ABSTRACT
This chapter concerns the nature of a priori statements, e.g. mathematical and logical propositions, and in particular, it critically discusses Mill’s, Kant’s and Frege’s accounts of them. However, before I turn to considering them, a prior question to consider is: why are a priori statements an issue anyway? A priori statements are important for a number of reasons. First, since logic plays a central role in Frege’s and Russell’s accounts of natural language meaning, we need an account of how a priori statements (which include logical statements) are meaningful. Second, logical and mathematical statements are important to literal, representational language – they are pervasive in scientific discourse and ordinary language – so again, determining how they are meaningful will be important to understanding how scientific and ordinary language are significant. Third, we have just introduced an empiricist theory of meaning (and later we will consider another, logical positivism), and if such empiricist theories are to account for the meaning of all representational language, then they need to provide an account of how logic and mathematical statements are meaningful and constitute knowledge. However, traditionally a priori statements pose a problem for empiricists since empiricism holds that all knowledge (and meaning) is based on, i.e. justified by, experience, but a priori propositions precisely are not based on experience. Thus, empiricism seems to imply, unhappily, that a priori statements do not constitute knowledge (and even that they are not meaningful).
