The Arché Papers on the Mathematics of Abstraction (eBook)

Roy T. Cook (Herausgeber)

eBook Download: PDF

2007 | 2007
XXXVIII, 454 Seiten
Springer Netherland (Verlag)
978-1-4020-4265-2 (ISBN)

Infos

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies.

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InSeptember2000theArcheCentrelauncheda ve-yearresearchprojecten- tled the Logical and Metaphysical Foundations of Classical Mathematics. Its goal was to study the prospects, philosophical and technical, for abstractionist foundations for the classical mathematical theories of the natural, real and complex numbers and standard set theory. Funding was provided by the then Arts and Humanities Research Board (now the Arts and Humanities Research Council) for the appointment of full-time postdoctoral research fellows and PhD students to collaborate with more senior colleagues in the project, and at the same time the British Academy awarded the Centre additional resources to establish an International Network of scholars to be associated with the work. This was the beginning of the serial 'Abstraction workshops' of which the Centre had staged no less than eleven by December 2006. We gra- fully acknowledge the generous support of the Academy and Council, sine qua non. The project seminars and Network meetings generated-and continue to generate-a large number of leading-edge research papers on all aspects of the project agenda. The present volume is the rst of what we hope will be a number of anthologies of these researches. With two exceptions,-the contribution by the late George Boolos and the co-authored paper by Gabriel Uzquiano and Ignacio Jane,-the papers that Roy Cook has collected in the present volume are all authored by sometime members of the project team or of the British Academy Network.

Inhalt

Preface: by Crispin Wright Introduction: by Roy T. Cook Part I: The Philosophy and Mathematics of Hume's Principle Boolos, G. [1997], 'Is Hume's Principle Analytic?', In Language, Thought, and Logic, R. Heck (ed.), Oxford, Oxford University Press: 245 – 261. Wright, C. [1999], 'Is Hume's Principle Analytic?', Notre Dame Journal of Formal Logic 40: 6 - 30. Heck, R. [1997], 'Finitude and Hume's Principle', Journal of Philosophical Logic 26: 589-617. Clark, P., ''Frege, Neo-Logicism and Applied Mathematics '' Fraser MacBride, [2000], 'On Finite Hume', Philosophia Mathematica 8:150-9. Fraser MacBride, [2002], 'Could Nothing Matter?', Analysis 62: 125-135. Demopoulos, W. [2003], 'The Philosophical Interest of Frege Arithmetic' Philosophical Books 44: 220-228 Part II: The Logic of Abstraction Shapiro, S. & Weir, A. [2000], 'Neo-logicist logic is not epistemically innocent', Philosophia Mathematica 8, 160-189. Cook, R. [2003], 'Aristotelian Logic, Axioms, and Abstraction', Philosophia Mathematica 11: 195-202. Rayo, A. [2002], 'Frege's Unofficial Arithmetic', Journal of Symbolic Logic 67: 1623-1638. Part III: Abstraction and the Continuum Hale, R. [2000], 'Reals by Abstraction', Philosophia Mathematica 8: 100-123. Cook, R. [2002], 'The State of the Economy: Neologicism and Inflation', Philosophia Mathematica 10: 43-66. Wright, C. [2000], 'Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege's Constraint', Notre Dame Journal of Formal Logic 41: 317-334. Shapiro, S. [2000], 'Frege Meets Dedekind: A Neologicist Treatment of Real Analysis', Notre Dame Journal of Formal Logic 41: 335-364. Part IV: Basic Law V and Set Theory Shapiro, S. & Weir, A. [1999], 'NewV, ZF and Abstraction', Philosophia Mathematica 7: 293-321. Uzquiano, G. & I. Jané [2004], 'Well- and Non-Well-Founded Extensions', Journal of Philosophical Logic 33: 437 – 465. Hale, R. [2000], 'Abstraction and Set Theory', Notre Dame Journal of Formal Logic 41: 379-398 Shapiro, S. [2003], 'Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility', British Journal for the Philosophy of Science 54: 59-91. Weir, A [2004], 'Neo-Fregeanism: An Embarassment of Riches', Notre Dame Journal of Formal Logic 44: 13 - 48 Cook, R. [2004], 'Iteration One More Time', Notre Dame Journal of Formal Logic 44: 63 - 92

Produkt-Details

• Erscheint lt. Verlag: 27.11.2007
• Reihe/Serie: The Western Ontario Series in Philosophy of Science
• Reihe/Serie: The Western Ontario Series in Philosophy of Science
• Zusatzinfo: XXXVIII, 454 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
• Themenwelt: Geisteswissenschaften ► Philosophie ► Erkenntnistheorie / Wissenschaftstheorie
• Themenwelt: Geisteswissenschaften ► Philosophie ► Logik
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: Abstraction • arithmetic • Formal Logic • Gottlob Frege • Logic • philosophy of mathematics • philosophy of science • Real analysis • set theory • symbolic logic
• ISBN-10: 1-4020-4265-5 / 1402042655
• ISBN-13: 978-1-4020-4265-2 / 9781402042652