On 1/22/2014 1:29 AM, Bruno Marchal wrote:
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,
LOL! I'm reminded of what Sidney Morgenbesser said to B. F. Skinner, "Let me see if I
understand your thesis. You think we shouldn't athropomorphize people?"
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's a point where I disagree with you. We can work on the mind body problem by
creating intelligent machines and when we have created them we will infer that they have
minds just as we infer other people have minds (nobody really believes in p-zombies) and
we will learn to engineer those minds. Note that there were people who tried an axiomatic
approach to defining life - and it led nowhere, while people working laboratories with
x-ray crystallography and stick-and-ball models discovered the double-helix.
Theorizing has it's place. Molecular biology was really inspired by a lecture that Erwin
Schroedinger gave (and later expanded into his book, "What is Life") and which pointed to
some of the basic characteristic the chemistry and physics of life must have. And one its
contributions was to emphasize there was no need for magic, no elan vital. I see
computationalism playing a similar role in the study of consciousness. But just like
molecular didn't so much solve the problem of life as dissolve it, I expect something
similar to happen in the study of consciousness.
That for all x x ≠ x + 1, is NOT an empirical question.
It's not an empirical question in Platonia, but in the real world (which I reify :-) ) it
is: One raindrop plus one raindrop makes one raindrop. The set of the swim team with
cardinality four plus the set of the basketball team with cardinality twelve is a set with
cardinality 14.
It is a truth, out of space and time, which is true in all models of RA, or PA,
or ZF, etc.
Yes, it's a truth of language; a rule we made up about the meaning of "successor" and
"equal" etc, that is a good theory of countable things.
Brent
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