Russell's Paradox – A Ripple in the Foundations of Mathematics

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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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Up and Atom says:

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

Eric Taylor says:

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

Yuvansh Shah says:

There is no problem with it

epicbehavior says:

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

epicbehavior says:

“Everything I say is a lie” works better.

Alan Foxman says:

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.

John says:

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

Howard Pope says:

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

Rowan Ackerman says:

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

Medusa Skull says:

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.

Christopher Craig says:

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

Christopher Craig says:

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

Christopher Craig says:

The relative characteristic of less or more.

JaQuan Friend says:

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?

chriszichriszable says:

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

rishab ghosh says:

Please do the sequel to this video.

Mewnik Mathematics says:

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

Jim Mooney says:

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.

C Cole says:

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

allan james says:

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

FobbyChino says:

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.

Glenn Davis says:

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.

Sherlock Holmes says:

Numbers are alphabets of the language of nature.

Hector Nonayurbusiness says:

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

Prashant Gawande says:

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.

Prashant Gawande says:

What if barber gets estrogen therapy?

jamie oxenreider says:

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

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