On 23 Jan 2014, at 00:34, meekerdb wrote:
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?"
I meant that the meaning of theories is brought by the theories
already present in the brain (generalized or not). If not you reify
reality, meaning, and this in a way which, when assuming comp, looks
like magic.
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.
We don't believe in human p-zombie. For robots, many would argue that
they are zombie, by construction.
Then, the "constructing AI" and the mind-body problem will be solved
by itself, can only solve the "easy problem", that is not the mind-
body problem, which needs to justify the bodies without assuming them.
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.
Right. defining "life" does not make sense. Biology is "easy". It is
not confronted to the hard problem, where the 3p complete explanation
seems to evacuate the 1p person. Comp reduces completely this problem
by reducing physics to number's psychology/theology. If not, let us
isolate the flaw in the argument.
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.
In the case of consciousness, such dissolution will corresponds to
Dennett kind of explaining the subject away. In biology, we can do
everything in the 3p (the 1p plural, actually, with comp). But for
consciousness, the 1p is not reducible. Now, that problem is solved
by ... the oldest solution we have: Theaetetus. The universal and
Löbian machine can refute Socrate's refutation of Theaetetus. All
critics of that definition contains a confusion of two arithmetical
hypostases, in the comp frame. We do have made progresses.
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.
If you believe that 1+1=1, you are in trouble.
That one drop added on one drop give one drop is not a refutation of
the arithmetical statement that 1+1=2. It is a misapplication of a
theory in a context which the theory does not handled.
You can refute the theory of group by showing that (N +) is not a group.
That's bad philosophy, I am afraid, Brent. Come on!
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;
Not at all. It has nothing to do with language. A computation stops or
not in arithmetic, independently of languages, theories, person and
universe. of course you need to agree on the addition table and
multiplication table to even just define what a computation is; but
that's all, and any other Turing complete structure woould do, with
the same machines stopping, or not stopping.
Of course, if there is a bigger natural number, none of this make
sense. The remedy seems worst than the disease here.
a rule we made up about the meaning of "successor" and "equal" etc,
that is a good theory of countable things.
And that's all what comp need.
Bruno
Brent
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