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

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150 paolo mancosuSteiner, Mark(1978b), ‘Mathematics, Explanation, and Scientific Knowledge’, Nous,12, 17–28.Tappenden, Jamie (2005), ‘Proof Style and Understanding in Mathematics I: Visualization,Unification and Axiom Choice’, in P. Mancosu, K. Jørgensen, and S. Pedersen(eds.), Visualization, Explanation and Reasoning Styles in Mathematics, (Dordrecht:Springer) pp. 147–214.Weber,ErikandVerhoeven,Liza(2002), ‘Explanatory Proofs in Mathematics’, Logiqueet Analyse, 179–180, 299–307.
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The Philosophy of Mathematical Prac
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The Philosophyof MathematicalPracti
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PrefaceWhen in the spring of 2005 I
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ContentsBiographiesviiiIntroduction
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iographiesixJohannes Hafner is Assi
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iographiesxiat the University of Pi
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IntroductionThe essays contained in
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introduction 31 Two traditionsMany
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introduction 5A characterization in
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introduction 7concerns. On the cont
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introduction 9consists in trying to
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introduction 11terms of their conse
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introduction 13and epistemological
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introduction 15classic that finally
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introduction 17influenced by set-th
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introduction 19in metaphyics when d
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introduction 21Maddy, Penelope (199
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visualizing in mathematics 23Pasch
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visualizing in mathematics 25unreli
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visualizing in mathematics 27comput
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visualizing in mathematics 29thinki
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visualizing in mathematics 31given
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visualizing in mathematics 33discov
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visualizing in mathematics 35the fu
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visualizing in mathematics 37except
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visualizing in mathematics 39David
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visualizing in mathematics 41Euclid
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2Cognition of StructureMARCUS GIAQU
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cognition of structure 452.2.1 Visu
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cognition of structure 47Fig. 2.2.a
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cognition of structure 492.3 Extend
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cognition of structure 51Fig. 2.4.d
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cognition of structure 53these case
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56 marcus giaquintosay that the str
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58 marcus giaquintoof them. In addi
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60 marcus giaquintoawareness of the
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62 marcus giaquintoof every such se
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64 marcus giaquintocases are catego
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66 kenneth mandersdiagram-based for
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68 kenneth mandersdemonstration mig
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70 kenneth manderspermitting, see
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72 kenneth manders3.2 Geometric gen
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74 kenneth mandersin this way: proh
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76 kenneth manderson conics (Apollo
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78 kenneth mandersThe Euclidean Dia
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4The Euclidean Diagram (1995)KENNET
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82 kenneth mandersand know to artic
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84 kenneth mandersirrelevant, unabl
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86 kenneth mandersthe text is liter
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88 kenneth mandersto remedy this by
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90 kenneth mandersFig. 4.1.Traditio
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92 kenneth mandersand therefore cou
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94 kenneth mandersCo-exact attribut
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96 kenneth manders(i)A(ii)ARQBDOCBR
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98 kenneth mandersdiagram of a prop
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100 kenneth mandersattributes (as w
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102 kenneth mandersconstructions. E
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104 kenneth mandersequal-angles pos
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106 kenneth mandersone of these pos
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108 kenneth mandersrecognize ‘cas
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110 kenneth mandersLet’s spell ou
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112 kenneth mandersSuppose the stat
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114 kenneth mandersAEBCFDGFig. 4.7.
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116 kenneth mandersnot just to sanc
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118 kenneth mandersdisqualifying th
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120 kenneth mandersprotagonist’s
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122 kenneth mandersstipulations in
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Page 292: 5Mathematical Explanation: Whyit Ma
Page 296: 136 paolo mancosuQuine and Goodman
Page 300: 138 paolo mancosuFirst, in the dire
Page 304: 140 paolo mancosuIf this is correct
Page 308: 142 paolo mancosufor instance Guldi
Page 312: 144 paolo mancosuvarious conceptual
Page 316: 146 paolo mancosucomplex book and I
Page 320: 148 paolo mancosu(‘It is not, the
Page 326: 6Beyond UnificationJOHANNES HAFNER
Page 330: eyond unification 153initially appe
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Page 338: eyond unification 157equations and
Page 342: eyond unification 159elementary pro
Page 346: eyond unification 161||x|| = √ x
Page 350: eyond unification 163cover also the
Page 354: eyond unification 165the necessary
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Page 362: eyond unification 169Now, can there
Page 366: eyond unification 171unification in
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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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