Ok so I was reading Hungerford's book on Abstract algebra and it uses the Bernays-Gödel set theory. In it he presents Russel's Paradox and says that if a statement is both true and false then that can be manipulated to make any statement true. How?
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1In classical logic, we have "ex falso quodlibet", $P \land \lnot P \Rightarrow Q$. – Daniel Fischer Jun 26 '13 at 15:20
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1Also related: Can the principle of explosion be removed from constructive logic? – MJD Jun 26 '13 at 15:23