The conceptual roots of mathematics: an essay on the philosophy of mathematics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Routledge
2000
|
| Edition: | 1. publ. |
| Series: | International library of philosophy
|
| Subjects: | |
| Links: | 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 |
| Physical Description: | XVII, 452 S. Ill., graph. Darst. |
| ISBN: | 041520738X |
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| 245 | 1 | 0 | |a The conceptual roots of mathematics |b an essay on the philosophy of mathematics |c J. R. Lucas |
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Record in the Search Index
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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
|
| any_adam_object | 1 |
| author | Lucas, John R. 1929-2020 |
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| callnumber-label | QA8 |
| callnumber-raw | QA8.4 |
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| callnumber-sort | QA 18.4 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 SG 700 |
| ctrlnum | (OCoLC)40754886 (DE-599)BVBBV012863782 |
| dewey-full | 510/.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.1 |
| dewey-search | 510/.1 |
| dewey-sort | 3510 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV012863782 |
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| indexdate | 2024-12-20T10:37:30Z |
| institution | BVB |
| isbn | 041520738X |
| language | English |
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| physical | XVII, 452 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Routledge |
| record_format | marc |
| series2 | International library of philosophy |
| 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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