Ramsey wrote down something like this argument shortly after his visit to Wittgenstein: Hence there must be infinitely many names in our language. But a language in which there were only finitely many names would not be able to represent this possibility. And whether or not there are in fact infinitely many things, we can represent in language the possibility that there are. My language - ‘ the language which I understand' - is fashioned with the primary purpose of saying how the world is and, correlatively, how it is not. īut if that is the case, we might think that the axiom of infinity admits a transcendental proof as follows. ’ presupposes for its significance what we try to assert by saying ‘there are n things'.īy extension the same thing applies to the axiom of infinity, which tries to say that there are ℵ 0 things: this is significant only if it is true. Confirmation that this is the correct interpretation of Wittgenstein's intentions is supplied by one of the remarks he wrote in the margin of Ramsey’s copy of the Tractatus in 1923: Whether an existential quantifier makes sense when interpreted according to Wittgenstein's symbolic convention thus depends on how many names there are in the language that could be substituted for the variable of quantification.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |