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

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the euclidean diagram (1995) 133Mueller,Ian(1981), Philosophy of Mathematics and Deductive Structure in Euclid’s Elements(Cambridge, MA: MIT Press).Newton, Isaac (1728), Universal Arithmetic.Pappus of Alexandria, Book 7 of the Collection, edited with translation and commentaryby Alexander Jones, 1986 (New York: Springer).Poncelet, JeanVictor(1822), Traité desPropriétés Projectives des Figures. (Paris: Bachelier);expanded/corr. 2nd edn, 1865 (Paris: Gauthier Villars).Sherry, David (1993), ‘Don’t Take Me Half the Way: On Berkeley on MathematicalReasoning’, Studies in History and Philosophy of Science, 24, 207–225.Tarski, Alfred(1959), ‘What is Elementary Geometry?’, in L. Henkin, P. Suppes, andA. Tarski (eds.), The Axiomatic Method, 16–29 (Amsterdam: North-Holland).Tropfke, J.(1923), Geschichte der Elementar-mathematik, Band.4, Ebene Geometrie. 2ndedn (Berlin/Leipzig: W. De Gruyter).
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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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Page 248: 112 kenneth mandersSuppose the stat
Page 252: 114 kenneth mandersAEBCFDGFig. 4.7.
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Page 294: mathematical explanation: why it ma
Page 326: 6Beyond UnificationJOHANNES HAFNER
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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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