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honestrosewater
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In another thread, I started to say that "tautology" and "contradiction" could be defined in terms of truth-functions- which seemed entirely plausible- but I can't figure out how to do it. A tautology is a proposition whose truth-value is always Truth (T); a contradiction is a proposition whose truth-value is always Falsehood (F). To give you an idea, I first tried: A proposition D is a tautology if, for any contingent proposition P, (D & P) <=> P. A proposition C is a contradiction if (C v P) <=> P. But these use "<=>" which means the proposition is a tautology! -so that won't work. ((D & P) <-> P) <-> ((C v P) <-> P) <-> D and (P v ~P) <-> D and (P & ~P) -> D etc. don't work because they're contingent and the definitions need to be tautologous. I can certainly build tautologies out of contingent propositions and connectives, but I need to figure out if I can build a definition that way. Any thoughts?