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Knowledge of Necessity: Logical Positivism and Kripkean Essentialism

  • Stephen K. McLeod (a1)

By the lights of a central logical positivist thesis in modal epistemology, for every necessary truth that we know, we know it a priori and for every contingent truth that we know, we know it a posteriori. Kripke attacks on both flanks, arguing that we know necessary a posteriori truths and that we probably know contingent a priori truths. In a reflection of Kripke's confidence in his own arguments, the first of these Kripkean claims is far more widely accepted than the second. Contrary to received opinion, the paper argues, the considerations Kripke adduces concerning truths purported to be necessary a posteriori do not disprove the logical positivist thesis that necessary truth and a priori truth are co-extensive.

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1 A.J. Ayer, Language, Truth and Logic (2nd ed., London: Victor Gollancz, 1946), 16–8.

2 Ibid., 17–8.

3 Ayer's remarks, which are explicitly anti-psychologistic, put the emphasis on how being a priori is a feature (albeit an epistemic, and therefore relational, feature) of a proposition rather than of our actual knowledge of it. We know that for every tautology, it is true. However, it's not the case that for every tautology, we know that it is true. There are tautologies which we do not know to be tautologies, since they have never been entertained in thought and there are tautologies we never could entertain given the limits of our finite minds. Ayer remarks (ibid., 18) that ‘it is common ground that deductive reasoning may lead to conclusions which are new in the sense that one had not previously apprehended them’. He holds (loc. cit.) that whenever it is true that p entails q, this is an analytic, and thus tautologous, matter and that it is thereby a priori that p entails q. Ayer's comments suggest that it is a priori even if no-one has entertained it. Further ‘a priori’ and ‘analytic’ are, in Ayer's taxonomy, co-extensive terms (ibid., 16). A priori propositions are necessary (ibid., 17). This is not a suggestion that necessity is a mere mark of the a priori. Rather, it is a claim that a proposition is necessary if and only if it is a priori. Whether a proposition p is analytic, a tautology, a priori or necessary in no way depends on our actually knowing that p. Rather, it concerns how the proposition would have to be known if it were known at all. When Ayer affirms (ibid., 72, cf. 85–6) that ‘the truths of mathematics and logic appear to everyone to be necessary and certain’ he cannot, in respect of certainty, be talking about all such truths, but only those which we believe.

4 C. Hughes, Kripke: Names, Necessity, and Identity (Oxford: Oxford University Press, 2004), 88–9, canvasses various ways in which ‘a proponent of the link between necessity and apriority’ might make their case. These are: (i) by claiming that every necessary truth is (in fact) known a priori; (ii) by claiming that every known necessary truth is known a priori; (iii) by claiming that every knowable necessary truth is known a priori; (iv) by claiming that every known necessary truth is knowable a priori. None of these, however, captures the thesis I attribute to Ayer and with which I agree. This is that when p is a necessary truth, for it to be known that p it is a requirement that at the point of entry to the stock of our knowledge, p is known a priori by someone. This differs from Hughes's mooted approaches in that it is a genetic thesis about the epistemic community, not about individual agents. It also differs in that the modality is stronger than in (iii) or (iv). The objections to (i) and (ii) are ones with which, as we saw in the previous footnote, Ayer agreed – thus, neither (i) nor (ii) is contained in the logical positivist thesis. The objection to (iii)/(iv) is a common one: that some necessary truths, such as that Hesperus is Phosphorus, are not knowable (by us) a priori. The debate ought then to centre on whether such claims are really necessary truths at all: see section II in the main text.

5 For discussion, see S.S. Chakravarti, ‘Kripke on Contingent A Priori Truths’, Notre Dame Journal of Formal Logic 20 (1979), 773–6 and H. Geirsson, ‘The Contingent A Priori: Kripke's Two Types of Examples’, Australasian Journal of Philosophy 69 (1991), 195–205.

6 See G.W. Fitch, ‘Are there necessary a posteriori truths?’, Philosophical Studies 30 (1976), 243–7; P. Tichý, ‘Kripke on Necessity A Posteriori’, Philosophical Studies 43 (1983), 225–41; N.U. Salmon, Frege's Puzzle (Cambridge, Mass.: MIT Press, 1986); S. Soames, Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity (Oxford: Oxford University Press, 2002). On the position I defend here, Kripke's purported cases of the necessary a posteriori emerge as in fact contingent and a posteriori. For Soames (ibid., 235–40, 278–9), since names refer directly, an utterance of the sentence ‘Peter Hempel is Carl Hempel’ semantically expresses the necessary a priori proposition that Carl Hempel is Carl Hempel but may, in the context of utterance, be uttered so as to assert a proposition that contains descriptive content, is contingent and is a posteriori (ibid., 237). While in harmony with Soames's conclusions about the relationships between alethic-modal status and epistemic status, on my account (if there are propositions at all) even the former proposition is contingent and a posteriori. Unlike the arguments of Fitch, Tichý, Salmon and Soames, the argument I advance aims to remain neutral about the existence of propositions. On that question, see S.A. Kripke, Naming and Necessity (Oxford: Blackwell, 1980), 21 and G.W. Fitch, ‘On Kripke and Statements’, Midwest Studies in Philosophy 28 (2004): 295–308.

7 In Kripke's examples no iterated modalities are involved. J.A. Benardete, Metaphysics: The Logical Approach (Oxford: Oxford University Press, 1989), 153–4, indicates a simpler, non-Kripkean, argument for the necessary a posteriori. This argument does use iterated modality. From an empirical premise, p, we may infer, by possibility introduction, ⋄p. But then, by the S5 principle that whatever is possible is necessarily possible, we get □⋄p. So if being a posteriori ‘spreads’ from premise to conclusion, as Kripke takes it to in his epistemology for a posteriori necessity, then it is a posteriori that □⋄p. I will not deal with Benardete's argument any further here. For the sake of caution, my defence of the claim that if p is necessary then p is a priori should be read as being restricted to cases in which p does not already contain a modal operator.

8 S.A. Kripke, ‘Identity and Necessity’ in M.K. Munitz (ed.) Identity and Individuation (New York: New York University Press, 1971), 135–64, 137.

9 For further details, see my ‘How to Reconcile Essence with Contingent Existence’, Ratio 21 (2008).

10 Kripke, ‘Identity and Necessity’, 86 nt 11.

11 For a closely related objection, see K. Fine ‘Essence and Modality’, Philosophical Perspectives 8 (1994), 1–16, 7.

12 The view I call ‘de re modalism’ is defended by D. Wiggins in ‘The De Re “Must”: a Note on the Logical Form of Essentialist Claims’ in G. Evans and J. McDowell (eds) Truth and Meaning: Essays in Semantics (Oxford: Oxford University Press), 131–160 and in Sameness and Substance (Oxford: Blackwell, 1980). It is also defended by C. McGinn Logical Properties (Oxford: Oxford University Press, 2000), though there are differences between his position and that of Wiggins.

13 G. Forbes, ‘Melia on Modalism’, Philosophical Studies 68 (1992), 57–63, 57. Cf. J. Melia, Modality (Chesham: Acumen, 2003), 81, a critic of modalism who writes that for the modalist the ‘correct logical form of “It is possible that P” is simply ⋄P . … modal truth is not to be articulated or understood in terms of possible worlds or possibilia’. See Chapter 4 of Melia's Modality and the references there for further details on (standard) modalism.

14 Such a language has been constructed: see e.g., Wiggins, ‘The De Re “Must”'. My concerns, here, however, are not with formal language.

15 D. Wiggins, Sameness and Substance, 107; Sameness and Substance Renewed (Cambridge: Cambridge University Press, 2001), 112.

16 See Wiggins, ‘The De Re “Must”’. For a related argument, see my ‘How to Reconcile Essence with Contingent Existence’.

17 According to McGinn, Logical Properties, 80: ‘Syntactically, we can … employ modal words as if they were sentence operators, functioning like negation in classical logic, but semantically they are copula modifiers always.’

18 ‘The De Re “Must”'.

19 Compare the observations of McGinn, ibid., 75 nt 4 and the analogy he draws with the case of negation.

20 Note that many of the claims the de re modalist takes to be de dicto modal will be, for Kripkeans, de re modal. This is because of the divergent accounts of the de re/de dicto distinction in play. (Kripkeans adopt the standard account of the de re/de dicto distinction.)

21 Thanks to an anonymous referee for an earlier paper for an example (‘Necessarily, if there is water on a planet then there are oxygen atoms on that planet.’) on which I base this example. The example I actually use involves the necessity of identity rather than the essentiality of material composition. The example used is chosen for its relative simplicity: the philosophical points at issue are not affected.

22 In connection with this, Wiggins (Sameness and Substance, 106–11; Sameness and Substance Renewed, 113–6) specifically argues against a sentential reading of the necessity of identity and offers instead a de re modalist reconstruction of the Barcan proof of the necessity of identity. See also my Modality and Anti-Metaphysics (Aldershot: Ashgate, 2001), 50–3.

23 Although not a de re modalist, N.U. Salmon, ‘The Logic of What Might Have Been’, Philosophical Review (1989) 98: 3–34, e.g., 13, is an example of an essentialist who views metaphysical necessity as distinct from logical necessity.

24 I acknowledge the support of Spanish Ministry of Education and Science research project HUM2006-04955/FISO, led by Professor Juan Vázquez of the Department of Logic and Moral Philosophy, University of Santiago de Compostela. Thanks to my fellow participants in the project for comments on a presentation of this work in June 2007.

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