A Priori Truths and Things-in-Themselves

Abstract

This chapter was first presented as a response to the question, ‘Are mathematical and logical truths synthetic a priori?’ The outlines of the partial answer that I can offer to this question have beea argued for on other occasions.1 In the present chapter, I shall first summarize the relevant aspects of the answer. The question was initially posed by Kant, and most existing discussions of it refer in so many words to Kant On pain of gross historical distortion, one therefore cannot help discussing the question in Kantian terms. Now the examples of mathematical reasoning Kant mentions and discusses are typically reproducible in first-order logic. Hence any historically accurate reading of the question turns it into a problem concerning the status of logical rather than mathematical truths. Again, by’ synthetic truths’ Kant did not mean truths that do not turn solely on the meanings of the terms they contain, as a contemporary philosopher is likely to mean. I have argued that the best explication we can offer of Kant’s notion of an analytic truth (in first-order logic) is what I have called surface tautology. Interpreted in this way, Kant’s doctrine of the existence of synthetic a priori truths in what he took to be mathematics turns out to be correct in an almost trivial fashion, for there are easily any number of valid (and provable) sentences of first-order logic that are not surface tautologies.