Online research in philosophy

This paper considers well known results of psychological researchinto the fallibility of human reason, and philosophical conclusionsthat some have drawn from these results. Close attention to theexact content of the results casts doubt on the reasoning that leadsto those conclusions.

This article discusses Charles Parsons' conception of mathematical intuition. Intuition, for Parsons, involves seeing-as: in seeing the sequences III and III as the same type, one intuits the type. The type is abstract, but intuiting the type is supposed to be epistemically analogous to ordinary perception of physical objects. And some non-trivial mathematical knowledge is supposed to be intuitable in this way, again in a way analogous to ordinary perceptual knowledge. In particular, the successor axioms are supposed to be knowable (...) intuitively. This conception has the resources to respond to some familiar objections to mathematical intuition. But the analogy to ordinary perception is weaker than it looks, and the warrant provided for non-trivial mathematical beliefs by intuition of this sort is weak-too weak, perhaps, to yield any mathematical knowledge. (shrink)