A definition of something specifies what it takes to be that sort of thing. (A definition of a word specifies the meaning of the word, which in turn specifies what it takes for something to fall in that word's extension: for the word to apply truly to it.) We usually assume that specifying "what it takes to be a certain sort of thing" means specifying that kind or individual's essence , or at least necessary and sufficient conditions for being that (kind of) thing. The problem is that many, probably most, of our words and concepts can't be defined in this way, not just because they are vague, as 'bald' is (it seems that there's no precise number of hairs that marks the boundary betwen being bald and not bald), but because there is no one quality that all things of that kind share (Wittgenstein argued in the Philosophical Investigations that the concept of a game is like this). The question of what kinds of definitions these sorts of words and concepts can have is a hard one, which philosophers and...

Basically, concepts are the components of our thoughts, which enable us to think about objects and properties in the world. Most philosophers agree that two concepts F and G are distinct if (and only if) one could believe (desire, hope, etc) that a is F without also believing that a is G , even if everything that is (or even could be) F is also G. (This is Frege's 'criterion of cognitive significance'.) Concepts are also the sorts of things that can be misapplied: I can think that a is F even though it isn't. Many (most?) philosophers also think that concepts don't just involve representing things in the world, but also involve at least some connections with other concepts: there are at least some inferences you should be prepared to make if you believe that this is a saxophone , say; although there might not be any single determinate set of inferences you would need to accept. Some philosophers think of concepts as abstract entities, perhaps like word meanings; these concepts...