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Naval

There Is No Settled Mathematics

Naval

Naval Ravikant

Business, Technology

4.82.4K Ratings

🗓️ 2 April 2021

⏱️ 3 minutes

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Summary

Transcript: http://nav.al/settled

Transcript

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0:00.0

There are two other scientific thinkers that I like who are unrelated to David Deutsch,

0:04.1

but come to very similar conclusions.

0:06.1

One is Nassim Tel-Ab, who's popularized the idea of the Black Swan,

0:09.8

which is that no number of white swans disproves the existence of a Black Swan.

0:14.4

You can never conclusively say all swans are white.

0:17.5

You can never establish final truth.

0:20.1

All you can do is work with the best explanation you have today,

0:23.6

which is still better than ignorance, far better,

0:26.1

but at any time a Black Swan can show up and disprove your theory,

0:30.2

and then you have to go find a better one.

0:32.1

The other fellow who I find fascinating is Gregory Chaiton.

0:35.4

He is a mathematician who is very much in the Kurt Gaudel vein,

0:40.3

where he tries to explore the limits and boundaries of what is possible in mathematics.

0:44.8

One of the points that he makes is that Gaudel's incompleteness theorem

0:48.8

doesn't say that mathematics is junk.

0:51.6

It's not a cause for despair.

0:54.1

Gaudel's incompleteness theorem says that no formal system, including mathematics,

0:58.2

it can be both complete and correct.

1:00.3

Either there are statements that are true that cannot be proven true in the system,

1:04.6

or there will be a contradiction somewhere inside the system.

1:07.2

So this could be a cause of despair for mathematicians who view mathematics

1:11.7

as this abstract, perfect, fully self-contained thing,

...

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