A profile of mathematical logic
This text explores the historical reasons for the formation of Aristotelian logic, the rise of mathematical logic, the nature of the formal axiomatic method and its use, and the main results of metatheory and their import. 1971 edition. Includes 22 figures and 19 tables. Appendixes. Bibliography. Indexes.
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Historical background of mathematical logic 1 Introduction
Mathematics before Aristotle
Argumentation before Aristotle
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analogous angles argument form Aristotle assumption axioms called Cantor cardinal number computing concept conclusion Consider the following consistent contains corresponding decision procedure defined definition denumerable domain of discourse elements equal equivalent Euclid Euclidean geometry example exists expression F F F F T F fifth postulate finite formal axiomatic method formal system given Godel number Goldbach's conjecture Hence incompleteness theorem inconsistent infinite number initial formulas invalid Juliet logicians machine mathematical logic means metalanguage metamathematical natural numbers non-Euclidean geometry object language paradox philosophical Plato possible predicate calculus premiss primitive recursive arithmetic priori problem proof propositional calculus propositional constants propositional variables provable provable-in-j prove quantifier question rational numbers real numbers recursive functions represented Saccheri sentence sequence set theory Skolem Socrates someone statement straight line Suppose syllogism symbols syntactical tautology tion transfinite transformation rules translated triangle truth functions truth table undecidable unsolvable valid