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Hi,

`I really want to apology for my spelling. I will not correct my post`

`(I could add errors!), but I want to correct a statement I made:`

On 18 Jul 2011, at 20:44, Bruno Marchal wrote:

Accepting what you can feel and see and test is the antithesis oftaking it for granted and the epitome of the scientific attitude.That is Aristotle definition of reality (in modern vocabulary). Butthe platonist defend the idea that what we feel, see and test, isonly number relation, and that the true reality, be it a universe ora god, is what we try to extrapolate.

`Of course this is a mistaken statement. Not all platonists are`

`pythagoreans. I thought writing this:`

`"But the platonists defend the idea that what we feel, see, and test`

`might be the shadow, or the border of something else, which might be`

`non physical.".`

`Plato knew the Pythagorean, and a part of the academia defended the`

`idea that the fundamental reality was mathematical. But other`

`Platonists, like Plato himself, were just more agnostic on this than`

`the so-called Mathematicians (notably Xeusippes). Plotinus show the`

`same agnosticism, despite its amazing enneads on the Numbers.`

Best, Bruno

We certainly don't see, feel, or test a *primitive* physicaluniverse. The existence of such a primitive physical reality is ametaphysical proposition. We cannot test that. This follows directlyfrom the dream argument. That is what Plato will try to explain withthe cave.The trouble with axiomatic methods is that they prove what you putinto them. They make no provision for what may loosely be called"boundary conditions". Physics is successful because it doesn'ttry to explain everything. Religions fall into dogma because theydo.I don't criticize physics, but aristotelian physicalism. which is,for many scientists, a sort of dogma.Religion fall into dogma, because humans have perhaps not yet thematurity to be able to doubt on fundamental question. To admit thatwe don't know if there is a (primitive) physical universe.Physicists use mathematics (in preference to other languages) inorder to be precise and to avoid self-contradiction.That is the main error of the physicists. They confuse mathematicswith a language.And the main error of mathematicians is they confuse proof withtruth.That is unfair because all what I use here is the (big) discovery ofGödel that arithmetical truth escapes all possible effective oraxiomatizable proof systems. So mathematicians are able todistinguish mathematically, in many case, the difference betweenproof and truth.Only intuitionist confuse proof and truth, (like S4Grz!) butclassical mathematicians note that not only proof does not entailtruth, but that even in the case where proof entails truth, thecontrary remains false: truth does not entail proof.The whole AUDA is based on the fact that arithmetical truth isbeyond all correct machines (proofs).Let me comment a little part of your dialog with Jason. I commentalso Jason."True" is just a value that is preserved in the logical inferencefrom axioms to theorem. It's not the same as "real".True is more than inference from axioms.I think Jason said that. I agree. Truth is preserved in theapplication of sound inference rules, but truth is far bigger thananything you can access by inference rules and axioms. Arithmeticaltruth is, compared to any machine, *very* big. The predicate truthcannot even be made arithmetical.For example, Godel's theorem is a statement about axiomaticsystems, it is not derived from axioms.Well, the beauty is that Gödel's second incompleteness theorem is atheorem of arithmetic. BDt -> Bf (or ~Bf -> ~B~Bf) is a theorem ofPA. It is the whole point of interviewing PA about itself. It canprove its own Gödel's theorem. That is missed in Lucas, Penrose, andmany use of Gödel's theorem by anti-mechanist. Simple, but not sosimple, machine have tremendous power of introspection. Löbian one,have, actually, maximal power of introspection.Sure it is. It's a logical inference in a meta-theory.Not at all. The second (deeper) theorem of Gödel, like the theoremof Löb, is a theorem of Peano Arithmetic. The tedious part consistsin translating the "Bx" in arithmetic, but Gödel's succeededfamously in the task (cf beweisbar ('x')).G axiomatise all such metatheorem that a theory can prove aboutitself, and G* formalize all the truth that the theory can prove +that the theory cannot prove about itself. In that way, Solovayclosed the research in the modal propositional provability/consistency logics, by finding their axiomatization, and this bothfor the provable part of the machine (which contains BDt -> Bf), andthe non provable part (which contains typically Dt, DDt, DDDt, DBf,DDBf, etc.).BrunoBrent --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@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.http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups "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.

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