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

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440 alasdair urquhartViennot, X.G.(1992), ‘A survey of polyomino enumeration’, in Actes du 4e ColloqueSéries Formelles et Combinatoires Algébrique, 15–19 Juin 1992, Montréal (Publications duLaboratoire de Combinatoire et d’Informatique).Zeidler,Eberhard(1995), Applied Functional Analysis: Applications to Mathematical Physics(Berlin: Springer-Verlag). Applied Mathematical Sciences, Volume 108.
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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
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10Mathematical Concepts:Fruitfulnes
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278 jamie tappendenmathematics have
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280 jamie tappendenthey were to be
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282 jamie tappendenwhich mathematic
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284 jamie tappendenmistake a pragma
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286 jamie tappendennumbers should b
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288 jamie tappendenplausibly, that
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290 jamie tappendeninduction, and t
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292 jamie tappendensupport to unant
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294 jamie tappendenpossibility woul
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296 jamie tappendenRoch (called, re
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298 jamie tappendenhave a hardheade
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300 jamie tappendenDedekind,Richard
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11Computers in MathematicalInquiryJ
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304 jeremy avigadlines, are describ
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306 jeremy avigad• Is knowledge g
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308 jeremy avigadWe often have good
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310 jeremy avigadmore recently, Hai
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312 jeremy avigadAlong the same lin
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314 jeremy avigadno practical guida
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316 jeremy avigadLevi, Isaac (1991)
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318 jeremy avigadmeans to understan
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320 jeremy avigadIn that respect, l
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322 jeremy avigadstandard theory ha
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324 jeremy avigadto be had by explo
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326 jeremy avigad... when he sudden
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328 jeremy avigad• the ability to
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330 jeremy avigadto screen off extr
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332 jeremy avigadthis aspect of und
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334 jeremy avigadagain doubles the
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336 jeremy avigadmathematics was vi
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338 jeremy avigadwish to pause here
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340 jeremy avigadwon’t help in ge
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342 jeremy avigadTwo integers a and
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344 jeremy avigadby (auto simp add:
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346 jeremy avigadthat results in an
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348 jeremy avigadright general cons
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350 jeremy avigadexpression z/n, we
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352 jeremy avigadCarr, David (1979)
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13What StructuralismAchievesCOLIN M
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356 colin mclartythen they could no
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358 colin mclartyTo put it generall
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360 colin mclartydefinitions of rea
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362 colin mclartymorphism with vu(X
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364 colin mclartyto each other. Som
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366 colin mclarty1930s (Washington,
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368 colin mclartyFlament, Dominique
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14‘There is No Ontology Here’:V
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372 colin mclartyremainder theorem
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374 colin mclartyThis arithmetic re
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376 colin mclartyAnd the equation h
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378 colin mclartyKronecker’s way
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380 colin mclartyThe key to the hom
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382 colin mclartycomplexities and s
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384 colin mclartycomponents of this
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386 colin mclartyX = q2 − 1q 2 +
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388 colin mclartycongruent modulo X
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390 colin mclartyof the scheme. Thi
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392 colin mclartyThen the idea is t
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394 colin mclartyThe proof shows th
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396 colin mclartyIn short the objec
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398 colin mclartyor Bourbaki’s se
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400 colin mclartyother words for al
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402 colin mclartyrams. The equation
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404 colin mclartyFowler, David (199
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406 colin mclartyMilne, James(1980)
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408 alasdair urquhartfrom the obser
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410 alasdair urquhartworld. However
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412 alasdair urquhartof Bourbaki-st
Page 852: 414 alasdair urquhartAt least two s
Page 856: 416 alasdair urquhartGauss, Carl Fr
Page 860: 418 alasdair urquhartSaunders Mac L
Page 864: 420 alasdair urquhartand Paul Lévy
Page 868: 422 alasdair urquhartA time-hallowe
Page 872: 424 alasdair urquhartThe theory of
Page 876: 426 alasdair urquhartinitial condit
Page 880: 428 alasdair urquhartWhy are higher
Page 884: 430 alasdair urquhartin his mathema
Page 888: 432 alasdair urquhartemerge from ph
Page 892: 434 alasdair urquhartThe theoretica
Page 896: 436 alasdair urquhartHopfield model
Page 900: 438 alasdair urquhartBibliographyAt
Page 906: Index of NamesAigner, M. 337, 351bA
Page 910: index of names 443Frege, G. ix-x, 7
Page 914: index of names 445McCune, W. 304, 3
Page 918: index of names 447Weiner, M. 71Weis
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