On 11 Jan 2013, at 21:42, meekerdb wrote:
On 1/11/2013 10:24 AM, Bruno Marchal wrote:
On 10 Jan 2013, at 20:02, meekerdb wrote:
On 1/10/2013 8:06 AM, Bruno Marchal wrote:
Empirical proofs can be ostensive.
But I prefer not using "proof" for that. It can only be
misleading when we do applied logic. I prefer to call that
"empirical evidences".
So I think the two kinds of 'proof' have little in common.
Almost nothing indeed.
Mathematical proofs are about transforming one set of
propositions into others. They are relevant to empirical
propositions only insofar as there is an interpretation that
maps the axioms to facts.
I agree. Axioms comes from empirical evidences. The consequences
of the axioms can be used to test the theory, and refute it, but
will never prove it to be true.
You should write, "...but will never empirically evidence it." :-)
Why?
Not sure I get the joke :?
We can empirically evidence a theory, we just cannot take those
evidences as a proof that the theory applies to "reality".
I was just tweaking you for using "prove" both for the
transformation from axiom to theorem and for empirically testing a
theory - right after you acknowledged they were quite different.
The 'proof' than connects the axioms to the theorem (consequence) is
completely different from 'proving' a theory is false (or true).
But that was my point. That's why there is no empirical proof at al
indeed.
Bruno
http://iridia.ulb.ac.be/~marchal/
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