The Language of Mathematics A Linguistic and Philosophical Investigation [Paperback]

The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement. Timothy GowersThis book, which blends techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language, was awarded the E.W. Beth Prize for outstanding dissertations in logic, language, and information.Introduction.-1.1 Challenges.- 1.2 Concepts.-1.2.1 Linguistics and Mathematic.-1.2.2 Time.- 1.2.3 Full Adaptivity.- .3 Scope.- 1.4 Structure.- 1.5 Previous Analyses.- 1.5.1 Ranta.- 1.5.2 de Bruijn.- 1.5.3 Computer Languages.- 1.5.4 Other Work.- 2 The Language of Mathematics.- 2.1 Text and Symbol.- 2.2 Adaptivity.- 2.3 Textual Mathematics.- 2.4 Symbolic Mathematics. -2.4.1 Rantas Account and Its Limitations.- 2.4.2 Surface Phenomena.- 2.4.3 Grammatical Status.- 2.4.4 Variables.- 2.4.5 Presuppositions .- 2.4.6 Symbolic Constructions.- 2.5 Rhetorical Structure.- 2.5.1 Blocks.- 2.5.2 Variables and Assumptions.- 2.6 Reanalysis.- 3 Theoretical Framework.- 3.1 Syntax.- 3.2 Types.- 3.3 Semantics.- 3.3.1 The Inadequacy of First-Order Logic.- 3.3.2 Discourse Representation Theory.- 3.3.3 Semantic Functions.- 3.3.4 Representing Variables.- 3.3.5 Localisable Presuppositions.- 3.3.6 Plurals.- 3.3.7 Compositionality.- 3.3.8 Ambiguity and Type.- 3.4 Adaptivity.- 3.4.1 Definitions in Mathematics.- 3.4.2 Real Definitions and Functional Categories.- 3.5 Rhetoril“*