zulooani.blogg.se

From these two pieces of information it follows by modus ponens that there exist functions. It is also known, a posteriori this time, that I have as many left shoes as right. It is a priori, I assume, since observational evidence is never given, that there are as many Fs as Gs iff there is a one to one function from the Fs to the Gs. From these two pieces of a priori knowledge it follows by modus ponens that there exist certain abstract objects, viz. On the other hand, it is also (often) known a priori that such and such an argument is invalid. I have never seen empirical evidence offered for this equivalence so I assume the knowledge is a priori. As everyone knows, an argument is valid iff every model of its premises is a model of its conclusions. Abstract objects are a priori deducible from (i) a priori premises and/or (ii) obvious, uncontroversial empirical facts.ĮXAMPLE i. The paradox is that, if we are to go by what philosophers say in other contexts, such bashfulness is quite unnecessary. (The only easy existence proof we know of in philosophy is Descartes's cogito.) Nobody supposes that there are easy proofs, from a priori or empirically obvious premises, of the existence of abstracta. But such arguments carry with them a palpable sense of daring and a distinct feeling of pulling a rabbit out of a hat.

This is not to say that a priori arguments are no longer attempted they are, for instance by Alvin Plantinga in The Ontological Argument, and Crispin Wright in Frege and the Conception of Numbers as Objects. And it would have to an a posteriori argument of a particular sort: an indispensability argument representing numbers, to use that example, as entities that "total science" cannot do without. GE Moore to IA RichardsĪbout a half a century ago, Quine established to most people's satisfaction that the argument for abstract objects, if there was going to be one, would have to be a posteriori in nature. Yablo It seems to me very curious that language should have grown up as if it were expressly designed to mislead philosophers and I do not know why it should have.