Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

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ContentsBiographiesviiiIntroduction 11. Visualizing in Mathematics 222. Cognition of Structure 433. Diagram-Based Geometric Practice 654. The Euclidean Diagram (1995) 805. Mathematical Explanation: Why it Matters 1346. Beyond Unification 1517. Purity as an Ideal of Proof 1798. Reflections on the Purity of Method in Hilbert’s Grundlagen derGeometrie 1989. Mathematical Concepts and Definitions 25610. Mathematical Concepts: Fruitfulness and Naturalness 27611. Computers in Mathematical Inquiry 30212. Understanding Proofs 31713. What Structuralism Achieves 35414. ‘There is No Ontology Here’: Visual and Structural Geometryin Arithmetic 37015. The Boundary Between Mathematics and Physics 40716. Mathematics and Physics: Strategies of Assimilation 417Index of Names 441
Page 2: The Philosophy of Mathematical Prac
Page 6: The Philosophyof MathematicalPracti
Page 10: PrefaceWhen in the spring of 2005 I
Page 16: BiographiesJeremy Avigad is an Asso
Page 20: xbiographies(OUP 1988). He has rece
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Page 28: 2 paolo mancosuare orthogonal to th
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20 paolo mancosuproposing to the re
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1Visualizing in MathematicsMARCUS G
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24 marcus giaquintowhere that exclu
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26 marcus giaquintoMiller himself h
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28 marcus giaquintoTypically diagra
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30 marcus giaquintoclearly not enou
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32 marcus giaquintothe internal ang
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34 marcus giaquintoPythagoras’s t
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36 marcus giaquintofunction f (in t
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38 marcus giaquintorecall the puzzl
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40 marcus giaquintothinking is repl
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42 marcus giaquintoMancosu, Paolo(2
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44 marcus giaquintoof knowing struc
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46 marcus giaquintoorder-preserving
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48 marcus giaquintoA category speci
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50 marcus giaquintoWe name the bott
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52 marcus giaquintoinitial element
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54 marcus giaquintoAttention shifti
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cognition of structure 57infinite c
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cognition of structure 59with the s
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cognition of structure 61ordinal nu
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cognition of structure 63to merely
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3Diagram-Based GeometricPracticeKEN
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diagram-based geometric practice 67
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the euclidean diagram (1995) 81I su
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the euclidean diagram (1995) 834.1.
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the euclidean diagram (1995) 85of s
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the euclidean diagram (1995) 87both
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the euclidean diagram (1995) 89a di
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the euclidean diagram (1995) 91diag
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the euclidean diagram (1995) 93Exac
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the euclidean diagram (1995) 95APFi
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the euclidean diagram (1995) 97rela
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the euclidean diagram (1995) 99perh
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the euclidean diagram (1995) 101The
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the euclidean diagram (1995) 103and
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the euclidean diagram (1995) 105a p
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the euclidean diagram (1995) 107nev
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the euclidean diagram (1995) 109Thu
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the euclidean diagram (1995) 111A p
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the euclidean diagram (1995) 113Wha
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the euclidean diagram (1995) 115ADC
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the euclidean diagram (1995) 117We
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the euclidean diagram (1995) 119by
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the euclidean diagram (1995) 121of
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the euclidean diagram (1995) 123AFi
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the euclidean diagram (1995) 125by
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the euclidean diagram (1995) 127bra
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the euclidean diagram (1995) 129Eit
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the euclidean diagram (1995) 131gra
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the euclidean diagram (1995) 133Mue
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mathematical explanation: why it ma
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6Beyond UnificationJOHANNES HAFNER
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eyond unification 153initially appe
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eyond unification 155This example w
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eyond unification 157equations and
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eyond unification 159elementary pro
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eyond unification 161||x|| = √ x
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eyond unification 163cover also the
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eyond unification 165the necessary
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eyond unification 167consideration.
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eyond unification 169Now, can there
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eyond unification 171unification in
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eyond unification 173E I (K) comes
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eyond unification 175(3) F(ϕ) = 0
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eyond unification 177AppendixAxioms
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7Purity as an Ideal of ProofMICHAEL
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purity as an ideal of proof 181Ther
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purity as an ideal of proof 183Anal
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purity as an ideal of proof 185Late
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purity as an ideal of proof 187even
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purity as an ideal of proof 189conf
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purity as an ideal of proof 191adva
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purity as an ideal of proof 193is p
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purity as an ideal of proof 195Ewal
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purity as an ideal of proof 197Viè
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purity of method in hilbert’s gru
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Two pages later, Hilbert remarks:pu
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mathematical concepts and definitio
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mathematical concepts: fruitfulness
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computers in mathematical inquiry 3
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12Understanding ProofsJEREMY AVIGAD
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understanding proofs 319theorem is
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understanding proofs 321theorems, p
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understanding proofs 323of abilitie
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understanding proofs 325explain the
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understanding proofs 327possible to
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understanding proofs 329Ryle intend
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understanding proofs 331to explain,
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understanding proofs 333an ordinary
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understanding proofs 335that to exp
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understanding proofs 337value of k,
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understanding proofs 339integers in
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understanding proofs 341the use of
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understanding proofs 343know that b
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understanding proofs 345procedures
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understanding proofs 347on the firs
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understanding proofs 34912.9 Unders
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understanding proofs 351Mathematics
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understanding proofs 353Tiwari, A.(
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what structuralism achieves 355Phil
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what structuralism achieves 357that
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what structuralism achieves 359numb
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what structuralism achieves 361This
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what structuralism achieves 363Even
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what structuralism achieves 365get
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what structuralism achieves 367But
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what structuralism achieves 369Reid
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‘there is no ontology here’ 371
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15The Boundary BetweenMathematics a
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the boundary between mathematics an
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16Mathematics and Physics:Strategie
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mathematics and physics: strategies
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Index of NamesAigner, M. 337, 351bA
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index of names 443Frege, G. ix-x, 7
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index of names 445McCune, W. 304, 3
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index of names 447Weiner, M. 71Weis
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