Results for 'Arithmetic Philosophy'

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  1.  4
    Husserl’s Philosophy of Arithmetic in Reviews.Carlo Ierna - 2013 - The New Yearbook for Phenomonology and Phenomenological Philosophy:198-242.
    This present collection of (translations of) reviews is intended to help obtain a more balanced picture of the reception and impact of Edmund Husserl’s first book, the 1891 Philosophy of Arithmetic. One of the insights to be gained from this non-exhaustive collection of reviews is that the Philosophy of Arithmetic had a much more widespread reception than hitherto assumed: in the present collection alone there already are fourteen, all published between 1891 and 1895. Three of the (...)
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  2.  46
    A Formalist Philosophy of Mathematics Part I: Arithmetic.Michael Gabbay - 2010 - Studia Logica 96 (2):219-238.
    In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.
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  3. It Adds Up After All: Kant's Philosophy of Arithmetic in Light of the Traditional Logic.R. Lanier Anderson - 2004 - Philosophy and Phenomenological Research 69 (3):501–540.
    Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of (...)
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  4.  59
    Geometry and Generality in Frege's Philosophy of Arithmetic.Jamie Tappenden - 1995 - Synthese 102 (3):319 - 361.
    This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and (...)
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  5.  40
    The Content and Meaning of the Transition From the Theory of Relations in Philosophy of Arithmetic to the Mereology of the Third Logical Investigation.Fotini Vassiliou - 2010 - Research in Phenomenology 40 (3):408-429.
    In the third Logical Investigation Husserl presents an integrated theory of wholes and parts based on the notions of dependency, foundation ( Fundierung ), and aprioricity. Careful examination of the literature reveals misconceptions regarding the meaning and scope of the central axis of this theory, especially with respect to its proper context within the development of Husserl's thought. The present paper will establish this context and in the process correct a number of these misconceptions. The presentation of mereology in the (...)
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  6. Husserl’s Early Semiotics and Number Signs: Philosophy of Arithmetic Through the Lens of “On the Logic of Signs ”.Thomas Byrne - forthcoming - Journal of the British Society for Phenomenology:1-17.
    This paper demonstrates that Edmund Husserl’s frequently overlooked 1890 manuscript, “On the Logic of Signs,” when closely investigated, reveals itself to be the hermeneutical touchstone for his seminal 1891 Philosophy of Arithmetic. As the former comprises Husserl’s earliest attempt to account for all of the different kinds of signitive experience, his conclusions there can be directly applied to the latter, which is focused on one particular type of sign; namely, number signs. Husserl’s 1890 descriptions of motivating and replacing (...)
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  7. Syntheticity, Intuition and Symbolic Construction in Kant's Philosophy of Arithmetic.Ofra Rechter - 1997 - Dissertation, Columbia University
    Kant notably holds that arithmetic is synthetic a priori and has to do with the pure intuition of time. This seems to run against our conception of arithmetic as universal and topic neutral. Moreover, trained in the tradition constituting the aftermath of W.V. Quine's attack on the the a priori and on the analytic/synthetic distinction, the modern philosopher of arithmetic is likely to consider Kant's position a nonstarter, and leave settling the question of what Kant's philosophy (...)
     
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  8.  28
    Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic.van Atten Mark - 2004 - Graduate Faculty Philosophy Journal 25 (2):205-225.
  9.  7
    The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic.Gary Urton - 1997 - University of Texas Press.
    Unraveling all the mysteries of the khipu--the knotted string device used by the Inka to record both statistical data and narrative accounts of myths, histories, and genealogies--will require an understanding of how number values and relations may have been used to encode information on social, familial, and political relationships and structures. This is the problem Gary Urton tackles in his pathfinding study of the origin, meaning, and significance of numbers and the philosophical principles underlying the practice of arithmetic among (...)
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  10.  14
    Arithmetic and Theory of Combination in Kant's Philosophy.Henry Walter Brann - 1974 - Philosophy and History 7 (2):150-152.
  11.  12
    Authentic and Symbolic Numbers in Husserl's Philosophy of Arithmetic.Burt C. Hopkins - 2002 - New Yearbook for Phenomenology and Phenomenological Philosophy 2:39-71.
  12.  62
    Mathematics for Humans: Kant's Philosophy of Arithmetic Revisited.Robert Hanna - 2002 - European Journal of Philosophy 10 (3):328–352.
    In this essay I revisit Kant's much-criticized views on arithmetic. In so doing I make a case for the claim that his theory of arithmetic is not in fact subject to the most familiar and forceful objection against it, namely that his doctrine of the dependence of arithmetic on time is plainly false, or even worse, simply unintelligible; on the contrary, Kant's doctrine about time and arithmetic is highly original, fully intelligible, and with qualifications due to (...)
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  13.  58
    Edmund Husserl, Philosophy of Arithmetic, Translated by Dallas Willard.Carlo Ierna - 2008 - Husserl Studies 24 (1):53-58.
  14.  14
    Philosophy of Arithmetic.Dale Jacquette - 2005 - Review of Metaphysics 59 (2):428-431.
  15. It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic.R. Lanier Anderson - 2004 - Philosophy and Phenomenological Research 69 (3):501-540.
    Officially, for Kant, judgments are analytic iff the predicate is “contained in” the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia. Hierarchies afford a straightforward sense of (...)
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  16. Wittgenstein’s Philosophy of Arithmetic.Marc A. Joseph - 1998 - Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie 37 (1):83-106.
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  17.  45
    Frege Explained: From Arithmetic to Analytic Philosophy.Joan Weiner - 2004 - Open Court.
    Frege's life and character -- The project -- Frege's new logic -- Defining the numbers -- The reconception of the logic, I-"Function and concept" -- The reconception of the logic, II- "On sense and meaning" and "on concept and object" -- Basic laws, the great contradiction, and its aftermath -- On the foundations of geometry -- Logical investigations -- Frege's influence on recent philosophy.
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  18.  21
    A Second Philosophy of Arithmetic.Penelope Maddy - 2013 - Review of Symbolic Logic 7 (2):1-28.
    This paper outlines a second-philosophical account of arithmetic that places it on a distinctive ground between those of logic and set theory.
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  19.  26
    Abstraction and Abstract Concepts: On Husserl's Philosophy of Arithmetic.Gianfranco Soldati - 2004 - In Arkadiusz Chrudzimski & Wolfgang Huemer (eds.), Phenomenology and Analysis: Essays on Central European Philosophy. Ontos. pp. 1--215.
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  20. Two Studies in the Reception of Kant's Philosophy of Arithmetic.Charles Parsons - 2010 - In Michael Friedman, Mary Domski & Michael Dickson (eds.), Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science. Open Court.
  21.  5
    Arithmetic and Number in the Philosophy of Symbolic Forms.Jeremy Heis - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 123-140.
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  22.  17
    Review of J. Weiner, Frege Explained: From Arithmetic to Analytic Philosophy[REVIEW]B. Michael - 2007 - Philosophia Mathematica 15 (1):126-128.
    This book is an expanded version of Joan Weiner's introduction to Frege's work in the Oxford University Press ‘Past Masters’ series published in 1999. The earlier book had chapters on Frege's life and character, his basic project, his new logic, his definitions of the numbers, his 1891 essay ‘Function and concept’, his 1892 essays ‘On Sinn and Bedeutung’ and ‘On concept and object’, the Grundgesetze der Arithmetik and the havoc wreaked by Russell's paradox, and a final brief chapter on Frege's (...)
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  23.  7
    Book Symposium: The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics by Bob Hale and Crispin Wright: On the Philosophical Interest of Frege Arithmetic.William Demopoulos - 2003 - Philosophical Books 44 (3):220-228.
    The paper considers Fregean and neo-Fregean strategies for securing the apriority of arithmetic. The Fregean strategy recovers the apriority of arithmetic from that of logic and a family of explicit definitions. The neo-Fregean strategy relies on a principle which, though not an explicit definition, is given the status of a stipulation; unlike the Fregean strategy it relies on an extension of second order logic which is not merely a definitional extension. The paper argues that this methodological difference is (...)
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  24.  4
    Philip Hugly & Charles Sayward: Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic, Edited by Pieranna Garavaso (Poznan Studies in the Philosophy of the Sciences and the Humanities, Vol. 90). Amsterdam/New York: Rodopi, 2006 (393 Pp.). [REVIEW]Claus Festersen - 2007 - SATS: Northern European Journal of Philosophy 8 (2):147-155.
  25.  15
    Wittgenstein's Philosophy of Arithmetic.Marc A. Joseph - 1998 - Dialogue 37 (01):83-.
    It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view (...)
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  26. Philip Hugly and Charles Sayward, Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic Reviewed By.Manuel Bremer - 2010 - Philosophy in Review 27 (3):188-191.
  27. Arithmetic and Theory of Combination in Kant’s Philosophy[REVIEW]Henry Walter Brann - 1974 - Philosophy and History 7 (2):150-152.
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  28. Philip Hugly and Charles Sayward, Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic.M. Bremer - 2007 - Philosophy in Review 27 (3):188.
  29. Mathematics for Humans: Kant's Philosophy of Arithmetic Revisited.Hanna Robert - 2002 - European Journal of Philosophy 10 (3):328-352.
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  30.  30
    Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic.Philip Hugly & Charles Sayward - 2006 - rodopi.
    In this book a non-realist philosophy of mathematics is presented. Two ideas are essential to its conception. These ideas are (i) that pure mathematics--taken in isolation from the use of mathematical signs in empirical judgement--is an activity for which a formalist account is roughly correct, and (ii) that mathematical signs nonetheless have a sense, but only in and through belonging to a system of signs with empirical application. This conception is argued by the two authors and is critically discussed (...)
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  31. Chapter 3: Objectivism and Realism in Frege's Philosophy of Arithmetic.Philip Hugly & Charles Sayward - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 90:73-101.
  32. Intuitionistic Remarks on Husserl’s Analysis of Finite Number in the Philosophy of Arithmetic.Mark van Atten - 2004 - Graduate Faculty Philosophy Journal 25 (2):205-225.
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  33. Review of Dr. E. Husserl's Philosophy of Arithmetic[REVIEW]E. W. Kluge - 1972 - Mind 81 (323):321 - 337.
  34. Kant's Philosophy of Arithmetic.Charles Parsons - 1982 - In Ralph Charles Sutherland Walker (ed.), Kant on Pure Reason. Oxford University Press.
  35.  24
    The Neo-Fregean Program in the Philosophy of Arithmetic.William Demopoulos - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 87--112.
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  36.  11
    Review of Dr. E. Husserl's Philosophy of Arithmetic[REVIEW]Gottlob Frege - 1977 - In Jitendranath Mohanty (ed.), Mind. M. Nijhoff. pp. 6--21.
  37. Review of Dr. E. Husserl's "Philosophy of Arithmetic". [REVIEW]Frege Frege - 1972 - Mind 81:321.
  38.  3
    Selected Papers of Abraham Robinson. Volume 2. Nonstandard Analysis and Philosophy. Edited and with an Introduction by Luxemburg W. A. J. And Körner S.. Yale University Press, New Haven and London 1979, Xlv + 582 Pp.Seligman George B.. Biography of Abraham Robinson, Pp. Xi–Xxx. A Reprint of XLVII 197.Luxemburg W. A. J.. Introduction to Papers on Nonstandard Analysis and Analysis, Pp. Xxxi–Xxxix.Körner S.. Introduction to Papers on Philosophy, Pp. Xli–Xlv.Robinson Abraham. Non-Standard Analysis, Pp. 3–11. A Reprint of XXXIV 292.Robinson Abraham. On Languages Which Are Based on Non-Standard Arithmetic, Pp. 12–46. A Reprint of XXXIV 516.Robinson Abraham. On Generalized Limits and Linear Functionals, Pp. 47–61. A Reprint of XXXIV 292.Robinson Abraham. On the Theory of Normal Families, Pp. 62–87. A Reprint of XXXVII 215.Bernstein Allen R. And Robinson Abraham. Solution of an Invariant Subspace Problem of K. T. Smith and P. R. Halmos, Pp. 88–98. A Reprint of XXXIV 292.Robinson Abraham. Topic. [REVIEW]Martin Davis - 1982 - Journal of Symbolic Logic 47 (1):203-210.
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  39. A Brentanian Philosophy of Arithmetic.D. Bell - 1989 - Brentano Studien 2:139-44.
  40.  16
    Revisiting Husserl's Philosophy of Arithmetic Edmund Husserl. Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts From 1887–1901. Translated by Dallas Willard. Dordrecht: Kluwer, 2003. Pp. Lxiv + 513. ISBN 1-4020-1546-1. [REVIEW]R. Tieszen - 2006 - Philosophia Mathematica 14 (1):112-130.
  41.  3
    Philip Hugly & Charles Sayward: Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic, Edited by Pieranna Garavaso . Amsterdam/New York: Rodopi, 2006.Claus Festersen - 2007 - SATS 8 (2).
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  42.  2
    I.—Review of Dr. E. Husserl's Philosophy of Arithmetic[REVIEW]E. W. Kluge - 1972 - Mind 81 (323):321-337.
  43.  8
    Frege Explained: From Arithmetic to Analytic Philosophy by Joan Weiner. [REVIEW]Nicholas J. J. Smith - 2007 - Philosophical Books 48 (1):78-79.
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  44.  1
    Richard Büchi J.. Weak Second-Order Arithmetic and Finite Automata. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 6 , Pp. 66–92.Richard Büchi J.. On a Decision Method in Restricted Second Order Arithmetic. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Nagel Ernest, Suppes Patrick, and Tarski Alfred, Stanford University Press, Stanford, Calif., 1962, Pp. 1–11. [REVIEW]Robert McNaughton - 1963 - Journal of Symbolic Logic 28 (1):100-102.
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  45. Poincaré on Mathematical Intuition. A Phenomenological Approach to Poincaré's Philosophy of Arithmetic.Jairo José Da Silva - 1996 - Philosophia Scientiae 1 (2):87-99.
  46. The Concept of Lebenswelt From Husserl's Philosophy of Arithmetic to His Crisis.B. M. D. Ippolito - 2002 - Analecta Husserliana 80:158-171.
     
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  47. Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts From 1887–1901. [REVIEW]Dale Jacquette - 2005 - Review of Metaphysics 59 (2):428-431.
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  48. Wittgenstein’s Philosophy of Arithmetic.Marc A. Joseph - 1998 - Dialogue 37 (1):83-106.
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  49. Joan Weiner. Frege Explained: From Arithmetic to Analytic Philosophy. Chicago: Open Court, 2004. Pp. Xvi + 179. ISBN 0-8126-9460-0. [REVIEW]B. Michael - 2006 - Philosophia Mathematica 15 (1):126-128.
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  50. Kreisel G.. A Variant to Hilbert's Theory of the Foundations of Arithmetic. The British Journal for the Philosophy of Science, Vol. 4 , Pp. 107–129. See Errata and Corrigenda, Ibid., P 357. [REVIEW]Andrzej Mostowski - 1957 - Journal of Symbolic Logic 22 (3):304-306.
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