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. |
目次
The Prehistory of Research into Foundations Sections | 3 |
Aristotles Theory of Science | 31 |
Historical Development of Symbolic Logic | 52 |
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多く使われている語句
A₁ algebra appear applied argument Aristotle's arithmetic atoms axiom of choice axiom system axiomatisation cardinal number Carnap closure conception condition consistency proof consistent construction contains corresponding deduction theorem deductive theory defined definition denoted densely ordered derivation discussion elementary logic elements entities Example expression finitary finite follows formal system formalised formula free variables Frege fulfils given Gödel number hence Hilbert's integers introduce intuitionistic logic intuitionistic mathematics logic of higher logical identity logical system m₁ m₂ metamathematics method natural numbers neighbourhood system notation notion F obtained ordinal parameters postulates predicate principle problem proof by recursion proof theory provable prove quantifiers rational numbers real numbers relation replaced result right column rules satisfies Section 76 semantic tableau sentence sentential logic sequence sequent f set theory statement subformula subset Suppose t₁ Tarski thesis of elementary valid valuation values well-ordered well-ordering theorem X₁