From: Platt Holden (pholden@sc.rr.com)
Date: Sun Apr 20 2003 - 16:30:28 BST
Scott:
Platt
> > What do you think of defining a philosphical axiom as a concept that has
> > to be accepted and used in the process of denying it?
> I would guess that you would get a lot of logical conundrums, but not a
> very useful philosophy.
> >Examples:
> >
> > What is, is.
> Let's see. Suppose I deny that what is, is.
> This implies that there is
> something that is, but is not. How about, "This statement is not".
A self-refuting statement.
> Another question: how can I use this axiom. What can I substitute for the
> word "What". A unicorn?
Sure. A unicorn is.
> > Consciousness is the faculty of perceiving what is.
> Well, you have defined "consciousness" as "perception", now what is
> perception? But, I admit, I know how to use the word "perception" for the
> most part. So since last night I perceived a unicorn in my dreams, I can
> conclude that a unicorn is.
Right. In your dreams.
> > What is is possessed by identity.
> This one I just disagree with, since I assume it defines "possessed by
> identity" to be synonymous to "what is". However, I deem identity to exist
> only by virtue of difference, and vice versa (for which I appeal to the
> logic of contradictory identity, no less).
Right.
> Anyway, on whether an axiomatic philosophy is possible, I doubt it. The
> virtue of a mathematical axiomatic system is that there is no need to go
> outside the axioms for further explication. (Not true, actually, since one
> needs the "rules for using an axiomatic system" which somehow one "just
> knows", but let it go).
>
> The only way I could see doing something similar in philosophy is to also
> borrow from mathematics that virtue. Here, for example, are the Peano
> axioms for arithmetic, which establish how one is to use 'number', '0', and
> 'successor of':
>
> 0 is a number.
> If n is a number, then the successor of n is a number.
> For all n (n a number) 0 is not the successor of n.
> If the successor of n = the successor of m (n and m numbers) then n = m. If
> a property P holds for 0 and if for any n (n a number) if P holds for n
> then P holds for the successor of n, then P holds for all numbers.
>
> (Note, all the surrounding verbiage, e.g. If..then.., and "a property holds
> for..", etc. can all be put into the formalism of first order predicate
> calculus, which is presupposed here.)
>
> The point being that these axioms implicitly define 'number', '0', and
> 'successor of', with no implication to or from anything outside the system.
> I don't know how to do that in philosophy, but if one did, I think one
> would be very deep in postmodern-land. In fact, in my pursuit of an "ironic
> metaphysics" I have sometimes pondered trying to incorporate this approach.
> But since it would require the logic of contradictory identity, and not
> first order predicate calculus, I suspect I am not going to get very far.
I bow to your superior mathematical mind. You lost me beginning with
"Here for example are the Peano axioms . . .
But would you agree that Pirsig's use of Quality and it's subdivisions
static and Dynamic are, for his philosophy, axiomatic?
Platt
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