Math Has A Fatal Flaw?

[Guest]

Keywords: Incompleteness, Inconsistency, and Undecidability

YouTube Link: Math Has A Fatal Flaw?

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[Guest]

WOW! (Words Of Wisdom!): "We must know. We will know!" -- David Hilbert.

[Guest]

Mathematics is not fatally flawed! It's not a perfect scientific system/language...

Mathematics works extraordinarily well, and human civilization has reached greats in its development and in the understanding of our world because of mathematics.

Go Mathematics!

[Guest]

Mathematics is not fatally flawed! It's not a perfect scientific system/language...

Mathematics works extraordinarily well, and human civilization has reached great heights in its development and in the understanding of our world because of mathematics.

Go Mathematics!

And much more progress can be achieved...

[Guest]

No, mathematics does not have a "fatal flaw". Kurt Koedel showed that any system of axioms, large enough to include the natural numbers, is either "inconsistent" or "incomplete". "Inconsistent" means it is possible to prove, using those axioms, both a statement and its contradiction. THAT might well be a "fatal flaw". It would mean that "proving" a statement doesn't really mean anything. But the evidence so far is that proofs DO mean something! It is far more likely that the axiom systems used in mathematics are "incomplete"- that is, that there exist some statement that can neither be proved nor disproved. That is NOT a "fatal flaw". If we find such a statement (and this has happened- the "parallel postulate", for example) we just add it to our axiom set.

[Guest]

FYI: Pythagoras' revenge: Humans didn't invent mathematics, it's what the world is made of.

Enjoy!

[Guest]

FYI: A universe without mathematics is beyond the scope of our imagination.

[Guest]

I think you may be at the wrong address. This is a math forum. Instagram is somewhere else.

[Guest]

Hmm. Could it be that humans (reasoning, computations, etc.) are flawed? And therefore, mathematics is flawed by that association...

A previous post does correct the problem. Thank Lord GOD! Amen!