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, passim)

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 computers,the conclusion that I am an immaterial dreaming machine cannotfollowThen you have to present a refutation of UDA+MGA, without begging the question.No, I can just present a refutation of Platonism. The conlcusion does't follo without it.

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 really 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 not one.Mathematicians don't care about the nature of the existence ofnaturalnumbers.Fine. Such an ontologically non-commital idea of AR cannot support your conclusion

Why?

They all agree with statement like "there exist prime number", etc.Yes, they tend to agree on a set of true existence statements, and to disagree on 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 ontology.You are the one opposing a paper in applied logic in the cognitive andphysical science. I suggest you look at books to better see whati amtaking about.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 ofuniverse, brains, doctors, ...). Of course I do not assume eitherthatsuch 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 existence 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.`

Boolos and Jeffrey, or Mendelson, or the Dover book by Martin Davis are excellent.It is a traditional exercise to define those machine inarithmetic.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. Unlessyoubelieve 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 beexplainedby that TOE.Explained by, not caused by. Things fell before Newton explained gravity

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 epiphenomena.Physics cannot be eliminated in favour of non existent numbers. 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.This has been refuted.By whom?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 *any* theory.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 propositions... he doesn't, since what is unproveable in one system may be proveable in another.

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 numberCertainly. 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. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.