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

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mathematical concepts: fruitfulness and naturalness 301Stahl, Hermann(ed.)(1899), Elliptische Functionen: Vorlesungen von Bernhard Riemann(Leipzig: Teubner).Tappenden, Jamie (2005), ‘The Caesar Problem in its Historical Context: MathematicalBackground’, Dialectica, 59 (fasc. 2), 237–264.(Forthcoming),‘Reflections on Mathematical Explanation: Why Do EllipticFunctions Have Two Periods?’.Weatherson, Brian(2006), ‘Natural Quantities’, manuscript.Weil, André(1940/2005) ‘Letter of 1940 to Simone Weil’, Notices of the AmericanMathematical Society, trans.M.Krieger,52, 3, pp. 335–341.(1984), Number Theory: An Approach through History; From Hammurapi to Legendre(Boston: Birkhäuser).
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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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124 kenneth manderscase is occasion
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126 kenneth mandersprecisely the di
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128 kenneth mandersgeometrical clai
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130 kenneth manderswe sought to att
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132 kenneth mandersarticulating the
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5Mathematical Explanation: Whyit Ma
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136 paolo mancosuQuine and Goodman
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138 paolo mancosuFirst, in the dire
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140 paolo mancosuIf this is correct
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142 paolo mancosufor instance Guldi
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144 paolo mancosuvarious conceptual
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146 paolo mancosucomplex book and I
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148 paolo mancosu(‘It is not, the
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150 paolo mancosuSteiner, Mark(1978
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152 johannes hafner and paolo manco
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180 michael detlefsen76a37-40, 77a2
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182 michael detlefsenThe objective
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184 michael detlefsencases, and reg
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186 michael detlefsenbe deduced fro
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188 michael detlefsenPurity was thu
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190 michael detlefsentheorem on the
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192 michael detlefsenanother basic
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194 michael detlefsenAristotle (anc
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196 michael detlefsenLagrange, Jose
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8Reflections on the Purity ofMethod
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200 michael hallettall these questi
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202 michael hallettto something imp
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204 michael hallettIrequireintuitio
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206 michael hallettSimilar points h
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208 michael halletthe calls the Pas
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210 michael hallettinvestigation, a
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212 michael hallettintrinsic to whi
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214 michael hallett1898/1899 lectur
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216 michael hallettThe things with
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218 michael hallettthe observable w
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220 michael hallettso, whether one
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222 michael hallettSo, to sum up th
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224 michael hallettfor the first ti
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226 michael hallettYQOXPFig. 8.3. M
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228 michael hallettTheorem in the p
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230 michael hallettcongruent by the
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232 michael hallettthis: What has t
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234 michael hallettSuppose now that
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236 michael hallettClearly, AB = BA
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238 michael hallettthat words like
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240 michael hallettbetween two circ
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242 michael hallettintuitively insp
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244 michael hallettordered Pythagor
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246 michael hallettradii using the
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248 michael hallettit in the passag
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250 michael hallettcentury, which a
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252 michael hallettBibliographyBern
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254 michael hallettsitätsbiblithek
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9Mathematical Conceptsand Definitio
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258 jamie tappendenA particularly i
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260 jamie tappendenthe relevant ide
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262 jamie tappendenlaws? Seventeen-
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264 jamie tappendenvariety of cases
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266 jamie tappendenfunctions ...) T
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268 jamie tappendenthe second, sinc
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270 jamie tappendenimprovement to p
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272 jamie tappendenopponents aggres
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274 jamie tappendenHale,BobandWrigh
Page 576: 10Mathematical Concepts:Fruitfulnes
Page 580: 278 jamie tappendenmathematics have
Page 584: 280 jamie tappendenthey were to be
Page 588: 282 jamie tappendenwhich mathematic
Page 592: 284 jamie tappendenmistake a pragma
Page 596: 286 jamie tappendennumbers should b
Page 600: 288 jamie tappendenplausibly, that
Page 604: 290 jamie tappendeninduction, and t
Page 608: 292 jamie tappendensupport to unant
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Page 616: 296 jamie tappendenRoch (called, re
Page 620: 298 jamie tappendenhave a hardheade
Page 624: 300 jamie tappendenDedekind,Richard
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Page 658: 12Understanding ProofsJEREMY AVIGAD
Page 662: understanding proofs 319theorem is
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Page 670: understanding proofs 323of abilitie
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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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