Poincare's Conjecture Follow-Up: Polling Intuitions

Suppose that the sort of analogical reasoning upon which one might base the belief that the 3-sphere is unique in its simplicity among three-dimensional manifolds is in fact highly reliable. (Is it the Nyaya school in classical Indian philosophy that considers analogical reasoning to be a basic source of knowledge?) Could one know that the 3-sphere is unique in that way on the basis of such reasoning? If not, how did this jibe with the fact that one can know a mathematical fact on the basis of testimony? (Could a disparity between our intuitions regarding the two cases, assuming there is such a disparity, be used to motivate Burge's idea that testimony preserves a priori warrant?)

Comments most welcome.