On 23 Jan 2014, at 19:42, meekerdb wrote:
On 1/23/2014 1:52 AM, Bruno Marchal wrote:
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.
Exactly my point. And the context where is *does* apply, where it
is *not* an empirical question, is in our language and Platonia.
OK, if you don't put too much metaphysics in Platonia. Comp's platonia
is just (N, +, *), a structure simpler than most used by most
physicists and mathematicians.
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.
Only the idealized computations of Turing. Computations in my
computer always stop.
Because you assume that it exists in some ontological sense. That
might be possible. My point is that if this was really the case, you
can't say "yes" to the doctor "qua computatio". You can say "yes" to
the doctor by invoking some magic.
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.
I think it also needs to know what are countable things. When the
doctor makes your prosthetic neuron he needs to know what the
connecting neurons are going to count.
He must bet only on some functionality. Then he can study comp and
understand that the materiality of the neurons is non sensical, but he
does not need that knowledge to bet on a substitution level.
Bruno
Brent
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