzzle for the Kripkean is to explain why it cannot be known a priori that \((\kappa \wedge \tau) \rightarrow\) Cicero=Tully. I deal with this in other work.
Russellianism about definite descriptions does not avoid these results, since Russellianism, if anything, makes it more plausible that \(\mathcal{K}_\mathcal{A} \square[(13)\rightarrow(15)]\). According to the Russellian, (13)’s meaning is given by a conjunction, one of whose conjuncts is (15).
It is sometimes suggested that conditionals presuppose that their antecedents are possible with respect to the conversational context. Since this will not count as a semantic presupposition, we can safely ignore it.
See Heim (1991). It’s generally agreed that any presupposition of a conditional’s antecedent must be borne by the entire conditional (i.e., it projects to the entire conditional).
For simplicity, this formulation (and much of my subsequent discussion) deliberately ignores cases where presuppositions are satisfied, in whole or in part, by induced contexts, rather than by syntactic material.
A: France might have exactly one king.
B: Well, then the King of France is male.
[Modal Subordination; cf. Roberts (1989)]
France has at least one king. If it has no more than one, the King of France is male.
[Partial Local, Partial Global Satisfaction]
In neither case does the speaker of the sentence in which the definite noun phrase ‘the King of France’ appears presuppose that France has a unique king. Nevertheless, in neither case is the presupposition either globally or locally satisfied. These are well-attested facts that I am happy to grant.
Does it affect my position on the epistemological status of conditionals? It does not. The proposition normally expressed by the speaker’s sentence (‘the King of France is male’ or ‘If France has no more than one king, the King of France is male’) is not knowable a priori (nor, I think, would we even wish to ascribe such knowledge, a priori or a posteriori, to the speaker).
It is true that, in such cases, an individual does seem to be hitting on a specific item of a priori knowledge, namely:
If France has exactly one king, the King of France is male.
But my view on the epistemological status of conditionals survives intact: the thing that the speaker can know a priori cannot itself have any semantic presuppositions that are not knowable a priori. The speaker cannot know a priori that the King of France is male, or that: if France has no more than one king, the King of France is male. What the speaker can know a priori is a conditional where the antecedent locally satisfies the presupposition expressed by the consequent. (It follows that such cases do not represent counterexamples to (E1) and (E2) below.) Thanks to an anonymous reviewer for pressing me on these points.
This mirrors the standard semantics for sentences of forms \(\ulcorner \square a=a \urcorner\) and \(\ulcorner \square P(a) \urcorner, \) where a is a singular term and P a predicate. These sentences are generally regarded as true iff \(\ulcorner {a=a}\urcorner\) and \(\ulcorner {P(a)} \urcorner\) are, respectively, true at every world where a refers (not at every world simpliciter).
Per the usual syntactic convention, t i is a trace recording movement of the co-indexed noun phrase at logical form.
The explanation for this is intuitive enough—when we use a definite noun phrase referentially, we presuppose that there is something for it to designate or refer to.
Conditional introduction means that the discourse referent does not become part of the basic “structure” we use to represent or keep track of the conversational score. So long as ‘the king of France’ is read de dicto, utterances of (32) and (33) neither require nor make it the case that it is common ground that there is a unique king of France. This sort of device for generating anaphorically bound readings for such expressions is familiar from the Discourse Representation Theoretic treatment of Donkey Anaphora.
See, e.g., Horwich (2000) for a line of attack similar in spirit to the one developed here.
I’m ignoring the semantic presupposition of ‘Jack the Ripper’ for simplicity’s sake.
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Acknowledgments
For discussion of the ideas in this paper, I am grateful to Anders J. Schoubye, Eduardo García-Ramírez, Ofra Magidor, Eric Swanson, Ian Proops, to audiences at Oxford and Arché, and to an anonymous referee for this journal.
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Charlow, N. Presupposition and the a priori. Philos Stud 165, 509–526 (2013). https://doi.org/10.1007/s11098-012-9965-9
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DOI: https://doi.org/10.1007/s11098-012-9965-9