On 9/21/2013 7:06 AM, Bruno Marchal wrote:
On 20 Sep 2013, at 18:36, meekerdb wrote:
On 9/20/2013 2:13 AM, Telmo Menezes wrote:
On Thu, Sep 19, 2013 at 9:04 PM, meekerdb <[email protected]> wrote:
Also some serious mathematicians are finitists.
The Meaning of Pure Mathematics
Author(s): Jan MycielskiSource: Journal of Philosophical Logic, Vol. 18, No.
3 (Aug., 1989), pp. 315-320Published by: SpringerStable URL:
http://www.jstor.org/stable/30227216 .
Come on! He believes that Platonism violates Occam. That is the same error
than believing that Everett violates Occam. Sometimes more is considerably
simpler than less, and that's the very inspiration of the "everything" list.
Just because I subscribe to the list doesn't oblige me accept its dogma. I
think Mycielski remark is irrelevant. Occam is no more than a rough guide
anyway.
Hi Brent,
Arguably, Occam might gain the status of theory once we accept
self-sampling. Of course you're not forced to accept it -- I'm
agnostic on it myself. But it's not beyond the pale that Occam could
actually be theory. No?
To be a theory there would have to be a clear meaning of what of is not to be
multiplied beyond necessity. Occam said 'entities', but by that measure the atomic
theory of matter is very much contrary to his principle. It's now usually interpreted
to mean a simple theory is best, without really specifying how 'simple' is to be
measured. The are proposals based on information theory and minimum message length, but
even there it's not clear how to compare the measure of say general relativity and loop
quantum gravity and string theory.
Just formalize them in first order logic, or in a first order logical theory and count
the number of bits used.
I can count the bits in a formalization of "There is a differentiable metric manifold" but
I'm not sure that captures the complexity or whatever it is that we're supposed to be
minimizing.
Brent
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