For many philosophers, modern philosophy begins in 1879 with the publication of Frege's Begriffsschrift, in which Frege presents the first truly modern logic in his symbolic language, Begriffsschrift, or concept-script. Macbeth's book, the first full-length study of this language, offers a highly original new reading of Frege's logic based directly on Frege's own two-dimensional notation and his various writings about logic.
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analysis Begriffsschrift Begriffsschrift sentence Bertrand Russell cept computational content concavity notation concavity with German conceived concept words conditional stroke course of values definition designate distinction extension fact first-level concepts formula language Frege claims Frege seems Frege suggests Frege thinks Frege's Latin italic Frege's logic Frege's mature Frege's view function and argument Function and Concept genuine hypothetical German letters given grasp Grundgesetze Grundlagen guage higher-level concepts identity instance judgment and inference judgment stroke language of arithmetic Latin italic letters laws of logic logical language logical relations loves Juliet Mathematics mature logic merely metic modes of inference natural language numeration system object names perspicuously predicate properly logical proposition quantificational logic rela relevant role Romeo rules of inference Russell Russell's paradox second-level concept sorts of letters strategy symbols tence theorems things thought expressed tion truth conditions truth-values understand universal quantifier variable variously analyzable
Page 6 - The time was one of intellectual intoxication. My sensations resembled those one has after climbing a mountain in a mist, when, on reaching the summit, the mist suddenly clears, and the country becomes visible for forty miles in every direction.
Page 6 - For years I had been endeavouring to analyse the fundamental notions of mathematics, such as order and cardinal numbers. Suddenly, in the space of a few weeks, I discovered what appeared to be definitive answers to the problems which had baffled me for years.