Posted: Jun 01, 2011 7:40 pm
Cito di Pense wrote:
Self-evident is not the same as necessary. Necessity is the result of deduction, and hence is not a priori.
Postulates are not the same as axioms. A postulate might be something you have decided to try to prove, otherwise, axioms and postulates would be the same. Why have two words if there is only one concept. Parsimony demands it.
Agreed, something can be necessary without being self-evident (also, something can be self-evident without being necessary).
And while it's true that the conclusion of a valid deductive argument follows necessarily from the premises (meaning if the premises are true, then the conclusion can't fail to be true), that doesn't mean that the conclusion as such is a necessary truth (the conclusion, along with its premises, could be contingently true). Moreover, a proposition is either necessarily or contingently true regardless of whether we arrive at that proposition via deduction (ex: it would still have been true that 2 and 2 makes 4 even if we had never deduced it).
In any case, a priori knowledge doesn't mean "not the result of deduction," it just means that it doesn't depend on empirical or experiential evidence. So even if it were granted that necessity is always only the result of deduction, it still wouldn't follow that necessity cannot be a priori.