Thursday, January 08, 2009
How mysterious is Platonism?
Arithmetical Platonism is supposed to be prima facie suspect because how, it’s asked, could we have arithmetical knowledge if the objects of that knowledge are in a world apart from us, a timeless world of Platonic objects, with which we cannot interact causally? I reply by wondering, how strange are abstract objects? You have just been reading this, for the obvious example. What have you been reading? You have been reading sentences. You look at the physical instances of these words, but you see the words, you read the words, and as you do so you are (hopefully) thinking about the thoughts expressed by means of them. So, there are, in the physical world around you, those physical instances of the shapes of (written modern English) words, and there are in your mind those thoughts; so, where are the sentences? What are the sentences? Sentences are made of words, and words are parts of a language (i.e. modern British English). They can be spoken or written, and can sometimes be spelt in different ways. Furthermore they have a meaning, a sense, and they have it essentially. The mere shape of a word is not a word, no more than meaningless strings of letters are words. Words, it seems, are abstract objects (I’m not entirely sure about that, or about what abstract objects are, so I’d welcome corrections) and you’ve just been reading some words of mine (and I’ll add that words can be true, insofar as they describe the world sufficiently accurately, or not, in case anyone wants to argue that thoughts and not words are truth-bearers:)