An historical introduction to the philosophy of mathematics: a reader
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London ; Oxford ; New York ; New Delhi ; Sydney
Bloomsbury Academic
2016
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxx, 815 Seiten Illustrationen |
| ISBN: | 1472525345 1472525671 9781472525345 9781472525673 |
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Datensatz im Suchindex
| _version_ | 1804176013095075840 |
|---|---|
| adam_text | Acknowledgments Xl
How to use the book xv
Introduction: Terminology and axioms xviii
Part one Ancients
Introduction to part I 3
1 Pythagoras, Parmenides, and Zeno s paradoxes 5
Introductory overview 6
Diogenes Laertius, Pythagoras on the origins of the world 17
Porphyry, Pythagorean uses of numbers 17
Kline, The Pythagoreans 18
Parmenides, The oneness of being 25
Marshall, The Eleatics: Parmenidean oneness and
Zeno s paradoxes 26
Aristotle, On Zeno s paradoxes 28
2 Plato 30
Introductory overview 31
The visible world and the unseen world 39
The divided line and the nature of mathematical objects 39
The forms and numbers 43
Two kinds of arithmetic 48
Knowledge is not perception 48
Knowledge is recollection 51
Contents
The recollection of absolute equality
The allegory of the cave
The importance of mathematical training
3 Aristotle
Introductory overview
Actual and potential infinity
Criticisms of Plato s theory of forms
Argument and recollection
Wisdom
Knowledge and perception
Science, form, and matter
Mathematics and the forms
The argument from division ‘and the separation of mathematics
Mathematics and abstraction
Abstraction and universality
Mathematical truth
Mathematics as a part of wisdom
Part two Moderns
Introduction to part II
4 The rationalists
Introductory overview
Descartes, Mathematics and doubt
Descartes, The certainty of mathematics
Descartes, The ontological argument for the existence of God
Descartes, Clear and distinct perception
Descartes, Analysis and synthesis
Descartes, Synthetic presentation of arguments
Leibniz, Meditations on Knowledge, Truth and Ideas
Locke, Against innate ideas
Leibniz, Mathematics and sense experience
Leibniz, In defense of innate ideas
Leibniz, On Locke s definition of number
Leibniz, On infinity
Leibniz, On axioms
t SC-
151
5 The empiricists 156
Introductory overview 157
Locke, General terms and abstract ideas 167
Locke, Unity and numbers 171
Locke, Infinity 173
Locke, Essences of mathematical figures 176
Locke, Knowledge and proof 177
Locke, Mathematical knowledge as knowledge of ideas 180
Locke, Axioms and abstract ideas 180
Locke, Trifling propositions and mathematics 182
Berkeley, The error of abstract ideas 183
Berkeley, The mind-dependency of number 188
Berkeley, Arithmetic and the doctrine of abstract ideas 189
Berkeley, Geometry and the doctrine of abstract ideas 191
Berkeley, On infinitesimals 193
Berkeley, On the calculus of Leibniz and Newton 194
Hume, Matters of fact and relations of ideas 202
Hume, Reasoning and relations of ideas 203
Hume, Using particular terms generally 204
Hume, The imperfection of geometry 208
6 Kant 21o
Introductory overview 211
The a priori in logic, mathematics, and science 223
Analytic and synthetic judgments 224
Synthetic a priori judgments 226
Intuition and pure intuition 228
Intuition and concepts 229
The transcendental schema and number 230
Geometry and empirical intuition 232
Mathematics and possible experience 234
Mathematics as reason in its dogmatic employment 236
Certainty and mathematical proof 241
Contents
ä ։
IM
eteenth and early twentieth centuries
Introduction to part III
7 Mill
Introductory overview
Mill, An inductive characterization of mathematics
Mill, Hypothetical theories 2r
Mill, Mathematical knowledge as inductive 2՜
Mill, A priori knowledge as knowledge of language 2
Mill, Necessity and conceivability 2
Mill, Arithmetic 2
Mill, Defining numbers 2՛
Mill, Geometry as physical science 2
Frege, On Mill s views of mathematics 2
8 Cantor s transfinites 2
Introductory overview 2
Cantor, On an Elementary Question in the Theory of Manifolds 2!
9 Logicism
Introductory overview
Frege, Preface to Begriffsschrift
Frege, Arithmatic is logic
Frege, Three principles
Frege, A rigorous ground for arithmetic
Frege, On the views of number of Kant and Leibniz
Frege, Numbers are objects
Frege, Characteristics of numbers
Frege, Mathematical objects, mental states,
and the context principle
Frege, Hume s principle, Leibniz s law, and the Caesar problem
Frege, The definition of number
Frege, Arithmetic is analytic
Russell, The natural numbers, Peano, and Frege
Russell, Frege s definition of number
Letters between Russell and Frege
2!
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3
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3
3
3
3*.
3-
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3.
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3‘
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Contents
10 Formalism :i=
Introductory overview 352
Hilbert, On the Infinite 363
11 Intuiţionism 376
Introductory overview 377
Heyting, Disputation 385
Brouwer, Intuition and Formalism 394
12 Conventionalism 405
Introductory overview 406
Carnap, Empiricism, Semantics, and Ontology 41 5
Ayer, The A Priori 428
13 Wittgenstein 440
Introductory overview 441
Wittgenstein, From Remarks on the Foundations
of Mathematics 44 5
14 Gddel s theorems 457
Introductory overview 458
Hintikka, Godel s Incompleteness Proof 461
Part four Contemporary views
Introduction to part IV 471
15 The Benacerraf problem 474
Introductory overview 475
Benacerraf, Mathematical Truth 487
Field, Knowledge of Mathematical Entities 500
16 The indispensability argument 505
Introductory overview 506
Quine, Holism and posits 519
Quine, On What There Is 52 -
Putnam, From Philosophy of Logic 533
Field, From Science without Numbers 545
17 Benacerraf s number puzzle and structuralism
Introductory overview
Benacerraf, What Numbers Could Not Be
Shapiro, Mathematical Structuralism
18 Modalism
Introductory overview
Putnam, Mathematics Without Foundations
19 Fictionalism
Introductory overview
Field, Fictionalism
20 Apriorism
Introductory overview ■
Gödel, Platonism and intuition
Katz, From Realistic Rationalism
21 Maddy s realism
Introductory overview
Maddy, Perception and Intuition
22 Naturalism
Introductory overview
Maddy, Three Forms of Naturalism
23 Plenitudinous platonism
Introductory overview
Balaguer, Full-Blooded Platonism
24 Neo-logicism
Introductory overview
Fleck, Frege s Theorem: An Introduction
25 Experimental mathematics
Introductory overview
Baker, Experimental Mathematics
Bibliography
Index
|
| any_adam_object | 1 |
| author2 | Marcus, Russell 1966- McEvoy, Mark |
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| building | Verbundindex |
| bvnumber | BV043419997 |
| classification_rvk | CC 2400 |
| ctrlnum | (OCoLC)939577995 (DE-599)HEB366554522 |
| 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 | 3510.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Book |
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| physical | xxx, 815 Seiten Illustrationen |
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| spelling | An historical introduction to the philosophy of mathematics a reader edited by Russell Marcus and Mark McEvoy London ; Oxford ; New York ; New Delhi ; Sydney Bloomsbury Academic 2016 xxx, 815 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Geschichte gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s Geschichte z DE-604 Marcus, Russell 1966- (DE-588)1088577954 edt McEvoy, Mark edt Erscheint auch als Online-Ausgabe, EPUB 978-1-4725-3291-6 Erscheint auch als Online-Ausgabe, PDF 978-1-4725-2948-0 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028837981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | An historical introduction to the philosophy of mathematics a reader Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4045791-6 |
| title | An historical introduction to the philosophy of mathematics a reader |
| title_auth | An historical introduction to the philosophy of mathematics a reader |
| title_exact_search | An historical introduction to the philosophy of mathematics a reader |
| title_full | An historical introduction to the philosophy of mathematics a reader edited by Russell Marcus and Mark McEvoy |
| title_fullStr | An historical introduction to the philosophy of mathematics a reader edited by Russell Marcus and Mark McEvoy |
| title_full_unstemmed | An historical introduction to the philosophy of mathematics a reader edited by Russell Marcus and Mark McEvoy |
| title_short | An historical introduction to the philosophy of mathematics |
| title_sort | an historical introduction to the philosophy of mathematics a reader |
| title_sub | a reader |
| topic | Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Mathematik Philosophie |
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