The infinite:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Routledge
2005
|
| Ausgabe: | 2. ed., [Nachdr.] |
| Schriftenreihe: | The problems of philosophy
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 268 S. |
| ISBN: | 0415252857 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
to the
Second
Edition
xi
Preface
xx
Introduction: Paradoxes of the Infinite
1
1
Paradoxes of the infinitely small
3
2
Paradoxes of the infinitely big
S
3
Paradoxes of the one and the many
9
4
Paradoxes of thought about the infinite
11
PART ONE: THE HISTORY
1
Early Greek Thought
17
1
Anaximander and to apeiron
17
2
The Pythagoreans
19
3
TheEleatics
23
4
Plato
26
5
Early Greek mathematics
28
2
Aristotle
34
1
Preliminaries
34
2
The problem
36
3
The solution: the potential infinite and the actual infinite
39
4
Application of the solution
40
5
A remaining difficulty
44
3
Medieval and Renaissance Thought
45
1
The Greek legacy: reactions and developments
45
2
Aquinas
48
3
Later developments: the mathematically infinite
50
4
Nicholas of
Cusa.
The end of the Renaissance
55
4
The Calculus
57
1
The fundamental principles of the calculus
57
VU
The Infinite
2
Abriefhistoryofthecalculus
ω
3
Taking stock 70
5
The Rationalists and the Empiricists
75
1
The rationalists J?
2
The empiricists °°
6
Kant
84
1
The background: an outline of Kant s philosophy °*
2
The metaphysically infinite and the mathematically infinite
86
3
The infinitude of the world. The antinomies ^
4
The infinitude of reason ^
7
Post-Kantian Metaphysics of the Infinite %
1
Hegel %
2
Currents of thought in post-Hegelian metaphysics of the
infinite I: the metaphysically big 10°
3
Currents of thought in post-Hegelian metaphysics of the
infinite
Π:
the metaphysically small 103
4
Currents of thought in post-Hegelian metaphysics of the
infinitem:
the existentialists 105
5
Nietzsche 108
8
The Mathematics of the Infinite, and the Impact of Cantor HO
1
Bolzano 112
2
Turn-of-thc-ccntury work on the foundations of mathematics
113
3
The main elements of Cantor s theory. Its early reception
И8
4
The theory of ordinals. The Burali-Forti paradox 123
5 Cantoťs
attitude to the paradoxes 127
6
Later development:
axiomatization ^
9
Reactions 131
1
Intuiţionism
131
2
Fînitism
133
3
Wittgenstein 137
4
Current thought 141
PART TWO: INFINITY ASSESSED
10
Transfinite
Mathematics 147
1
The iterative conception of a set. The paradox of the Set
of all
Sete *47
2
Ordinals as sets
151
3
Cardinals. Measuring infinite sets 152
vui
Contents
4
The continuum hypothesis
154
5
Further thoughts on the infinite by addition and the infinite
by division
156
11
The
Löwenheim-Skolem
Theorem
159
1
An introduction to the
Lőwenheim-Skolem
theorem.
Reactions and counter-reactions
159
2
The solution to Skolem s paradox. Scepticism and
relativism
163
3
Scepticism and relativism rebutted
165
4
Meaning and understanding. The
Löwenheim-Skolem
theorem finally defused
167
5
A lingering paradox
169
12 Gödel s
Theorem
172
1
Introduction: the Euclidean paradigm
172
2
A sketch of the proof of
Gödel s
theorem
174
3
Hubert s programme
178
4
The human mind and computers
180
5
Self-consciousness
181
6
Meaning and understanding
182
13
Saving and Showing
186
1
The saying/showing distincton in the Tractatus
187
2
The very idea of a saying/showing distinction
190
3
Wittgenstein s early views on the infinite
192
4
The infinite and the ineffable
197
14
Infinity Assessed. The History Reassessed
201
1
The infinite and the ineffable: early Greek thought,
medieval and Renaissance thought, post-Kantian thought
202
2
Aristotle and Kant: an unsuccessful compromise?
203
3
The empiricists: an uncompromising success?
205
4
The Wittgensteinian critique. Aristotle and Kant
vindicated?
206
5
The impossibility of an infinite co-incidence, and the law
of the excluded middle
208
6
A problem for
intuiţionism
211
15
Human Fmitude
218
1
The nature of human fimtude
218
2
Time
221
3
The infinite as an Idea of reason. The saying/showing
distinction revisited
222
IX
The Infinite
4
The poignancy of human nnitude. Death
226
5
Being finite
230
Glossary
234
Notes
236
Bibliography
250
Index
261
|
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| id | DE-604.BV036581734 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:43:23Z |
| institution | BVB |
| isbn | 0415252857 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020502629 |
| oclc_num | 705683774 |
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| owner | DE-355 DE-BY-UBR DE-Aug4 |
| owner_facet | DE-355 DE-BY-UBR DE-Aug4 |
| physical | XXI, 268 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Routledge |
| record_format | marc |
| series2 | The problems of philosophy |
| spelling | Moore, A. W. Verfasser aut The infinite A. W. Moore 2. ed., [Nachdr.] London [u.a.] Routledge 2005 XXI, 268 S. txt rdacontent n rdamedia nc rdacarrier The problems of philosophy Philosophie (DE-588)4045791-6 gnd rswk-swf Unendlichkeit (DE-588)4136067-9 gnd rswk-swf Unendlichkeit (DE-588)4136067-9 s DE-604 Philosophie (DE-588)4045791-6 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020502629&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moore, A. W. The infinite Philosophie (DE-588)4045791-6 gnd Unendlichkeit (DE-588)4136067-9 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4136067-9 |
| title | The infinite |
| title_auth | The infinite |
| title_exact_search | The infinite |
| title_full | The infinite A. W. Moore |
| title_fullStr | The infinite A. W. Moore |
| title_full_unstemmed | The infinite A. W. Moore |
| title_short | The infinite |
| title_sort | the infinite |
| topic | Philosophie (DE-588)4045791-6 gnd Unendlichkeit (DE-588)4136067-9 gnd |
| topic_facet | Philosophie Unendlichkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020502629&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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