Le 04-janv.-06, à 19:30, Brent Meeker a écrit :
Bruno Marchal wrote:
Hi John,
I think you may have problems because you are not used neither
trained in axiomatic thinking. The idea consists in NOT defining the
objects we want to talk about, and keeping just some needed
properties from which we prove other theorem.
Let me give an example with the idea of knowledge. Many philosophers
agree that knowledge should verify the following law, and I take it
as the best definition of knowledge we can have:
1) If I know some proposition then that proposition is true
2) If I know some proposition then I know that I know that proposition
3) If I know that some proposition a entails some proposition b, then
if I know a, I will know b.
But that doesn't capture meaning of "know".
But nobody knows or agree on the *meaning* of "know", that's was my
point. If *you* think it leaves something out, for a mathematician it
means that you agree with the definition!
And then you propose a stronger theory by adding 4:
It leaves out 4) If I know some proposition then I have experience
causally connected to the fact that makes it true. See c.f. Gettier's
paradox.
Now, that "4" *is* problematical because it refers to a undefined
notion of causality, which itself can only be defined axiomatically.
Bruno
http://iridia.ulb.ac.be/~marchal/
