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  1. Carlo Ierna (2013). Husserl’s Philosophy of Arithmetic in Reviews. The New Yearbook for Phenomonology and Phenomenological Philosophy:198-242.score: 210.0
    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. Michael Gabbay (2010). A Formalist Philosophy of Mathematics Part I: Arithmetic. Studia Logica 96 (2):219-238.score: 156.0
    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. Michael D. Potter (2000). Reason's Nearest Kin: Philosophies of Arithmetic From Kant to Carnap. Oxford University Press.score: 150.0
    This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.
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  4. Jamie Tappenden (1995). Geometry and Generality in Frege's Philosophy of Arithmetic. Synthese 102 (3):319 - 361.score: 144.0
    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. Fotini Vassiliou (2011). The Content and Meaning of the Transition From the Theory of Relations in Philosophy of Arithmetic to the Mereology of the Third Logical Investigation. Research in Phenomenology 40 (3):408-429.score: 144.0
    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. Gary Urton (1997). The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic. University of Texas Press.score: 138.0
    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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  7. R. Lanier Anderson (2004). It Adds Up After All: Kant's Philosophy of Arithmetic in Light of the Traditional Logic. Philosophy and Phenomenological Research 69 (3):501–540.score: 132.0
    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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  8. Robert Hanna (2002). Mathematics for Humans: Kant's Philosophy of Arithmetic Revisited. European Journal of Philosophy 10 (3):328–352.score: 132.0
    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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  9. Joan Weiner (2004). Frege Explained: From Arithmetic to Analytic Philosophy. Open Court.score: 126.0
    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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  10. Philip Hugly & Charles Sayward (2006). Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic. rodopi.score: 126.0
    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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  11. Mark Van Atten (2004). Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic. Graduate Faculty Philosophy Journal 25 (2):205-225.score: 126.0
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  12. Penelope Maddy (2013). A Second Philosophy of Arithmetic. Review of Symbolic Logic 7 (2):1-28.score: 126.0
    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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  13. Marc A. Joseph (1998). Wittgenstein's Philosophy of Arithmetic. Dialogue 37 (01):83-.score: 126.0
    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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  14. William Demopoulos (2003). 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. Philosophical Books 44 (3):220-228.score: 126.0
    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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  15. Burt C. Hopkins (2002). Authentic and Symbolic Numbers in Husserl's Philosophy of Arithmetic. New Yearbook for Phenomenology and Phenomenological Philosophy 2:39-71.score: 126.0
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  16. Henry Walter Brann (1974). Arithmetic and Theory of Combination in Kant's Philosophy. Philosophy and History 7 (2):150-152.score: 126.0
  17. Manuel Bremer (2010). Philip Hugly and Charles Sayward, Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic Reviewed By. Philosophy in Review 27 (3):188-191.score: 126.0
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  18. Gianfranco Soldati (2004). Abstraction and Abstract Concepts: On Husserl's Philosophy of Arithmetic. In Arkadiusz Chrudzimski & Wolfgang Huemer (eds.), Phenomenology and Analysis: Essays on Central European Philosophy. Ontos. 1--215.score: 126.0
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  19. M. Bremer (2007). Philip Hugly and Charles Sayward, Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic. Philosophy in Review 27 (3):188.score: 126.0
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  20. Claus Festersen (2007). 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] SATS: Northern European Journal of Philosophy 8 (2):147-155.score: 126.0
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  21. Charles Parsons (2010). Two Studies in the Reception of Kant's Philosophy of Arithmetic. In Michael Friedman, Mary Domski & Michael Dickson (eds.), Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science. Open Court.score: 126.0
     
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  22. Mark van Atten (2004). Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic. Graduate Faculty Philosophy Journal 25 (2):205-225.score: 126.0
  23. Gottlob Frege & E. W. Kluge (1972). Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW] Mind 81 (323):321-337.score: 120.0
  24. B. Michael (2007). Review of J. Weiner, Frege Explained: From Arithmetic to Analytic Philosophy. [REVIEW] Philosophia Mathematica 15 (1):126-128.score: 120.0
  25. Carlo Ierna (2008). Edmund Husserl, Philosophy of Arithmetic, Translated by Dallas Willard. Husserl Studies 24 (1):53-58.score: 120.0
  26. E. W. Kluge (1972). Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW] Mind 81 (323):321 - 337.score: 120.0
  27. R. Tieszen (2006). 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] Philosophia Mathematica 14 (1):112-130.score: 120.0
  28. Nicholas J. J. Smith (2007). Frege Explained: From Arithmetic to Analytic Philosophy - By Joan Weiner. Philosophical Books 48 (1):78-79.score: 120.0
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  29. Gottlob Frege (1977). Review of Dr. E. Husserl's Philosophy of Arithmetic. In. [REVIEW] In Jitendranath Mohanty (ed.), Readings on Edmund Husserl's Logical Investigations. Nijhoff. 6--21.score: 120.0
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  30. Dale Jacquette (2005). Philosophy of Arithmetic. Review of Metaphysics 59 (2):428-431.score: 120.0
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  31. Charles Parsons (1982). Kant's Philosophy of Arithmetic. In Ralph Charles Sutherland Walker (ed.), Kant on Pure Reason. Oxford University Press.score: 120.0
  32. D. Bell (1989). A Brentanian Philosophy of Arithmetic. Brentano Studien 2:139-44.score: 120.0
     
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  33. Jairo José Da Silva (1996). Poincaré on Mathematical Intuition. A Phenomenological Approach to Poincaré's Philosophy of Arithmetic. Philosophia Scientiae 1 (2):87-99.score: 120.0
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  34. William Demopoulos (2006). The Neo-Fregean Program in the Philosophy of Arithmetic. In. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. 87--112.score: 120.0
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  35. B. M. D. Ippolito (2002). The Concept of Lebenswelt From Husserl's Philosophy of Arithmetic to His Crisis. Analecta Husserliana 80:158-171.score: 120.0
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  36. Richard Zach (2005). Book Review: Michael Potter. Reason's Nearest Kin. Philosophies of Arithmetic From Kant to Carnap. [REVIEW] Notre Dame Journal of Formal Logic 46 (4):503-513.score: 108.0
  37. Carlo Ierna (2012). Husserl's Psychology of Arithmetic. Bulletin d'Analyse Phénoménologique 8 (1):97-120.score: 102.0
    In 1913, in a draft for a new Preface for the second edition of the Logical Investigations, Edmund Husserl reveals to his readers that "The source of all my studies and the first source of my epistemological difficul­ties lies in my first works on the philosophy of arithmetic and mathematics in general", i.e. his Habilitationsschrift and the Philosophy of Arithmetic: "I carefully studied the consciousness constituting the amount, first the collec­tive consciousness (consciousness of quantity, of multiplicity) (...)
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  38. Jessica M. Wilson (2000). Could Experience Disconfirm the Propositions of Arithmetic? Canadian Journal of Philosophy 30 (1):55--84.score: 72.0
    Alberto Casullo ("Necessity, Certainty, and the A Priori", Canadian Journal of Philosophy 18, 1988) argues that arithmetical propositions could be disconfirmed by appeal to an invented scenario, wherein our standard counting procedures indicate that 2 + 2 != 4. Our best response to such a scenario would be, Casullo suggests, to accept the results of the counting procedures, and give up standard arithmetic. While Casullo's scenario avoids arguments against previous "disconfirming" scenarios, it founders on the assumption, common to (...)
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  39. M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.score: 72.0
    Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in (...)
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  40. Kristina Engelhard & Peter Mittelstaedt (2008). Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW] Journal for General Philosophy of Science 39 (2):245 - 271.score: 72.0
    Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in (...)
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  41. Carlo Ierna (2014). A Letter From Edmund Husserl to Franz Brentano From 29 XII 1889. Husserl Studies:1-8.score: 72.0
    Among the correspondence between Husserl and Brentano kept at the Houghton Library of Harvard University there is a letter from Husserl to Brentano from 29 XII 1889, whose contents were completely unknown until now. The letter is of some significance, both historically as well as systematically for Husserl’s early development, painting a vivid picture of his relation and indebtedness to his teacher Franz Brentano. As in his letter to Stumpf from February 1890, Husserl describes the issues he had encountered during (...)
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  42. Sean Walsh (2014). Empiricism, Probability, and Knowledge of Arithmetic. Journal of Applied Logic 12 (3):319–348.score: 66.0
    The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional (...) of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity, while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic. Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the~$\omega$-rule or to the non-computability and non-continuity of probability assignments. Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments, such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated. In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar. (shrink)
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  43. Michael D. Potter (2004). Set Theory and its Philosophy: A Critical Introduction. Oxford University Press.score: 66.0
    Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil (...)
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  44. Jonathan Barnes (2011). Method and Metaphysics: Essays in Ancient Philosophy I. Oxford University Press.score: 66.0
    Ancient philosophers -- The history of philosophy -- Philosophy within quotation marks? -- Anglophone attitudes -- Brentano's Aristotle -- Heidegger in the cave -- 'There was an old person from Tyre' -- The Presocratics in context -- Argument in ancient philosophy -- Philosophy and dialectic -- Aristotle and the methods of ethics -- Metacommentary -- An introduction to Aspasius -- Parmenides and the Eleatic One -- Reason and necessity in Leucippus -- Plato's cyclical argument -- Death (...)
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  45. J. Philip Miller (1982). Numbers in Presence and Absence: A Study of Husserl's Philosophy of Mathematics. Distributors for the U.S. And Canada, Kluwer Boston, Inc..score: 66.0
    CHAPTER I THE EMERGENCE AND DEVELOPMENT OF HUSSERL'S 'PHILOSOPHY OF ARITHMETIC'. HISTORICAL BACKGROUND: WEIERSTRASS AND THE ARITHMETIZATION OF ANALYSIS In ...
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  46. Charles Sayward (2005). Why Axiomatize Arithmetic? Sorites 16:54-61.score: 66.0
    This is a dialogue in the philosophy of mathematics that focuses on these issues: Are the Peano axioms for arithmetic epistemologically irrelevant? What is the source of our knowledge of these axioms? What is the epistemological relationship between arithmetical laws and the particularities of number?
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  47. William Demopoulos (2001). Reason's Nearest Kin: Philosophies of Arithmetic From Kant to Carnap Michael Potter. British Journal for the Philosophy of Science 52 (3):599-612.score: 66.0
  48. John MacFarlane (2001). Review: Potter, Reason's Nearest Kin: Philosophies of Arithmetic From Kant to Carnap. Journal of the History of Philosophy 39 (3):454-456.score: 66.0
  49. Richard Heck (2011). Frege's Theorem. Clarendon Press.score: 66.0
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
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