On 14 Feb 2011, at 19:53, 1Z wrote:
CT needs arithmetical platonism/realism.
No it doesn't. It may need bivalence, which is not the same thing (me,
Reread the definition of AR. I define AR by bivalence.
If you believe the contrary,
could you give me a form of CT which does not presuppose it?
"Every effectively calculable function is a computable function"
What is an effectively computable function? What is a computable
function. Function computable form what to what?
See my papers.
That is just what I am criticising. You need the ontological
premise that mathematical entities have real existence,
and it is a separate premise from comp. That is my
response to your writings.
The only ontology is my conciousness, and some amount of consensual
reality (doctor, brain, etc.).
If I agree only to the existence of doctors, brains and silicon
the conclusion that I am an immaterial dreaming machine cannot
Then you have to present a refutation of UDA+MGA, without begging the
No, I can just present a refutation of Platonism. The conlcusion
Platonism in your sense is not used at all in the reasoning.
It does not assume that physical things
"really" or primitively exists, nor does it assume that numbers
exist in any sense. Just that they exist in the mathematical sense.
There is no generally agreed mathematical sense. If mathematical
anti-realists are right, they don't exist at all and I am therefore
Mathematicians don't care about the nature of the existence of
Fine. Such an ontologically non-commital idea of AR cannot support
They all agree with statement like "there exist prime
Yes, they tend to agree on a set of true existence statements, and to
what existence means.
Only during the pause café. It does not change their mind on the
issues in their papers.
Read a book on logic and computability.
Read a book on philosophy, on the limitations of
apriori reasoning, on the contentious nature of mathematical
You are the one opposing a paper in applied logic in the cognitive
physical science. I suggest you look at books to better see what
You are the one who is doing ontology without realising it.
On consciousness. Not on numbers,
You're saying *my* consciousness *is* a number!
Where? Consciousness, like truth, is not even definable in arithmetic.
I keep insisting on that all the time.
which I use in the usual
mathematical or theoretical computer sense. The reasoning is agonstic
on God, primary universe, mind, etc. at the start.
The only ontology used in the reasoning is the ontology of my
consciousness, and some amount of consensual reality (existence of
universe, brains, doctors, ...). Of course I do not assume either
such things are primitoively material, except at step 8 for the
reductio ad absurdo. Up to step seven you can still believe in a
primitively material reality.
You cannot eliminate the existence of matter in favour of the
of numbers without assuming the existence of numbers
I assume no more than the axiom of Robinson Arithmetic. Physicists
assumes them too, albeit not explicitly.
Jeffrey, or Mendelson, or the Dover book by Martin Davis are
It is a traditional exercise to define those machine in
I have no doubt, but you don't get real minds and universes
out of hypothetical machines.
You mean mathematical machine. They are not hypothetical. Unless
believe that the number seven is hypothetical,
I do. Haven't you got that yet?
I did understand that seven is immaterial.
Not just immaterial. Non existent.
Ex(x = s(s(s(s(s(s(s(0)))))) is provable in Robinson Arithmetic.
And you tell me that your are formalist, so be it.
But I am OK with seven
being hypothetical. It changes nothing in the reasoning.
I am not running on some immaterial TM that exists only in your head
How do you know that?
in which case I get
hypothetical minds and hypothetical universes.
I am not generated by a hypothesis: I generate hypotheses.
Confusion level. If you suppose a TOE you are supposed to be
by that TOE.
Explained by, not caused by. Things fell before Newton explained
That was my point.
In that sense you are generated by an hypothesis,
I am not generated by a hypothesis, even a true one, any more
than my house is built on a map, even an accurate one.
That's why I put 'in that (uninteresting) sense'.
Comp will imply that such a primary matter cannnot interfer at all
with your consciousness, so that IF comp is correct physics has to be
reduced to number theory, and such a primary matter is an invisible
Physics cannot be eliminated in favour of non existent numbers.
have to exist for the conclusion to follow
Physics is not eliminated, on the contrary, physics is explained from
something non physical. This provides solid foundations for physics.
Numbers have to exist, indeed. But you are formalist, so please take
existence by RA proves Ex P(x). No need for more than that, given that
the goal is to have a formal theory explaining qualia and quanta, or
why numbers believes in qualia and quanta.
Occam does the rest.
By mathematical logicians since Gödel. Perhaps before by Dedekind.
A weak form of formalism can subsist, but conventionalism does not.
Arithmetical reality kicks back, and cannot be captured completely by
There is not mathematical theory of reality: reality is ontology.
I agree, although I would say that reality is ontology+epistemology
+observability+sensibility (among other thing). Sensation are real.
It is a weakness of Tegmark to assume that there is a mathematical
theory of just mathematics. With comp we know that the internal
epistemology of just arithmetic is bigger than the whole of
mathematics itself. I know this is not an easy point. A good analogy
is provided by the 'Skolem paradox' phenomenon.
If what you mean is that Godel proves there are true unproveable
he doesn't, since what is unproveable in one system may be proveable
I agree. But I don't see the relevance at all.
We know today that we have to posit numbers to reason on
them. We don't have to posit their "real" existence (whatever that
means), but we have to posit their existence.
Unreal existence is not enough to support the conclusion
that I am a number
Certainly. That is why I give a detailed argument. You don't address
it by criticizing its starting definition, by attributing too much
metaphysical sense to arithmetical realism.
The conclusion is metaphysical, so the premiss must be
Comp is theological, and the conclusion is theological.
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