Logic: Depth Grammar of Rationality : a Textbook on the Science and History of Logic

abstract analysis argument Aristotelian Aristotle Aristotle's assumption axiomatic system axioms basic called class calculus complete concept concerned conclusion consequence consists constructed decision procedure defined definition derived disjunct empirical science equivalent existence existential expression fact fallacy formal logic formal system Frege function functors grammar human implication individual induction knowledge laws linguistic logical language logical truth logicians Lukasiewicz major premiss many-valued logic mathematical logic meaning metalogic method modal logic modern logic natural deduction negation negative notation objective operations paradox particular philosophical philosophy of logic possible predicate logic present principle problem proof propositional logic quantifiers rational reality reasoning relation relationship rules of inference Russell Russell's Russell's paradox scientific semantic sense sentence signify simple Socrates statement structure supposition syllogism syllogistic symbols syntactic tautology theorems theory things thought Tractatus traditional truth condition truth-tables universal valid variables vernacular Wittgenstein words