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The Arché Papers on the Mathematics of Abstraction

  • Kartonierter Einband
  • 492 Seiten
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InSeptember2000theArchéCentrelauncheda ve-yearresearchprojecten- tled the Logical and Metaphysical Foundations of Classical Mathem... Weiterlesen
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Beschreibung

InSeptember2000theArchéCentrelauncheda 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 generatedand continue to generatea 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 Jané,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.

Comprises a survey of the philosophical and technical work being done at Arché: The AHRB Centre for the Philosophy of Logic, Language, Mathematics, and Mind at the University of St Andrews

Provides an overview of the Neo-Fregean position in philosophy of mathematics

Collects together hard to find material on Neo-Fregean set theory and real analysis

Contains papers by distinguished philosophers of mathematics, including George Boolos, William Demopoulos, Bob Hale, Richard Heck, Crispin Wright, Stewart Shapiro, and rising stars such as Roy T. Cook, Agustin Rayo, and Gabriel Uzquiano

Contains a preface by Crispin Wright



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

Produktinformationen

Titel: The Arché Papers on the Mathematics of Abstraction
Editor:
EAN: 9789048170906
ISBN: 9048170907
Format: Kartonierter Einband
Herausgeber: Springer Netherlands
Anzahl Seiten: 492
Gewicht: 739g
Größe: H235mm x B155mm x T26mm
Jahr: 2010
Auflage: Softcover reprint of hardcover 1st ed. 2007

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