Heisenberg, Goedel & Logic - The Arthur Young Series

[yoursuchagoodguy]

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I apologize. I misunderstood your statement.

And I should have read your entire comment.

I confess I stopped reading when you changed the subject to your love of freedom and your very very impressive pursuit of a phd.

So in future I will not only "check my comprehension in english language" I will also

"check my comprehension OF THE English language"

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i suggest you to read the Ernest Nagel James R. Newman paper on this subject for your better understanding of Goedel

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science is all about mathematical phenomena and patterns occuring in nature, so if maths are incomplete in nature then all science is.

[yoursuchagoodguy]

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Godel's Incompleteness Theorem does not say mathematics is incomplete. It refers only to certain types of Formal Mathematical systems. Most mathematics is done informally. It's an important distinction.

Godel's Thm discusses what is provable within any such formal system. It says nothing about what can be proved by other means.

If you are interested you might read Torkel Franzén's book Gödel's Theorem: An Incomplete Guide to its Use and Abuse

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@yoursuchagoodguy yes but Godel says that all formal systems which are powerful enough for self reference must be incomplete because there will be always a sentence G leading to contradiction. So if you are interested for really powerful formal mathematical systems you have this goedel limit. You say that most maths are done informaly. What do you mean by "informaly"? Mathematicians thought must be mathematical and logical and obeying to some formal rules, except if you believe in magic.

[yoursuchagoodguy]

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Any Godel sentence is specific to the formal system, which can therefore be subsumed by one in which the sentence is taken as an axiom. This is a common misuse of Godel by non mathematicians. See Franzen's book.

I use "informally" in the standard accepted logical sense. That is, I mean not within a formal system. As I said before, the distinction is important to avoid another common misuse of Godel. Refer to any undergraduate text on Set Theory & Logic.

Better yet, go to school.

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@yoursuchagoodguy of course you can add the G sentence inside the system as an axiom to make it complete. in maths you can do everything you like and this freedom is what i love, and the reason i'm doing a phd in math. but if you add the G sentence inside the system, the new system you have has a new G sentence and it is in fact incoplete. or if you add the negation of G sentence you end up having these strange supernatural numbers.

[yoursuchagoodguy]

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You say "of course you can add the G sentence inside the system as an axiom to make it complete" ?

NO!

The new system will then have some other G' sentence that is true but not provable from this new set of axioms. Hence it will also be incomplete.

You clearly do not understand Godel's theorem.

Please stop pretending.

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@yoursuchagoodguy when I said "to make it complete" i implied "with the intention to make it complete" and then I stated that this goal is not possible. is it so hard for you?

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don't you think that both Godel's incompeteness and Heisenberg's Principle must have a common source? they both involve a formal system observing or referencing another formal system.

[yoursuchagoodguy]

At 2:08 the statement "Logic is Incomplete" is wrong.

Godel's COMPLETENESS Theorem shows that Logic (First Order Predicate Calculus), is COMPLETE.

Incompleteness Theorems apply to 1st order systems that attempt to characterize arithmetic.

Also, Heisenberg's Principle is about Physics.

Godel's Theorems are about Mathematics.

Mathematical objects do not exist in the physical universe.

[LooksAeterna]

@yoursuchagoodguy You're obsessively right, but I am sure he meant the incompleteness of any logic worth mentioning and braodly used ins scientific application.

Moreover, there is a common element of both uncertainty and incompleteness lending itself very suggestively to the intution that there be no such thing as an absolutely objective reality and truth.

I think Gödel went paranoid over the proximity of his results to his own platonic intuition - without delivering complete certainty =:)

[goodsnservices]

The statement that you can't know the nature of anything with certainty is a bogus over-generalization. On the whole, you can know the nature of things with great certainty, just not the very small at a single moment in time, because you can't measure it without changing it because your measuring method is not passive observation. Just take an ordinary ruler and try to divide the smallest increment in half, then half again to prove it. No perfect precision.

[labarum312]

You have completely misunderstood uncertainty. Heisenberg's work has nothing to do with the accuracy of measurement. It is part of teh nature of things. The double slit experiment with a measuring device at one slit not only affects the electrons it comes into contact with but those going through the other slit that should not be affected at all. It is the act of measuring that collapses the packet regardless of whether the electron has made contact with the measurer.

[goodsnservices]

Tell THAT to Feynman.

I know a whole lot more about uncertainty and Heisenberg than you think. Schroedinger was wrong.

[yuothineyesasian]

Stephen Hawking once joked, "When I hear someone talk about Schroedinger's cat, I get my gun."