This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blackburn, S. [1994], The Oxford dictionary of philosophy, Oxford, Oxford University Press.
Blanchette, P. [1996], “Frege and Hilbert on consistency”, Journal of Philosophy 93, 317–336.
Boolos, G. [1987], “The consistency of Frege’s Foundations of arithmetic” in On being and saying: Essays for Richard Cartwright, edited by Judith Jarvis Thompson, Cambridge, Massachusetts, The MIT Press, 3–20; reprinted in [5], 183–201.
Boolos, G. [1997], “Is Hume’s principle analytic?”, in Language, thought, and logic, edited by Richard G. Heck, Jr., New York, Oxford University Press, 245–261; reprinted in [5].
Boolos, G. [1998], Logic, logic, and logic, Cambridge, Massachusetts, Harvard University Press.
Burge, T. [1998], “Frege on knowing the foundation”, Mind 107, 305–347.
Coffa, A. [1991], The semantic tradition from Kant to Carnap, Cambridge, Cambridge University Press.
Cook, R. and P. Ebert [2005], “Abstraction and identity”, Dialectica 59, 1–19.
Dedekind, R. [1888], Was sind und was sollen die Zahlen?, Brunswick, Vieweg; translated as The nature and meaning of numbers, in Essays on the theory of numbers, edited by W. W. Beman, New York, Dover Press, 1963, 31–115.
Dummett, M. [1991], Frege: Philosophy of mathematics, Cambridge, Massachusetts, Harvard University Press.
Ebert, P. [2005], The context principle and implicit definitions: Towards an account of our a priori knowledge of arithmetic, Ph.D. thesis, University of St. Andrews.
Fine, K. [2002], The limits of abstraction, Oxford, Oxford University Press.
Frege, G. [1884], Die Grundlagen der Arithmetik, Breslau, Koebner; The foundations of arithmetic, translated by J. Austin, second edition, New York, Harper, 1960.
Frege, G. [1893], Grundgesetze der Arithmetik 1, Olms, Hildescheim.
Hale, B. [1987], Abstract objects, Oxford, Basil Blackwell.
Hale, B. [2000a], “Reals by abstraction”, Philosophia Mathematica (3) 8, 100–123; reprinted in [18], 399–420.
Hale, B. [2000b], “Abstraction and set theory”, Notre Dame Journal of Formal Logic 41, 379–398.
Hale, B. and Wright, C. [2001], The reason’s proper study, Oxford, Oxford University Press.
Heck, R. [1997], “Finitude and Hume’s principle”, Journal of Philosophical Logic 26, 589–617.
Hodes, H. [1984], “Logicism and the ontological commitments of arithmetic”, Journal of Philosophy 81, 123–149.
Jeshion, R. [2001], “Frege’s notions of self-evidence”, Mind 110, 937–976.
Linnebo, Ø. [2004], “Predicative fragments of Frege arithmetic”, Bulletin of Symbolic Logic 10, 153–174.
Parsons, C. [1964], “Frege’s theory of number”, Philosophy in America, edited by Max Black, Ithaca, New York, Cornell University Press, 180–203; reprinted in Mathematics in Philosophy, by C. Parsons, Ithaca, New York, Cornell University Press, 1983, 150–175.
Resnik, M. [1997], Mathematics as a science of patterns, Oxford, Oxford University Press.
Shapiro, S. [1991], Foundations without foundationalism: A case for second-order logic, Oxford, Oxford University Press.
Shapiro, S. [1997], Philosophy of mathematics: Structure and ontology, New York, Oxford University Press.
Shapiro, S. [2000], “Frege meets Dedekind: A neo-logicist treatment of real analysis”, Notre Dame Journal of Formal Logic 41, 335–364.
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.
Shapiro, S. [2006], “Structure and identity”, in Identity and modality, edited by Fraser MacBride, Oxford, Oxford University Press, 164–173.
Shapiro, S. and A. Weir [2000], “Neo-logicist’ logic is not epistemically innocent”, Philosophia Mathematica (3) 8, 163–189.
Tarski, A. [1933], “Der Warheitsbegriff in dem formalisierten Sprachen”, Studia philosophica 1, 261–405; translated as “The concept of truth in formalized languages”, [33], 152–278.
Tarski, A. [1935], “On the concept of logical consequence”, in [33], 417–429.
Tarski, A. [1956], Logic, semantics and metamathematics, Oxford, Clarendon Press; second edition, edited by John Corcoran, Indianapolis, Hackett Publishing Company, 1983.
Tennant, N. [1987], Anti-realism and logic, Oxford, Oxford University Press.
Wright, C. [1983], Frege’s conception of numbers as objects, Aberdeen, Aberdeen University Press.
Wright, C. [1997], “On the philosophical significance of Frege’s theorem”, Language, thought, and logic, edited by Richard Heck, Jr., Oxford, Oxford University Press, 201–244; reprinted in [18], 272–306.
Wright, C. [1998], “On the harmless impredicativity of N= (Hume’s principle)”, The philosophy of mathematics today, edited by Mathias Schirn, Oxford, Oxford University Press, 339–368; reprinted in [18], 229–255.
Wright, C. [1999], “Is Hume’s Principle analytic”, Notre Dame Journal of Formal Logic 40, 6–30; reprinted in [18], 307–332.
Wright, C. [2000], “Neo-Fregean foundations for real analysis: Some reflections on Frege’s constraint”, Notre Dame Journal of Formal Logic 41, 317–334.
Wright, C. and Bob Hale [2000], “Implicit definition and the a priori”, in New essays on the a priori, edited by P. Boghossian and C. Peacocke, Oxford, Oxford University Press, 286–319; reprinted in [18], 117–150.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Shapiro, S. (2009). The Measure of Scottish Neo-Logicism. In: Lindström, S., Palmgren, E., Segerberg, K., Stoltenberg-Hansen, V. (eds) Logicism, Intuitionism, and Formalism. Synthese Library, vol 341. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8926-8_4
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8926-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8925-1
Online ISBN: 978-1-4020-8926-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)