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Published online by Cambridge University Press: 01 January 2020
There is a widely held view that the expressions ‘necessary truth’, ‘a priori truth’ and ‘analytic truth’ either express the same concept or, at least, refer to all and only the same items. Philosophers who hold this view, and who are sometimes described as ‘empiricists’, often draw the conclusion that the truths of logic and mathematics, if necessary, are also a priori and are, in some important sense, empty or not about the world. The subject matter of these disciplines, then, is said to differ in a philosophically important way from that of the empirical sciences, such as physics or chemistry. Rationalists, in contrast, have traditionally held that some a priori truths, either of logic or mathematics (or of some other area), are synthetic and, hence, non-analytic: i.e., there are synthetic a priori truths.
1 For example, a recent reviewer for the “London Times literary Supplement,” notes: “Philosophers whose introduction to logical theory was provided by P. F. Strawson's work of that title have for two decades accepted that the necessary, the analytic and the a priori were coextensive, and therefore that the contingent, the synthetic and the a posteriori were likewise coextensive.” (January 10, 1971)
2 In referring to selections of Kant and Blanshara, as well as ones written by Empiricists, Nagel and Brandt point out: “In point of fact, however, most thinkers who have expressed themselves on the subject have maintained that sensory experience (and more generally so-called inductive procedures, involving the generalization of observed connections among sensory data) cannot establish the necessity of any statement. In consequence, the class of necessary statements has usually been held to be coextensive with the class of statements knowable a priori, and this assumption is implicit in all the selections in this chapter.” See: Nagel, Ernest and Brandt, Richard B. Meaning and Knowledge (New York, N.Y.: Harcourt, Brace & World, Inc., 1965).Google Scholar
3 Sloman, Aaron “‘Necessary’, ‘A Priori’ and ‘Analytic’,” Analysis, Vol. XXVI, No. 1 (1965-66), p. 15.Google Scholar
4 See: Woolhouse, R. S. Locke's Philosophy of Science and Knowledge (New York: Barnes and Noble, 1971), p. 176.Google Scholar
5 The examples are given in Kripke's, Saul “Naming and Necessity,” in Semantics of Natural Languages, ed. Davidson, D. and Harman, G. (Dordrecht-Holland, 1971).Google Scholar
6 The example used by Kripke is Goldbach's conjecture that an even number greater than 3 must be the sum of two prime numbers.
7 For a more extensive development of this idea, see: Erwin, Edward “The Confirmation Machine,” in Boston Studies in the Philosophy of Science, Vol. VIII (New York: Humanities Press, 1972), editors, Buck, Roger and Cohen, Robert S..Google Scholar
8 Among others, there is the difficulty alluded to earlier of separating the evidence for a belief from evidence for relevant background beliefs.
9 That cannot be done because there is evidence that improvement is likely to occur in at least that percentage of neurotics in the same period of time even in the absence of treatment, although the exact percentage is controversial. See: Ullman, Leonard P. and Krasner, Leonard A Psychological Approach to Abnormal Behavior(Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1969), p. 44.Google Scholar
10 I have discussed the topics of this paper with a number of people and would like to thank the following for their helpful comments: Lowell Kleiman, Sidney Gendin, Michael Slote, David Benfield, Jamie Benfield, Peter Unger, Lawrence Resnick, Michael Levin and John Robison.
