Analysis and Its Paradoxes

Abstract

Consider the following proposition.

(1) To be an instance of knowledge is to be an instance of justified true belief not essentially grounded in any falsehood.

If true, (1) illustrates an important type of philosophical analysis. For convenience of exposition, I will assume that (1) is a correct analysis. But nothing in my views about analysis hinges upon this. To suppose that (1) gives an analysis, however, leads to the notorious problem that philosophers nowadays are apt to call “the” paradox of analysis, as follows. If the property of justified true belief not essentially grounded in any falsehood is the analysans ofthe property of knowledge, it would seem that they are the same property, and hence that

(2) To be an instance of knowledge is to be an instance of knowledge would have to be the same proposition as (1). But propositions (1) and (2) seem clearly diverse; for example, (2) is trivial (in the sense that understanding it entails believing it), while (1) can be informative and in fact was only recently arrived at by philosophers.

Classical writings on analysis suggest another paradox of analysis (see, e.g., Moore 1963b). Consider this proposition.

(3) An analysis of the property of being a brother is that to be a brother is to be a male sibling.

If (3) is true, it would seem that the property of being a brother would have to be the same property as the property of being a male sibling, and that

(4) An analysis of the property of being a brother is that to be a brother is to be a brother

would also have to be true - and in fact would have to be the same proposition as (3). Yet (3) is true and (4) is false.