[FOM] What produces certainty in mathematical proofs?

Max Weiss mmweiss at interchange.ubc.ca
Thu Sep 20 14:57:50 EDT 2007

I thought one thing we learned from Kripke was to distinguish the metaphysical concept of necessity from epistemological concepts like apriority, certainty and so on.  Necessity should be distinguished from apriority on the grounds that e.g. it is necessary but not apriori that Water=H2O.  And if necessity coincided with certainty, then we could refute a mathematical proposition merely by finding it dubitable.

-----Original Message-----

> Date: Thu Sep 20 08:07:28 PDT 2007
> From: "Alex Blum" <blumal at mail.biu.ac.il>
> Subject: Re: [FOM] What produces certainty in mathematical proofs?
> To: "Foundations of Mathematics" <fom at cs.nyu.edu>
> 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 
> kind.   
> Can this underlying logic of identity be extended to a wider class of cases?
> Alex Blum
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