Philosophy of mathematics: Volume 1 Historical readings in the philosophy of mathematics
Gespeichert in:
| Weitere beteiligte Personen: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Abingdon, Oxon ; New York, NY
Routledge
2017
|
| Schriftenreihe: | Critical concepts in philosophy
|
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029434042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xlv, 255 Seiten |
| ISBN: | 9781138886629 |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Editor s Acknowledgements xii
Acknowledgements xiii
Chronological table of reprinted articles and chapters xvii
Introduction xxvi
VOLUME I HISTORICAL READINGS IN THE
PHILOSOPHY OF MATHEMATICS
1 Meno 80b—86b 1
PLATO
2 Phaedo 72e-77d 31
PLATO
3 Republic book 6, 507a-511e 37
PLATO
4 Republic book 7, 525a-527c 42
PLATO
5 Metaphysics book B, part II 48
ARISTOTLE
6 Metaphysics book E, part I 52
ARISTOTLE
7 Metaphysics book Z, part X—XI 54
ARISTOTLE
8 Metaphysics book Th, part IX 59
ARISTOTLE
V
9
10
11
12
13
14
15
16
17
18
19
20
21
22
60
64
69
74
76
80
83
89
103
109
117
119
121
126
CONTENTS
Metaphysics book I, parts I—II
ARISTOTLE
Metaphysics book K, parts II-IV and VII
ARISTOTLE
Metaphysics book M, parts I-III
ARISTOTLE
Physics book B, part II
ARISTOTLE
Physics book C, parts VI-VIII
ARISTOTLE
De Anima (On the soul), book C, parts VI-VIII
ARISTOTLE
Discourse on the Method, part 2
RENÉ DESCARTES
An essay concerning human understanding, book I, chapter II
JOHN LOCKE
An essay concerning human understanding, book IV, chapter II
JOHN LOCKE
Treatise concerning the principles of human knowledge,
sections 118-134
GEORGE BERKELEY
Reply to Bay le’s note L, sections 23-25
GOTTFRIED LEIBNIZ
Monadology, sections 28-38
GOTTFRIED LEIBNIZ
The art of discovery
GOTTFRIED LEIBNIZ
Preliminary discourse to the encyclopedia of Diderot, part I
D’ALEMBERT, J. L.
VI
CONTENTS
23 Critique of Pure Reason, Bl-73
IMMANUEL KANT
24 Prolegomena to any future metaphysics, sections 6-13
(inc. Remarks I and II)
IMMANUEL KANT
25 A system of logic, book II, chapter VI
JOHN STUART MILL
26 A system of logic, book III, chapter XXIV
JOHN STUART MILL
27 The nature and meaning of numbers
RICHARD DEDEKIND
28 Geometry and experience
ALBERT EINSTEIN
VOLUME II EARLY 20TH CENTURY PHILOSOPHIES:
LOGICISM, INTUITIONISM, FORMALISM
AND LOGICAL EMPIRICISM
PART 1
Logicism and its critics
29 Foundations of arithmetic, sections 55-109
GOTTLOB FREGE
30 Bertrand Russell ys letter to Frege, and Frege’s reply to Russell
BERTRAND RUSSELL AND GOTTLOB FREGE
31 Principia Mathematical introduction to
the 2nd ed. and introduction
ALFRED NORTH WHITEHEAD AND BERTRAND RUSSELL
32 Mathematics and logic in
HENRI POINCARE 33 * *
33 Introduction to mathematical philosophy, chapters 1-3,
12-13 and 18
BERTRAND RUSSELL
VÜ
135
168
175
184
203
246
1
3
39
47
171
200
CONTENTS
34 On the philosophical significance of Frege’s Theorem 241
CRISPIN WRIGHT
35 Is Hume’s Principle analytic? 277
GEORGE BOOLOS
PART 2
Intuitionism 291
36 On the significance of the principle of excluded middle
in mathematics, especially in function theory 293
LUITZEN EGBERTUS JAN BROUWER
37 The intuitionist foundations of mathematics 309
AREND HEYTING
38 Disputation 320
AREND HEYTING
39 The philosophical basis of intuitionistic logic 332
MICHAEL DUMMETT
PART 3
Formalism 361
40 On the infinite 363
DAVID HILBERT
41 Finitism 399
WILLIAM TAIT
PART 4
Logical empiricism 421
42 Language, truth, and logic, chapter IV 423
A.J. AYER 43 *
43 General theory of knowledge, sections 7 and 38 435
MORITZ SCHLICK
viii
CONTENTS
44 Empiricism, semantics and ontology 449
RUDOLF CARNAP
VOLUME III CONTEMPORARY FOUNDATIONS,
SET THEORY AND STRUCTURALISM
45 Investigations in the foundations of set theory I I
ERNST ZERMELO
46 Word and object, chapter 7 27
WILLARD V. QUINE
47 What numbers could not be 64
PAUL BENACERRAF
48 Mathematical truth 84
PAUL BENACERRAF
49 Realism in mathematics, chapter 2 99
PENELOPE MADDY
50 Mathematics without foundations 140
HILARY PUTNAM
51 Mathematics without numbers, introduction
and chapter 1 155
GEOFFREY HELLMAN
52 The structuralist view of mathematical objects 199
CHARLES PARSONS
53 Mathematics is megethology 235
DAVID LEWIS
54 Three varieties of mathematical structuralism 255
GEOFFREY HELLMAN 55 *
55 What are sets and what are they for? 281
ALEX OLIVER AND TIMOTHY SMILEY
IX
CONTENTS
56 Category theory as an autonomous foundation 316
0YSTEIN LINNEBO AND RICHARD PETTIGREW
VOLUME IV PROOF AND MATHEMATICAL
JUSTIFICATION
57 On formally undecidable propositions of Principia
Mathematica and related systems I 1
KURT GÖDEL
58 What is Cantor’s continuum problem? 29
KURT GÖDEL
59 The iterative conception of set 51
GEORGE BOOLOS
60 A renaissance of empiricism in the recent philosophy
of mathematics 66
IMRE LAKATOS
61 Arithmetical truth and hidden higher-order concepts 89
DANIEL ISAACSON
62 Believing the axioms. I 109
PENELOPE MADDY
63 Does V equal L? 146
PENELOPE MADDY
64 The epistemic status of probabilistic proof 176
DON FALLIS
65 Purity as an ideal of proof 194
MICHAEL DETLEFSEN
66 An introduction to GödeVs theorems, chapters 44—45 211
PETER SMITH 67
67 Knowledge of mathematics without proof 243
A.C. PASEAU
X
CONTENTS
VOLUME V THE INDISPENSABILITY ARGUMENT
68 Two dogmas of empiricism 1
WILLARD V. QUINE
69 Steps toward a constructive nominalism 20
NELSON GOODMAN AND W. V. QUINE
70 Philosophy of logic 40
HILARY PUTNAM
71 Science without numbers, preliminary remarks and chapters 1-5 73
HARTRY FIELD
72 Is mathematical knowledge just logical knowledge? 106
HARTRY FIELD
73 Nominalist platonism 140
GEORGE BOOLOS
74 Mathematics and indispensability 153
ELLIOTT SOBER
75 Naturalism in mathematics, chapter 6 171
PENELOPE MADDY
76 A subject with no object: strategies for nominalistic
interpretation of mathematics, introduction and conclusion 197
JOHN P. BURGESS AND GIDEON ROSEN
77 The indispensability of mathematics, chapters 4-6 289
MARK COLYVAN
78 Are there genuine mathematical explanations
of physical phenomena? 357
ALAN BAKER
79 Scientific platonism 371
A C. PASEAU
Index 403
xi
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| indexdate | 2024-12-20T17:51:40Z |
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| isbn | 9781138886629 |
| language | English |
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| series2 | Critical concepts in philosophy |
| spellingShingle | Philosophy of mathematics |
| title | Philosophy of mathematics |
| title_auth | Philosophy of mathematics |
| title_exact_search | Philosophy of mathematics |
| title_full | Philosophy of mathematics Volume 1 Historical readings in the philosophy of mathematics edited by A.C. Paseau |
| title_fullStr | Philosophy of mathematics Volume 1 Historical readings in the philosophy of mathematics edited by A.C. Paseau |
| title_full_unstemmed | Philosophy of mathematics Volume 1 Historical readings in the philosophy of mathematics edited by A.C. Paseau |
| title_short | Philosophy of mathematics |
| title_sort | philosophy of mathematics historical readings in the philosophy of mathematics |
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