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

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The Philosophyof MathematicalPracticePaolo Mancosu1
Page 2: The Philosophy of Mathematical Prac
Page 8: 1Great Clarendon Street, Oxford ox2
Page 12: vipreface(introduction and research
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
Page 32: 4 paolo mancosuYet it is pertinent
Page 36: 6 paolo mancosuphilosophers of math
Page 40: 8 paolo mancosu2 Corfield’s Towar
Page 44: 10 paolo mancosu4) What is the role
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16 paolo mancosufruitfulness in uni
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18 paolo mancosuamount of humility
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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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