Kurt Godel: The World's Most Incredible Mind (Part 3 of 3)

Kurt Godel: The World's Most Incredible Mind.

"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel

Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory.

1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system.

2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers.

Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete.

Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. "

What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent.

For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics.

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Category:

Science & Technology

Tags:

• Kurt Godel
• Incompleteness Theorem

[MsMrNoface]

Enjoyed these three - Very thought provoking vids.

[astroboomboy]

Best explanation of Gödel I have heard so far in a short and concise manner.

[NewInfinityRecursion]

we are paralel, computer at to, random, exzist in computers. we are from atoms, phisics computers are, what is computer what are you, you are the same.

[daytonadudenheimer]

on youtube we get to grade professors' lectures: this guy gets an A++

[TalmadgeMonroe]

Thanx for uploading.