On 21 Jan 2014, at 21:33, meekerdb wrote:
On 1/21/2014 2:32 AM, Bruno Marchal wrote:
Only to make the UDA non valid. It works, if Brent meant a
mathematical ultrafinitism. But this change comp, like it changes
elementary arithmetic (which suppose at least that 0 ≠ s(x), and x
≠ y implies s(x) ≠ s(y), which can't be true in ultrafinitism).
Ultrafinitism makes all current physical theories meaningless.
How can that be when all current physical theories are tested by
computation on finite digital computers and all observations are
finite rational numbers?
We just bet that physics is well approximated by computations, and
indeed all known laws seems to be computable (except the "collapse").
I guess it makes sense in most case.
I'd say the meaning of theories comes in their application - not
from an axiom system.
Because you reify reality, an put the meaning there. But we can't do
that when working on the mind-body problem, so we need a mathematical
notion of reality, and the notion of model (in logician sense) plays
that role.
That for all x x ≠ x + 1, is NOT an empirical question. It is a
truth, out of space and time, which is true in all models of RA, or
PA, or ZF, etc.
Bruno
Brent
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