On 13 Jul 2006 18:46:19 -0700, "firstname.lastname@example.org" <email@example.com> wrote:
>Stephen Montgomery-Smith wrote: >> [snip] >> The responses have led me to think that some people here believe in the >> modern axiomatic system like a religion. > >An axiomatic system is just a method of singling out a set of >propositions (those that follow from the axioms). For example, >the Peano axioms for natural numbers select a very definite >subset of all the posible propositions (those that follow from >the axioms). > >Axiomatic systems are thus just tools. In particular, the idea >of "believing in the modern axiomatic system" makes as >much sense as that of "believing in hammers".
I suspect people do believe in hammers. They believe in their senses for probably no better reason than they have no better alternatives to believe in as long as they have to believe in something. And that would seem to be the only alternative Aristotle's reliance on syllogistic inference for the establishment of truth left them.