Essay Fregean Mathematics Neo Philosophy Proper Reason Study Towards

Essay Fregean Mathematics Neo Philosophy Proper Reason Study Towards-42
It will be recognized as the most powerful presentation yet of a neo-Fregean program.doctrine that can be advanced with respect to any branch of mathematics.

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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.

There are multiple formal characterizations of the natural numbers available.

Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal.

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.

This is just one orientation to relative priority one could take, however.

Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally ‘legitimate’.

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Comments Essay Fregean Mathematics Neo Philosophy Proper Reason Study Towards

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

  • Logicism and Neologicism Stanford Encyclopedia of.
    Reply

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

  • Abstraction Reconceived The British Journal for the.
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    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
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    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.…

  • Debating Neologicism Frege and the neo-Fregeans
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    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 - Publications - Publications - Research - Philosophy
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    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…

  • Frege's Natural Numbers - Faculty Support Site
    Reply

    Frege's main contributions to logic and the philosophy of mathematics are, on the one hand. to a number of recent "neo-Fregean" proposals for how to update them. During this phase, he again publishes several articles, especially a series of essays on the. Hale, B. & Wright, C. 2001 The Reason's Proper Study.…

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

    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.…

  • Recent Themes in the History of Early Analytic Philosophy
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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.…

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

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