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antinomy applied arguments Aristotle asserted axiomatic system axioms bivalent logic Bochenski C. I. Lewis calculus of classes called Carnap CCpqCNqNp chapter Combinatory logic connex contains Contraposition converse domain deduced defined developed Domains and Fields dyadic functor element equiform equivalence Example existential closure existential quantifier Explanation expression composed expression formed false father followed formed by substituting Frege and Peano Hilbert History identity individual constants Literature logicians Lukasiewicz material implication mathematical logic matrix metalogical modal logic monadic monadic predicates negation normal form null class p/Aba p/Ema parenthesis Peano-Russell notation pipe-smokers preceeded Primitive Terms Principle px D y/x q/AqApr q/Eba q/Iba q/Ibm Quine r/ApAqr r/Eba r/Iba r/Oba rigorous rule 9 rules of deduction Rules of Formation sentential calculus signifies smoking a pipe Syllogistic syntactical categories theorem theory of types triadic relation trivalent logic truth functors truth values unit classes universal closure variables