[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index][Subject Index][Author Index]
Re: WAS-- Re: Hanson 2006, Mortimer, Baeker response
On Sun, 25 Jun 2006 02:00:40 +0200 "Andreas Johansson"
> On 6/24/06, Phil Bigelow <firstname.lastname@example.org> wrote:
> > On Sun, 25 Jun 2006 01:25:16 +0200 Andreas Johansson
> > writes:
> > > On 6/23/06, Phil Bigelow <email@example.com> wrote:
> > > The test of a scientific theory is if it agreess with
> > > The
> > > test of theorem is if it follows logically from the axioms.
> > While there is a difference, it appears to be rather minor.
> It appears quite major to me. In science, you start with
> and see what theory you can concoct to describe them, in maths you
> start with axioms and see what theorems follow. Induction vs
> > One is
> > physical, the other is mental. Is a mental "test" itself an
> I'm not sure what you're getting at here, but I'd say neither
> nor mental tests are observations.
In order to test something, even mentally, you make an "observation" (in
this case a virtual observation, to borrow from computer animation
rhetoric). "Thought experiments" are a form of mental "observation".
The assumptions that the mind uses in these thought experiments are based
on axioms. The axioms, themselves, are based on earlier real-world
> > >From Webster's Dictionary:
> > Axiom: a statement that needs no proof because its truth is
> > self-evident.
> > So, how do mathematicians canonize axioms? In other words, what
> is the
> > process involved in determining that a mathematical concept is
> > or "self-evident"?
> > If there *is* such a process, then I'll wager it probably involves
> > form of testing. Which is not that different than the testing of
> > scientific hypotheses and theories.
> That's not how the word "axiom" is used in mathematics. You don't
> determine that something is an axiom - you declare it to be so by
>From Websters Dictionary:
Fiat: An order or issued by authority; sanction.
If we exclude those fiats issued by madmen, then there must be a widely
accepted logical rationale that backs up a mathematical fiat (a "declared
What, exactly, is this mental process? Why should it be considered
different from a part of the scientific method?