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cousin_it comments on Unsolved Problems in Philosophy Part 1: The Liar's Paradox - Less Wrong
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You won't create anything worthwhile in math if you don't study it. To break your current system, consider the proposition "This proposition is either false, contradictory, or ambiguous".
You are absolutely correct. I haven't thought this through. Thank you for the lesson.
Edit: I did take the lesson that I should think more before making such a claim, however, I wanted to point out that your sentence poses no problem and was not the point.
this p. is false is contradictory this p. is condradictory/ambigous is false The conjunction of contradictory and false is contradictory so you have a unique solution. This is also what intuition tells us since the proposition cannot be true and cannot be false and that would be contradictory.
I don't understand your solution. If the proposition is contradictory, then it's true - just look at what it says.
Or maybe I don't understand how we are supposed to assign truth values to disjunctions ("either/or") in your system: can a disjunction still be contradictory if one of its clauses is true? And surely if X is contradictory, then the clause "X is contradictory" must be true... or is it?
Ok, I get it now. So, I was wrong on that too. Thank you.