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I'm still reeling from the three things I learned in this post: 1. Bertrand Russell studied the "I am lying" paradox, which I always thought was nothing more t
by chrisbrandow 5y ago
I'm still reeling from the three things I learned in this post:
1. Bertrand Russell studied the "I am lying" paradox, which I always thought was nothing more than a clever meme.
2. Bertrand Russell is responsible for type theory
3. That type theory came out of his study of the paradox.
- __MatrixMan__ 5y agoThe distinction between countable and uncountable infinities also stems from the liar's paradox.
- Koshkin 5y agoHow so? The set of reals is uncountably infinite. Looks like a self-contained fact (that can be proved by a "diagonal argument").
- kazinator 5y agoBut diagonalization and self-referential paradoxes are related (in ways that are not necessarily obvious). Think along the lines that you have some sentence Px which asserts that sentence Py is false. Now imagine a table where both the rows and columns are P0, P1, P2, .. populated with these sentences. The diagonal is where you have the self-reference: Pi asserting that Pi is false.
- ProfHewitt 5y agoBertrand Russell introduced orders on propositions to block construction of paradoxes such as “The Liar” [Russell 1908]. Without orders on propositions, the “self-referential” proposition I’mFalse (such that I’mFalse⇔¬I’mFalse) could be constructed using the following recursive definition: I’mFalse:Proposition<i>≡¬I’mFalse. Since Ψ is a propositional variable in the definition, ¬Ψ:Proposition <i+1>. Consequently, I’mFalse:Proposition <i>⇒I’mFalse:Proposition<i+1>, which is a contradiction. For more information see the following: https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021 https://www.youtube.com/watch?v=AJP1VL7shiI https://www.youtube.com/watch?v=AJP1VL7shiI