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madness
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In propositional logic we study rules of logical inference from propositions, such as ## (p\rightarrow q) \leftrightarrow (\lnot q \rightarrow \lnot p) ##, or ## \lnot (p \land \lnot p) \leftrightarrow (p \lor \lnot p) ##. Do we ever define the set of propositions we are dealing with? Some propositions, such as "this statement is false", appear problematic. Do we require some set theory to formally establish propositional logic?