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George Boolos and Richard G. HeckJnr. Die Grundlagen der Arithmetik, §§82–3. The philosophy of mathematics today, edited by Matthias Schirn, Clarendon Press, Oxford University, Oxford and New York 1998, pp. 407–428. - Richard G. HeckJnr. The finite and the infinite in Frege's Grundgesetze der Arithmetik. The philosophy of mathematics today, edited by Matthias Schirn, Clarendon Press, Oxford University, Oxford and New York 1998 pp. 429–466. - Crispin Wright. On the harmless impredicativity of N = (‘Hume's principle’). The philosophy of mathematics today, edited by Matthias Schirn, Clarendon Press, Oxford University, Oxford and New York 1998 pp. 339–368. - Michael Dummett. Neo-Fregeans: in bad company? The philosophy of mathematics today, edited by Matthias Schirn, Clarendon Press, Oxford University, Oxford and New York 1998 pp. 369–387. - Crispin Wright. Response to Dummett. The philosophy of mathematics today, edited by Matthias Schirn, Clarendon Press, Oxford University, Oxford and Ne

William Demopoulos

Bulletin of Symbolic Logic 6 (4):498-504 (2000)

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Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.details According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) Download Export citation Bookmark 62 citations
Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege's Constraint.Crispin Wright - 2000 - Notre Dame Journal of Formal Logic 41 (4):317--334.details We now know of a number of ways of developing real analysis on a basis of abstraction principles and second-order logic. One, outlined by Shapiro in his contribution to this volume, mimics Dedekind in identifying the reals with cuts in the series of rationals under their natural order. The result is an essentially structuralist conception of the reals. An earlier approach, developed by Hale in his "Reals byion" program differs by placing additional emphasis upon what I here term Frege's Constraint, (...) Download Export citation Bookmark 38 citations

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