Heisenberg, Goedel & Logic - The Arthur Young Series

God, Science, Mysticism -- The Arthur Young Series

Theory of Process Seminar, Day One
Recorded December 13, 1980

Heisenberg and Goedel. Letter to Heisenberg regarding the photon as ultimate uncertainty. Goedel showed the incompleteness of logic. TOP is a rationalization, but it is one that accepts uncertainty as the generating principle.

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[yoursuchagoodguy]

@interted

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"

[interted]

@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?

[yoursuchagoodguy]

@interted

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.

[interted]

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

[interted]

@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]

@interted

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.

[interted]

@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]

@interted

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

[interted]

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

[interted]

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.