The Foundations of Mathematics: A Study in the Philosophy of ScienceNorth-Holland Publishing Company, 1959 - 741 ページ "One of my main motives in writing this book has been the wish to strengthen the ties between foundational research and general philosophy, and to make available both to philosophers and to mathematicians a broad survey of problems and results with such comments as might help in showing their philosophical importance." Evert W. Beth, in the Preface. |
他の版 - すべて表示
多く使われている語句
a₁ applied argument Aristotle Aristotle's arithmetic atoms axiom of choice axiom system axiomatisation B₁ Boolean algebras calculus cardinal number completeness theorem conception condition consider consistency proof consistent construction contains corresponding decision problem defined definition by recursion denoted densely ordered derivation discussion elementary logic elements entities Example expression finitary finite follows formal system formalised formula free variables Frege fulfils function geometry given Gödel Gödel number hence Hilbert's Hilbert's axioms ideal infinite integers interpretation introduce intuitionistic mathematics logical identity M₁ Math metamathematics method natural numbers neighbourhood system notion obtain ordinal paradoxes parameters philosophy Plato Poincaré transformation postulates predicate principles problem proof provable prove pythagorean field quantifiers rational numbers real numbers relation result rules satisfies Section semantic tableau sentence sentential logic sequence set theory statement subset Suppose symbolic logic Tarski theory of science thesis valid valuation well-ordered