Re: [sl4] foundationalism

From: B Ziomek (
Date: Sun Feb 15 2009 - 08:24:08 MST

It really depends on what you mean by an axiom. For simplicity's sake, let's
take Euclid's:'s_Elements#First_principles

The postulates really are definitions rather than ideas that someone dreamed
up. A line is a line because it fulfills such criteria. If other axioms
could be made that described other phenomena treatable as basic, there is no
reason that modern maths and sciences (or at least something roughtly
equivalent) could not have been derived from them as well, although thinking
of such alternative phenomena is a difficult task.

On Sun, Feb 15, 2009 at 2:45 PM, Petter Wingren-Rasmussen <> wrote:

> One of the things that really fascinates me about axioms is that although
> they cant be proved, their extrapolations have been used to put man on the
> moon.
> Could completely different axioms lead to the same result?


This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:04 MDT