Holdings: The conceptual roots of mathematics

The conceptual roots of mathematics: an essay on the philosophy of mathematics

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Bibliographic Details
Main Author:	Lucas, John R. 1929-2020 (Author)
Format:	Book
Language:	English
Published:	London [u.a.] Routledge 2000
Edition:	1. publ.
Series:	International library of philosophy
Subjects:	Filosofische aspecten Grondslagen Mathématiques - Philosophie Wiskunde Mathematik Philosophie Mathematics > Philosophy
Online Access:	Inhaltsverzeichnis
Physical Description:	XVII, 452 S. Ill., graph. Darst.
ISBN:	041520738X

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MARC


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adam_text	THE CONCEPTUAL ROOTS OF MATHEMATICS AN ESSAY ON THE PHILOSOPHY OF MATHEMATICS J.R. LUCAS LONDON AND NEW YORK CONTENTS SECTION PAGE CHAPTER 1 PLATO S PHILOSOPHIES OF MATHEMATICS 1.1 MENO 1 1.2 A PRIORI 3 1.3 RELEVANCE 5 1.4 WHAT ARE WE TALKING ABOUT? 9 1.5 HOW DO WE KNOW? 13 1.6 MODALITY 20 1.7 COGENCY 22 1.8 DEDUCTION 24 1.9 WHENCE THE PREMISSES? 27 CHAPTER 2 GEOMETRY 2.1 EUCLID 33 2.2 THE FIFTH POSTULATE 34 2.3 NON-EUCLIDEAN GEOMETRIES 39 2.4 FORMAL AND PHYSICAL GEOMETRY 44 2.5 CONCEPTUAL CONSTRAINTS 49 2.6 WHICH GEOMETRY? 54 2.7 THE THEORY OF CROUPS 57 2.8 PYTHAGOREAN GEOMETRY HAS A BETTER METRIE 60 2.9 DESARGUES 63 2.10 CONCLUSIONS 64 CHAPTER 3 FORMALISM 3.1 MORE GEOMETRICO 68 3.2 FORMALISING 70 3.3 MAXIMUM COGENCY 70 3.4 THE THEORY OF FORMAL SYSTEMS 75 3.5 MEANING AND INTERPRETATION 81 3.6 EPISTEMOLOGICAL FORMALISM 84 3.7 THE LOGICIST PROGRAMME 87 XM THE CONCEPTUAL ROOTS OF MATHEMATICS CHAPTER 4 NUMBERS: THE CARDINAL APPROACH 4.1 4.2 4.3 4.4 4.5 4.6 4.7 CHAPTEI 5.1 5.2 5.3 5.5 5.5 5.6 5.7 CHAPTEI 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 CHAPTER 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 ETYMOLOGY THE USES OF NUMBERS HOW MANY? NOUGHT QUOTIFIERS AND QUOTITIES FREGE S EXTENSIONS AND SETS PARADIGM SETS 5 NUMBERS: THE ORDINAL APPROACH THE SUPERLATIVE APPROACH DEDEKIND S SUCCESSOR AND SO ON GROUNDING THE ORDINALS HOW TO COUNT ORDINALS AND CARDINAIS CONCLUSION 6 NUMBERS: THE ABSTRACT APPROACH THE THIRD APPROACH PEANO MONOMORPHISM AND NON-STANDARD MODELS IMMIGRATION CONTROL THE FIFTH POSTULATE SORITES ARITHMETIC DIALOGUES RECURSIVE REASONING THE NATURAL NUMBERS 7 THE INFINITE IN DEFENCE OF DOUBT CARDINALITY THE MOSTEST CHARACTERIZATION OF INTUITIONISM PROOFS AND DIALOGUES VERIFICATIONIST ARGUMENTS FOR INTUITIONISM SELECTIVE SCEPTICISM ULTRAFINITISM LAX FINITISM 90 92 95 101 102 106 109 114 115 118 120 122 123 124 126 127 132 138 143 145 146 152 154 157 159 165 169 172 181 187 189 192 THE CONCEPTUAL ROOTS OF MATHEMATICS 7.10 7.11 LAPTER 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 LAPTER 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 ACTUALISING POTENTIALITY ALL 8 THE IMPLICATIONS OF GOEDEL S PONS ASINORUM THE FLAVOUR OF THE GOEDELIAN ARGUMENT GOEDEL NUMBERING TRANSLATION DIAGONALIZATION CONDITIONS COROLLARIES AND CONSEQUENCES CHURCH S THEOREM AND TURING S THEOREM GOEDEL S SECOND THEOREM MECHANISM GOEDEL S THEOREM AND PROVABILITY 9 TRANSITIVE RELATIONS LOGIC EQUIVALENCE RELATIONS FUNCTIONS IDENTITY IN DIFFERENCE ORDERING RELATIONS MACROSTRUCTURE AND MICROSTRUCTURE THE CONTINUUM THE MARRIAGE OF EQUIVALENCE WITH ORDER CONVERSE TRANSITIVITY PARADIGM PARTIAL ORDERINGS LATTICES AND SET THEORY TREES AND MEREOLOGY 193 196 THEOREM 199 200 201 203 206 210 212 214 216 218 219 224 226 232 234 236 239 245 249 253 255 257 261 XV THE CONCEPTUAL ROOTS OF MATHEMATICS CHAPTEI 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 CHAPTEI 11.1 11.2 11.3 11.4 11.5 11.6 11.7 CHAPTER 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 CHAPTER 13.1 13.2 13.3 13.4 13.5 13.6 13.7 * 10 PROTOTOPOLOGY TOGETHERNESS AXIOMATIC APPROACHES WHITEHEAD S PROGRAMME FAILURE POINTED AND LINEAR HOPES ALTERNATIVES MOOREOLOGY MORE MEREOLOGY 11 MAGNITUDE AND MEASURE QUANTUM? AND QUOT? THE POINT OF MEASURING EQUIVALENCE STRUCTURES ADDITION RULES LIMITS AND ZERO ZENO MEASURES AND NUMBERS 12 DOWN WITH SET THEORY MULTITUDES AND MAGNITUDES RUSSELL S PARADOX RESPONSES TO PARADOX FORMAL APPROACHES THE SKOLEM PARADOX THE AXIOM OF CHOICE THE CONTINUUM HYPOTHESES AXIOMS AND EXISTENCE THE AXIOM OF EXTENSIONALITY CONCLUSION 13 CHASTENED LOGICISM? LOGICISM WHAT IS LOGIC? BOOLEAN PLUS ITERATED MODALITIES COMPLETENESS PARADOX SECOND-ORDER LOGIC 271 272 274 277 279 282 283 285 291 292 294 298 301 302 306 311 314 315 319 322 323 328 330 333 337 340 342 343 348 353 356 358 XVI THE CONCEPTUAL ROOTS OF MATHEMATICS 13.8 ANALYTIC AND A PNON TRUTH 361 CHAPTER 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 CHAPTER 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 14 MATHEMATICAL KNOWLEDGE SYNTHETIC A PRIORI 1 ? NOT SEEING BUT DOING PATTERN RECOGNITION LAKATOS COGENCY AND DIALOGUE ON BEHALF OF THE FOOL HUBERT THE BED THEORY OF TRUTH MATHEMATICAL KNOWLEDGE 15 REALISM REVISITED EXISTENCE AND REALITY SELF-SUBSISTENT OBJEETS MEANING AND IMPREDICATIVITY BIVALENCE AND DETERMINACY COMPETING TRUTHS CONTINGENCY AND STRUCTURE COHERENCE AND DEPTH LAWS OF THE LAWS OF NATURE CHASTENED ISMS ENVOI SUMMARIES INDEX 363 366 368 372 377 379 383 388 394 399 403 407 413 415 418 422 424 427 433 435 442 XVLL
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author	Lucas, John R. 1929-2020
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spelling	Lucas, John R. 1929-2020 Verfasser (DE-588)124931537 aut The conceptual roots of mathematics an essay on the philosophy of mathematics J. R. Lucas 1. publ. London [u.a.] Routledge 2000 XVII, 452 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International library of philosophy Filosofische aspecten gtt Grondslagen gtt Mathématiques - Philosophie Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 Äquivalent Druck-Ausgabe, Paperback 978-0-415-51372-2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008753726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lucas, John R. 1929-2020 The conceptual roots of mathematics an essay on the philosophy of mathematics Filosofische aspecten gtt Grondslagen gtt Mathématiques - Philosophie Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4045791-6 (DE-588)4037944-9
title	The conceptual roots of mathematics an essay on the philosophy of mathematics
title_auth	The conceptual roots of mathematics an essay on the philosophy of mathematics
title_exact_search	The conceptual roots of mathematics an essay on the philosophy of mathematics
title_full	The conceptual roots of mathematics an essay on the philosophy of mathematics J. R. Lucas
title_fullStr	The conceptual roots of mathematics an essay on the philosophy of mathematics J. R. Lucas
title_full_unstemmed	The conceptual roots of mathematics an essay on the philosophy of mathematics J. R. Lucas
title_short	The conceptual roots of mathematics
title_sort	the conceptual roots of mathematics an essay on the philosophy of mathematics
title_sub	an essay on the philosophy of mathematics
topic	Filosofische aspecten gtt Grondslagen gtt Mathématiques - Philosophie Wiskunde gtt Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Filosofische aspecten Grondslagen Mathématiques - Philosophie Wiskunde Mathematik Philosophie Mathematics Philosophy
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