The language of mathematics : a linguistic and philosophical investigation

The language of mathematics : a linguistic and philosophical investigation

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 mathem...

Description complète

Enregistré dans:
Détails bibliographiques
Auteur principal : Ganesalingam Mohan (Auteur)
Format : Livre
Langue : anglais
Titre complet : The language of mathematics : a linguistic and philosophical investigation / by Mohan Ganesalingam
Publié : Berlin, Heidelberg : Springer Berlin Heidelberg , 2013
Cham : Springer Nature
Collection : Theoretical computer science and general issues (Online)
Accès en ligne : Accès Nantes Université
Accès direct soit depuis les campus via le réseau ou le wifi eduroam soit à distance avec un compte @etu.univ-nantes.fr ou @univ-nantes.fr
Note sur l'URL : Accès sur la plateforme de l'éditeur
Accès sur la plateforme de l'éditeur (Springer)
Accès sur la plateforme Istex
Condition d'utilisation et de reproduction : Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017
Sujets :
Computer Science
Language Translation and Linguistics
Artificial Intelligence (incl. Robotics)
Mathematical Logic and Formal Languages
Computer Imaging, Vision, Pattern Recognition and Graphics
Natural Language Processing (NLP).
Artificial Intelligence.
Formal Languages and Automata Theory
Documents associés : Autre format: The Language of Mathematics
Autre format: The Language of Mathematics
LEADER 07444clm a2200709 4500
001 PPN169139875
003 http://www.sudoc.fr/169139875
005 20241001155300.0
010 |a 978-3-642-37012-0 
017 7 0 |a 10.1007/978-3-642-37012-0  |2 DOI 
035 |a (OCoLC)847121251 
035 |a Springer978-3-642-37012-0 
035 |a SPRINGER_EBOOKS_LN_PLURI_10.1007/978-3-642-37012-0 
035 |a Springer-11645-978-3-642-37012-0 
100 |a 20130507d2013 u u0frey0103 ba 
101 0 |a eng  |2 639-2 
102 |a DE 
135 |a dr||||||||||| 
181 |6 z01  |c txt  |2 rdacontent 
181 1 |6 z01  |a i#  |b xxxe## 
182 |6 z01  |c c  |2 rdamedia 
182 1 |6 z01  |a b 
183 |6 z01  |a ceb  |2 RDAfrCarrier 
200 1 |a The language of mathematics  |e a linguistic and philosophical investigation  |f by Mohan Ganesalingam 
214 0 |a Berlin, Heidelberg  |c Springer Berlin Heidelberg 
214 2 |a Cham  |c Springer Nature  |d 2013 
225 0 |a Theoretical Computer Science and General Issues  |x 2512-2029  |v 7805 
330 |a 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 Gowers. 
359 1 |a 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 Ranta s 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 Rhetorical Structure -- 3.5.1 Explanation -- 3.5.2 Blocks -- 3.5.3 Variables and Assumptions -- 3.5.4 Related Work: DRT in NaProChe -- 3.6 Conclusion -- 4 Ambiguity.-4.1 Ambiguity in Symbolic Mathematics.-4.1.1 Ambiguity in Symbolic Material.-4.1.2 Survey: Ambiguity in Formal Languages.-4.1.3 Failure of Standard Mechanisms -- 4.1.4 Discussion.-4.1.5 Disambiguation without Type -- 4.2 Ambiguity in Textual Mathematics.-4.2.1 Survey: Ambiguity in Natural Languages.-4.2.2 Ambiguity in Textual Mathematics -- 4.2.3 Disambiguation without Type -- 4.3 Text and Symbol -- 4.3.1 Dependence of Symbol on Text -- 4.3.2 Dependence of Text on Symbol -- 4.3.3 Text and Symbol: Conclusion -- 4.4 Conclusion -- 5 Type -- 5.1 Distinguishing Notions of Type -- 5.1.1 Types as Formal Tags -- 5.1.2 Types as Properties -- 5.2 Notions of Type in Mathematics -- 5.2.1 Aspect as Formal Tags -- .2.2 Aspect as Properties -- 5.3 Type Distinctions in Mathematics -- 5.3.1 Methodology -- 5.3.2 Examining the Foundations -- 5.3.3 Simple Distinctions -- 5.3.4 Non-extensionality.-5.3.5 Homogeneity and Open Types -- 5.4 Types in Mathematics -- 5.4.1 Presenting Type: Syntax and Semantics -- 5.4.2 Fundamental Type -- 5.4.3 Relational Type -- 5.4.4 Inferential Type -- 5.4.5 Type Inference -- 5.4.6 Type Parametrism -- 5.4.7 Subtyping -- 5.4.8 Type Coercion -- 5.5 Types and Type Theory -- 6 TypedParsing -- 6.1 Type Assignment -- .1.1 Mechanisms -- 6.1.2 Example -- 6.2 Type Requirements -- 6.3 Parsing -- 6.3.1 Type -- 6.3.2 Variables.-6.3.3 Structural Disambiguation -- 6.3.4 Type Cast Minimisation -- 6.3.5 Symmetry Breaking -- 6.4 Example -- 6.5 Further Work -- 7 Foundations -- 7.1 Approach -- 7.2 False Starts -- 7.2.1 All Objects as Sets -- 7.2.2 Hierarchy of Numbers -- 7.2.3 Summary of Standard Picture -- 7.2.4 Invisible Embeddings -- 7.2.5 Introducing Ontogeny -- 7.2.6 Redefinition -- 7.2.7 Manual Replacement -- 7.2.8 Identification and Conservativity -- 7.2.9 Isomorphisms Are Inadequate -- 7.3 Central Problems -- 7.3.1 Ontology and Epistemology -- 7.3.2 Identification -- 7.3.3 Ontogeny -- 7.4 Formalism -- 7.4.1 Abstraction -- 7.4.2 Identification -- 7.5 Application.-7.5.1 Simple Objects.-7.5.2 Natural Numbers -- 7.5.3 Integers -- 7.5.4 Other Numbers -- 7.5.5 Sets and Categories -- 7.5.6 Numbers and Late Identification -- 7.6 Further Work -- 8 Extensions -- 8.1 Textual Extensions -- 8.2 Symbolic Extensions -- 8.3 Covert Arguments -- Conclusion. 
371 0 |a Accès en ligne pour les établissements français bénéficiaires des licences nationales 
371 0 |a Accès soumis à abonnement pour tout autre établissement 
371 1 |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales  |c chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 
410 | |0 200114832  |t Theoretical computer science and general issues (Online)  |x 2512-2029 
452 | |t The Language of Mathematics  |b Texte imprimé  |y 9783642370137 
452 | |t The Language of Mathematics  |b Texte imprimé  |y 9783642370113 
610 1 |a Computer Science 
610 2 |a Language Translation and Linguistics 
610 2 |a Artificial Intelligence (incl. Robotics) 
610 2 |a Mathematical Logic and Formal Languages 
610 2 |a Computer Imaging, Vision, Pattern Recognition and Graphics 
610 2 |a Computer Imaging, Vision, Pattern Recognition and Graphics 
610 2 |a Computer Imaging, Vision, Pattern Recognition and Graphics 
610 2 |a Natural Language Processing (NLP). 
610 2 |a Artificial Intelligence. 
610 2 |a Formal Languages and Automata Theory 
615 |a @Computer Science  |n 11645  |2 Springer 
676 |a 006.6  |v 23 
680 |a T385 
680 |a TA1637-1638 
680 |a TK7882.P3 
700 1 |3 PPN170284670  |a Ganesalingam  |b Mohan  |f 19..-....  |4 070 
801 3 |a FR  |b Abes  |c 20240814  |g AFNOR 
801 1 |a DE  |b Springer  |c 20240603  |g AACR2 
856 4 |u https://doi.org/10.1007/978-3-642-37012-0  |z Accès sur la plateforme de l'éditeur 
856 4 |u https://doi.org/10.1007/978-3-642-37012-0  |z Accès sur la plateforme de l'éditeur (Springer) 
856 4 |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-R7N5ZP27-D  |z Accès sur la plateforme Istex 
856 4 |5 441099901:830857818  |u https://budistant.univ-nantes.fr/login?url=https://doi.org/10.1007/978-3-642-37012-0 
915 |5 441099901:830857818  |b SPRING13-00800 
930 |5 441099901:830857818  |b 441099901  |j g 
991 |5 441099901:830857818  |a Exemplaire créé en masse par ITEM le 30-09-2024 16:14 
997 |a NUM  |b SPRING13-00800  |d NUMpivo  |e EM  |s d 
998 |a 978635