[FOM] What produces certainty in mathematical proofs?
blumal at mail.biu.ac.il
Thu Sep 20 11:07:28 EDT 2007
Feng Ye wrote:
>On what ground can we decide certainty, or evaluate a judgment regarding certainty? What proofs or evidences can one
>offer for a judgment regarding certainty?
Speculation: We know(from Saul Kripke) that identity/non-identiy
statements(whose refering expressions refer "rigidly" such as constants
or variables and some but not all descriptive phrases) are true/false
iff necessarily true or false. Hence one instance will
confirm/discomfirm the identity/non-identity. Thus one confirming
instance of "water=H2O" to use his classic identiy statement should
confirm it as a certainty. There are other innumerable examples of this
Can this underlying logic of identity be extended to a wider class of cases?
More information about the FOM