“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
If this sentence is true, it means you used to beat your spouse. If it is false, it means that you currently beat your spouse. Therefore, it proves that you are married and at some point in time you beat your spouse.
It’s not a paradox, it’s a dumb logic puzzle. It’s no different than saying something nonsensical like “This sentence contains 2 words”.
No, if it is false, then it is simply wrong. A wrong sentence doesn’t imply something else is right, it’s just wrong.
“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
@science_memes
“J Lou has stopped beating their spouse.”
If this sentence is true, it means you used to beat your spouse. If it is false, it means that you currently beat your spouse. Therefore, it proves that you are married and at some point in time you beat your spouse.
That sentence has a presupposition. The sentence I used can be fully formalized in a logic with predicates for knowledge of an entity and truth
@science_memes
Also has a presupposition.