Essay Fregean Mathematics Neo Philosophy Proper Reason Study Towards

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Both versions of logicism—strong and weak—maintain that in expressing them; or, as Kant might have preferred it, by virtue of internal relations among the concepts involved.

A successful logicist reduction of any branch of mathematics will therefore show that its truths (strong version) or its theorems (weak version) are analytic.

Some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is ‘more basic’ or ‘more fundamental’ than the others. First, we review some of these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions.

Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege's foundationalist epistemology, the ordinals are plausibly more basic than the cardinals.

So there must be such an object in order to get an ordinal at all.

So the smallest ordinal, in that sense, is one (or ‘first’). But there is a zero ordinal, in the mathematical sense.

The point is so simple that it needs a sophisticated intellect to overlook it; and it shows Frege to have been right, as against Dedekind, to have made the use of the natural numbers as finite cardinals intrinsic to their characterisation., Chapter 3): ‘Men do not think they know a thing unless they have grasped the ‘why’ of it’.

So proper foundational knowledge is of-a-piece with what Jaegwon Kim calls ‘explanatory knowledge’ – knowledge why – as opposed to mere descriptive knowledge – knowledge that ( to have an (or the) explanation for what one knows.

Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics.

In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources.


Comments Essay Fregean Mathematics Neo Philosophy Proper Reason Study Towards

  • Philosophy of Mathematics -

    Hale, Bob, and Crispin Wright 2001, The Reason's Proper Study essays towards a neo-Fregean philosophy of mathematics. Oxford Oxford University Press.…

  • Bob Hale - Publications - Publications - Research - Philosophy

    The Reason's Proper Study Essays towards a Neo-Fragean Philosophy of Mathematics Oxford University. Dummett's critique of Wright's attempt to resuscitate Frege Philosophia. Field on the contingency of mathematical objects. Mind…

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    Philosophy of mathematics e.g. Frege-inspired neo-logicism and rationalism14. The Reason's Proper Study Essays Towards a Neo-Fregean Philosophy of.…

  • Logicism and Neologicism Stanford Encyclopedia of.

    Aug 21, 2013. The foundationalism is with respect to those parts of mathematics. Reason's Proper Study Essays towards a Neo-Fregean Philosophy of.…

  • Cardinals, Ordinals, and the Prospects for a Fregean Foundation

    Jul 3, 2018. Some influential philosophers of mathematics have argued for a. C. The Reason's Proper Study Towards a Neo-Fregean Philosophy of Mathematics. D. J. and Wasserman, R. eds, Metametaphysics New Essays on the.…

  • Debating Neologicism Frege and the neo-Fregeans

    A fundamental one in the philosophy of mathematics. It is often tied to the related. According to Frege, mathematical objects were logical objects. Hence a. Principle Hale, Wright, The Reason Proper Study, Intro, p.1-2. Are we to accept. Hale, B. and Wright, C. 2001, The Reason's Proper Study – Essays towards a.…

  • Bob Hale RIP 1945-2017 - - 3AM Magazine

    Dec 16, 2017. Much of his work was in the philosophy of mathematics. Reason's Proper Study Essays towards a Neo-Fregean Philosophy of Mathematics.…

  • Abstraction Reconceived The British Journal for the.

    Jan 11, 2015. Neologicists have sought to ground mathematical knowledge in. The Reason's Proper Study Essays towards a Neo-Fregean Philosophy of.…

  • Speaking with Shadows A Study of Neo-Logicism - jstor

    According to the species of neo-logicism advanced by Hale and Wright, mathema knowledge is essentially. The British Journal for the Philosophy of Science 105 specify which objects. Frege's grand design was to demonstrate that arithmetic inherits the. Reason's Proper Study, Oxford Clarendon Press, pp. 189-213.…

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