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

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60 marcus giaquintoawareness of the structure of the set of nodes under the relation ‘there is a pathup from x to y’. That is very different from the structure of the set of branchesin S under the relation of precedence ‘
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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
Page 94: visualizing in mathematics 35the fu
Page 98: visualizing in mathematics 37except
Page 102: visualizing in mathematics 39David
Page 106: visualizing in mathematics 41Euclid
Page 110: 2Cognition of StructureMARCUS GIAQU
Page 114: cognition of structure 452.2.1 Visu
Page 118: cognition of structure 47Fig. 2.2.a
Page 122: cognition of structure 492.3 Extend
Page 126: cognition of structure 51Fig. 2.4.d
Page 130: cognition of structure 53these case
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Page 146: cognition of structure 61ordinal nu
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Page 154: 3Diagram-Based GeometricPracticeKEN
Page 158: diagram-based geometric practice 67
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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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