Is mathematics the only certain knowledge?

Comments

Two answers come to mind:

(1) If we grant that mathematics is known with certainty, I think the same can be made for the laws of logic--for example, if P, then P... or either P or not-P.

(2) I can think of some reasons for supposing that even mathematical truths and the laws of logic aren't known with certainty. For one thing, axiomatized systems of reasoning (such as the logic and mathematics) are able to undergo modification, as a result of new discoveries--for example, the Euclidean axiom that the shortest distance between two points is a straight line is not an axiom in Eisteinian geometry (since gravity wells curve space). For another thing, I don't think we can automatically infer, from the fact that we find it impossible to imagine the falsity of something, that our beliefs about that subject must be true. Why couldn't we be so bad off that we are incapable of imagining what's true, and capable only of imagining some falsehood as truth?

Descartes takes this issue up in his Meditations on First Philosophy (especially in the First and Second Meditations). See what you think of his thoughts on this issue.

Read another response by Nicholas D. Smith

Read another response about Knowledge, Mathematics