Bertrand Russell’s set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege.

Thank you to Professor Joel David Hamkins for your help with this video.

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*Sources*

https://plato.stanford.edu/entries/russell-paradox/

https://plato.stanford.edu/entries/frege-theorem/

https://plato.stanford.edu/entries/frege/

https://youtu.be/bqGXdh6zb2k

https://youtu.be/xXD57a5BEO0

*Music*

https://www.epidemicsound.com/

What is a number? (no using the word number)

Easy solution to Barber's Paradox. The barber is a woman.

There is no problem with it

One deck of cards is the same as one x 52 cards.

“Everything I say is a lie” works better.

So…The Barber exists in a quantum state where he both does, and does not, shave himself. In such a state he is, in effect, 2 people in one. Ergo 2 = 1. And if two equals 1, then it is axiomatic that 1 = 2. Consequently, there are two barbers and they shave each other. Or to say it simply: He shaves himself.

He is a barber, so of course he shaves his own beard. This is dumb lol

You are so beautiful and intelligent! I am deeply impressed!

Number: a construct to be used to more precisely describe a quality of an object, a group of objects, or the lack of objects.

Isn't math just a language? Just like all languages, it is just a tool and tool can be made to fit the purpose. Tool by itself doesn't have a purpose until you, a conscious being, can find it a purpose. For example, a stone by itself is not a tool until you use it to crack nuts.

can you make a square comprised of equal, internal circles?

@10:18 when you laugh and cry so hard at the same time.

The relative characteristic of less or more.

I think i got it… Is this question summing it up: Is it possible for God (being able to do all) to make a rock so big that he couldn’t lift it?

The Frege breakdown animation is so funny… "No one loves you!" HAHAHA

Please do the sequel to this video.

A number is an adjective of a descriptive condition of a set.

Simple. The barber gets amnesia whenever he gets hairy, and forgets his rule. Then remembers it again when he's done. Logic doesn't consider time or location as a factor.

Ahh… I genuinely loved set theory and discrete mathematics back in my CS undergrad days.

"Super cool dude" – he'd have liked that.

I'm so glad Up and Atom is a channel on youtube. Keep up the good work. I can't wait to binge on all your videos.

Sounds like Russell came up with multiplying two negatives philosophically/mathematically. It works (?) in math, but pretty difficult to explain in a philosophical sense of logical solid conceptual reality.

Like your videos, they’re really thought provoking.

Numbers are alphabets of the language of nature.

Physics does have contradictions though, Quantum vs Relativity for example. The Russell paradox sounds like the black hole of mathematics.

It’s same as being a person; become good to all and you’re not good to all anymore, and become bad to all and you’re not bad to all anymore. Seems politicians figured out the paradox much before.

What if barber gets estrogen therapy?

Truth: the only Real number is 1 all other numbers are a logical imagination-JR. Oxenreider