this post was submitted on 24 Oct 2024
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"This sentence contains 2 words" is a sensible sentence. It has 5 words, so what the sentence says is false.
The self-reference in the sentence is similar to that of the Liar's paradox. Cousins of that paradox have been used to prove major limitative results in mathematical logic such as
https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
In usual logic, a false sentence implies every sentence.
https://en.wikipedia.org/wiki/Material_conditional
Also, if sentence P is false, then "P is false" is true
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