Foundations of Logic and Mathematics |
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Contents
General Remarks about Nonlogical Calculi Axiom Systems | 37 |
An Elementary Mathematical Calculus | 38 |
Higher Mathematical Calculi | 42 |
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Common terms and phrases
abstract terms applied axiom system basis C-false C-true sentences C₁ calculus B-C called class of sentences constructed customary interpretation D₁ D₂ deduction defined definitions descriptive signs designata designates discussed elementary terms empirical science Euclidean system example expressions factual content false finite cardinal number formulated Frege fuer geometrical calculus given hence K₁ K₂ kind L-determinate L-implicate L-true language system logical calculus logical signs lower functional calculus mathe mathematical calculus matical metalanguage method mond ist blau mond ist kalt moon is blue normal interpretation object-language observations Peano system physical calculus physical geometry physical theory pragmatics predicates premisses primitive sentences procedure proof provable real numbers Rudolf Carnap rule SL rules of formation rules of inference rules of transformation S₁ S₂ semantical rules sentences of C₁ sentential calculus singular sentences specific calculus specific signs T₁ T₂ tences theorems tion translation true interpretation truth conditions Unified Science Unity of Science variable