The Arché Papers on the Mathematics of Abstraction

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