The a priori poses special problems for empiricism. Mathematics and logic are the best examples we have of knowledge, the most certain and the most precise, yet they do not seem to be based on experience. Propositions such as ‘5 + 2 = 7’ and ‘Nothing can be true and false at the same time’ also appear to be necessary and are true no matter what our experiences are. How can such truths be based on experience? Curiously enough, the a priori also poses a problem for rationalism, since there is no clear account of what it is to be known independently of experience. This chapter will explain some of the approaches empiricists have taken to the problem and why they have been led to skepticism about the very existence of a priori knowledge. But first we must become clearer about the basic distinctions on which the debate is based.

Necessity, the analytic and the a priori

Necessity and contingency

Necessary truths are propositions whose negations imply a contradiction. That ‘5 + 2 = 7’ is such a proposition. To hold that it does not equal seven, but six or eight instead is contradictory. Similarly ‘Whatever is, is’ cannot be denied without contradiction. If John went to the store, he went to the store. We cannot claim that he did and did not go in the same sense, since this is contradictory.