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Philosophy of Mathematics:

An Introduction to a World of Proofs and Pictures
Front Cover
3 Reviews
Psychology Press, 1999 - Philosophy - 215 pages
Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics:
* the mathematical image
* platonism
* picture-proofs
* applied mathematics
* Hilbert and Godel
* knots and nations
* definitions
* picture-proofs and Wittgenstein
* computation, proof and conjecture.
The book is ideal for courses on philosophy of mathematics and logic.
  

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Review: Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philosophy)

User Review  - Usman W. Chohan - Goodreads

FULLY AGREE WITH THE FOLLOWING QUOTE: A philosopher who has nothing to do with geometry is only half a philosopher, and a mathematician with no element of philosophy in him is only half a ... Read full review

Review: Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philosophy)

User Review  - Jonathan Urquhart - Goodreads

I didn't understand a word. Amazing. Read full review

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Contents

Introduction The Mathematical Image
1
Platonism
8
Some Recent Views
9
What is Platonism?
11
The Problem of Access
15
The Problem of Certainty
18
Platonism and its Rivals
23
Pictureproofs and Platonism
25
Lakatos
107
Concluding Remarks
112
Constructive Approaches
113
From Kant to Brouwer
114
Brouwers Intuitionism
115
Bishops Constructivism
117
Dummetts Antirealism
118
Logic
120

What Did Bolzano Do?
28
Different Theorems Different Concepts?
29
Inductive Mathematics
30
Special and General Cases
33
Instructive Examples
34
Representation
37
A Kantian Objection
39
Three Analogies
40
Are Pictures Explanatory?
42
So Why Worry?
43
What is Applied Mathematics?
46
Representations
47
Artifacts
49
Bogus Applications
51
Does Science Need Mathematics?
52
Representation vs Description
55
Structuralism
57
Hilbert and Gödel
62
Early Formalism
63
Hilberts Formalism
64
Hilberts Programme
68
Small Problems
70
Gödels Theorem
71
Gödels Second Theorem
75
The Upshot for Hilberts Programme
77
Knots and Notation
79
Knots
81
The Dowker Notation
83
The Conway Notation
84
Polynomials
86
Creation or Revelation?
88
Sense Reference and Something Else
92
What is a Definition?
94
The FregeHilbert Debate
95
Reductionism
102
Graph Theory
103
Problems
122
Proofs Pictures and Procedures in Wittgenstein
130
Following a Rule
132
Platonism
136
Algorithms
138
Knowing Our Own Intentions
139
Radical Conventionalism
140
Bizarre Examples
141
Naturalism
142
The Sceptical Solution
144
Modus Ponens or Modus Tollens?
145
What is a Rule?
146
Grasping a Sense
147
Platonism vs Realism
149
Surveyability
151
The Sense of a Picture
152
Computation Proof and Conjecture
154
Fallibility
155
Surveyability
157
Inductive Mathematics
158
Perfect Numbers
160
Computation
162
Is 𝝅 Normal?
164
Fermats Last Theorem
165
The Riemann Hypothesis
166
Clusters of Conjectures
167
Polya and Putnam
168
Conjectures and Axioms
170
Calling the Bluff
172
Calling the Bluff
179
A Report from the Front
181
The Mathematical Image
191
Notes
193
Bibliography
199
Index
208
Copyright

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References from web pages

JAMES ROBERT BROWN Philosophy of Mathematics: An Introduction to ...
Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. New York: Routledge 1999. Pp. ix + 215. Cdn$105/US$80.00 (Cloth: ISBN ...
homepage.mac.com/ mcolyvan/ papers/ BrownRev.pdf

Philosophy of Mathematics, an Introduction to the world of proofs ...
[Archive] Philosophy of Mathematics, an Introduction to the world of proofs and pictures. Science Book Reviews.
www.physicsforums.com/ archive/ index.php/ t-1530.html

BIBCAT AJI-0335
Search for. Other Libraries. Item Information. Philosophy of mathematics : an introduction to the world of proofs and pictures / James Robert Brown. ...
bibcat.bibliocentre.ca/ web2/ tramp2.exe/ do_keyword_search/ guest?setting_key=durham_uoit& servers=durham& index=cn& query...

Philosophy of Mathematics: An Introduction to the World of Proofs ...
Institution: Google Indexer Sign In as Personal Subscriber · Oxford Journals · Humanities · British Jnl. for the Philosophy of Sci. ...
bjps.oxfordjournals.org/ cgi/ reprint/ 52/ 2/ 413

ingentaconnect Philosophy of Mathematics: An Introduction to the ...
Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures James Robert Brown. Source: British Journal for the Philosophy of Science, ...
www.ingentaconnect.com/ content/ oup/ phisci/ 2001/ 00000052/ 00000002/ art00413;jsessionid=5lolyk5r9rm5.alexandra?format=print

Phil 411, Fall 2007 (Overview)
Brown, "Philosophy of mathematics: An introduction to the world of proofs and pictures", 1999. Ch. 8 "What is a definition?" [on reserve] ...
www.phil.cmu.edu/ dschlimm/ 411/ overview.html

La lettre de la Preuve
Philosophy of mathematics: An introduction to the world of proofs and pictures. by James Robert Brown. James Robert Brown's recent book, Philosophy of ...
www.lettredelapreuve.it/ Newsletter/ 000102.html

The Bulletin of Symbolic Logic, Volume 9
James Robert Brown Philosophy of mathematics, an introduction to the world of proofs and pictures, reviewed by Janet Folina, page 504. ...
www.math.ucla.edu/ ~asl/ bsl/ 09-toc.htm

Science and constructive mathematics
Philosophy of Mathematics: An Introduction to the World of Proofs. and Pictures. London and New York: Routledge. Hellman, G. 1993a. Gleason’s theorem is not ...
www.blackwell-synergy.com/ doi/ abs/ 10.1111/ j.0003-2638.2003.00394.x

PHILOSOPHY OF MATHEMATICS: AN INTRODUCTION TO THE WORLD OF PROOFS ...
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About the author (1999)

James Robert Brown is Professor of Philosophy at University of Toronto.

Bibliographic information