Bookmark and Share

Philosophy of Mathematics

Edited by Øystein Linnebo (Birkbeck College)
Assistant editor: Sam Roberts (Birkbeck College, University of Oslo)
Most recently added entries found
Search inside:
(import / add options)   Order:
1 — 50 / 122
  1. added 2017-01-22
    Amirouche Moktefi & Francine F. Abeles (eds.) (2016). 'What the Tortoise Said to Achilles': Lewis Carroll's Paradox of Inference. London: The Lewis Carroll Society.
    Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  2. added 2017-01-21
    Parzhad Torfehnezhad (2017). In Carnap’s Defense: A Survey on the Concept of a Linguistic Framework in Carnap’s Philosophy. Abstracta 9 (1):03-30.
    The main task in this paper is to detail and investigate Carnap’s conception of a “linguistic framework”. On this basis, we will see whether Carnap’s dichotomies, such as the analytic-synthetic distinction, are to be construed as absolute/fundamental dichotomies or merely as relative dichotomies. I argue for a novel interpretation of Carnap’s conception of a LF and, on that basis, will show that, according to Carnap, all the dichotomies to be discussed are relative dichotomies; they depend on conventional decisions concerning the (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  3. added 2017-01-17
    Alan Baker (forthcoming). Mathematical Spandrels. Australasian Journal of Philosophy:1-15.
    abstractThe aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  4. added 2017-01-17
    Mateusz M. Radzki (forthcoming). On Axiom Systems of Słupecki for the Functionally Complete Three-Valued Logic. Axiomathes:1-13.
    The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 and A1–A9. The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  5. added 2017-01-17
    Toby Meadows (forthcoming). Review of "Rigor and Structure" by John P. Burgess. [REVIEW] .
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  6. added 2017-01-17
    Raphaël Sandoz (forthcoming). Applying Mathematics to Empirical Sciences: Flashback to a Puzzling Disciplinary Interaction. Synthese:1-24.
    This paper aims to reassess the philosophical puzzle of the “applicability of mathematics to physical sciences” as a misunderstood disciplinary interplay. If the border isolating mathematics from the empirical world is based on appropriate criteria, how does one explain the fruitfulness of its systematic crossings in recent centuries? An analysis of the evolution of the criteria used to separate mathematics from experimental sciences will shed some light on this question. In this respect, we will highlight the historical influence of three (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  7. added 2017-01-17
    Sean Cox & Philipp Lücke (forthcoming). Characterizing Large Cardinals in Terms of Layered Posets. Annals of Pure and Applied Logic.
  8. added 2017-01-17
    Strauven Wanda (forthcoming). The Unseen Déjà-Vu: From Erkki Huhtamo’s Topoi to Ken Jacobs’ Remakes. Foundations of Science:1-6.
    This commentary on Edwin Carels’ essay “Revisiting Tom Tom: Performative anamnesis and autonomous vision in Ken Jacobs’ appropriations of Tom Tom the Piper’s Son” broadens up the media-archaeological framework in which Carels places his text. Notions such as Huhtamo’s topos and Zielinski’s “deep time” are brought into the discussion in order to point out the difficulty to see what there is to see and to question the position of the viewer in front of experimental films like Tom Tom the Piper’s (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  9. added 2017-01-17
    Elizabeth de Freitas, Nathalie Sinclair & Alf Coles (eds.) (2017). What is a Mathematical Concept? Cambridge University Press.
    Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, (...)
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  10. added 2017-01-17
    H. Cohen Daniel, Commentary on Ami Mamolo on Argumentation and Infinity.
    There is more to mathematics than proofs; there are also arguments, which means that mathematicians are human arguers complete with their biases. Among those biases is a preference for beauty, It is a bias insofar as it is a deaprture from objectivity, but it is benign, accounting for the popularity of Cantor's "Paradise" of non-denumerable infinities as a travel destination for mathematicians and the relatively little interest in Robinson's infinitesimals.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  11. added 2017-01-17
    Charles Parsons (2016). Reply to Feferman, Koellner, Tait, and Sieg. Journal of Philosophy 113 (5/6):286-307.
    I comment on Feferman’s views on set theory, in particular criticizing a priori arguments claiming that the continuum hypothesis has no determinate truth value and commenting on his responses to my paper on his skepticism about set theory. I respond to criticisms of his of the structuralism that I have advocated and comment on his view of proof theory. On Koellner’s paper, I register little disagreement but note a difference of sympathy about views such as constructivism. On Tait’s paper, I (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  12. added 2017-01-17
    W. W. Tait (2016). Kant and Finitism. Journal of Philosophy 113 (5/6):261-273.
    An observation and a thesis: The observation is that, whatever the connection between Kant’s philosophy and Hilbert’s conception of finitism, Kant’s account of geometric reasoning shares an essential idea with the account of finitist number theory in “Finitism”, namely the idea of constructions f from ‘arbitrary’ or ‘generic’ objects of various types. The thesis is that, contrary to a substantial part of contemporary literature on the subject, when Kant referred to number and arithmetic, he was not referring to the natural (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  13. added 2017-01-17
    Solomon Feferman (2016). Parsons and I: Sympathies and Differences. Journal of Philosophy 113 (5/6):234-246.
    In the first part of this article, Feferman outlines his ‘conceptual structuralism’ and emphasizes broad similarities between Parsons’s and his own structuralist perspective on mathematics. However, Feferman also notices differences and makes two critical claims about any structuralism that focuses on the “ur-structures” of natural and real numbers: it does not account for the manifold use of other important structures in modern mathematics and, correspondingly, it does not explain the ubiquity of “individual [natural or real] numbers” in that use. In (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  14. added 2017-01-17
    Tomasz Wysocki (2016). Explanatory Circles, Induction, and Recursive Structures. Thought: A Journal of Philosophy 5 (4).
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  15. added 2017-01-17
    Blake D. Dutton (2016). 9. Platonism and the Apprehensible Truths of Philosophy. In Augustine and Academic Skepticism: A Philosophical Study. Cornell University Press. pp. 195-213.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  16. added 2017-01-17
    C. W. Krabbe Erik, Commentary on Michel Dufour's "On the Difference Between Fallacy and Sophism".
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  17. added 2017-01-17
    W. Sieg (2016). On Tait on Kant and Finitism. Journal of Philosophy 113 (5/6):274-285.
    In his “Kant and Finitism” Tait attempts to connect his analysis of finitist arithmetic with Kant’s perspective on arithmetic. The examination of this attempt is the basis for a distinctive view on the dramatic methodological shift from Kant to Dedekind and Hilbert. Dedekind’s 1888 essay “Was sind und was sollen die Zahlen?” gives a logical analysis of arithmetic, whereas Hilbert’s 1899 book “Grundlagen der Geometrie” presents such an analysis of geometry or, as Hilbert puts it, of our spatial intuition. This (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  18. added 2017-01-17
    Mamolo Ami, Exploring Argumentation, Objectivity, and Bias: The Case of Mathematical Infinity.
    This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece. Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise. This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  19. added 2017-01-17
    François Beets (2015). Arithmetic as Propaedeutic to Theology: The Brethren of Purity. Balkan Journal of Philosophy 7 (1):71-76.
    In the 10th century, the Brethren of Purity conceived a henological arithmetic which they believed could explain the mathematical structure of the cosmos, and could lead the student to the discovery of the real substance of his own soul, a discovery which is the first step towards knowledge of metaphysical and theological truth.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  20. added 2017-01-17
    Lukáš Bielik (2015). The Indispensability Argument for Induction. Balkan Journal of Philosophy 7 (1):45-54.
    Developing the ideas presented in Jacquette, the paper presents an indispensability argument aimed at justification of induction. First, Hume’s problem of induction is introduced via slightly different reconstructions. Second, several traditional attempts to solve Hume’s problem are presented. Finally, Jacquette’s proposal to justify induction by an indispensability argument is developed. I conclude with presenting a kind of indispensability argument for induction.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  21. added 2017-01-17
    Gregor Schneider & Daniel Roth (2014). The Interpretation of Classes in Axiomatic Set Theory. In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 275-314.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  22. added 2017-01-17
    Karl-Georg Niebergall (2014). Assumptions of Infinity. In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 229-274.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  23. added 2017-01-17
    İhsan Fazlıoğlu (2014). Between Reality and Mentality -Fifteenth Century Mathematics and Natural Philosophy Reconsidered-. Nazariyat, Journal for the History of Islamic Philosophy and Sciences 1 (1):1-39.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  24. added 2017-01-17
    Peter Schuster & Laura Crosilla (2014). Finite Methods in Mathematical Practice. In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 351-410.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  25. added 2017-01-17
    Austin Heath (2014). Mathematical Infinity and the Presocratic Apeiron. Stance 7:59-68.
    The Presocratic notion of apeiron, often translated as “unbounded,” has been the subject of interest in classical philosophy. Despite apparent similarities between apeiron and infinity, classicists have typically been reluctant to equate the two, citing the mathematically precise nature of infinity. This paper aims to demonstrate that the properties that Anaximander, Zeno, and Anaxagoras attach to apeiron are not fundamentally different from the characteristics that constitute mathematical infinity. Because the sufficient explanatory mathematical tools had not yet been developed, however, their (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  26. added 2017-01-17
    James Trafford (2014). Expanding the Universe of Universal Logic. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.
    In, Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract "core" of logics in general, where logical syntax and semantics are "two sides of the same coin". Thecentral suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic. However, the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  27. added 2017-01-17
    Yusa Michiko (2014). Parsing the Topos and Dusting the Mirror. Journal of Japanese Philosophy 2 (1):7-32.
    In order to clarify Nishida’s notion of topos, I trace its forma­tion, starting with the notion of “pure experience,” of which he says: “To experience is to know the thing as it is.” By taking the act of “to know” as the thread that connects the ideas of pure experience and topos, I examine his early writings leading up to 1929, going beyond 1926, when Nishida’s essay “Basho” was published. Over against the commonly held “objectified” view of the topos as (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  28. added 2017-01-17
    Kurt Lampe (2014). APPENDIX 2. Annicerean Interpolation in D.L. 2.86–93. In The Birth of Hedonism: The Cyrenaic Philosophers and Pleasure as a Way of Life. Princeton University Press. pp. 211-222.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  29. added 2017-01-17
    C. -C. Tang (2013). Toward a Really Temporalized Theory of Event: A Luhmannian Critique and Reconstruction of Sewell's Logics of History. Social Science Information 52 (1):34-61.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  30. added 2017-01-17
    Bernd Buldt, Review of "Frank Quinn: A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today". [REVIEW]
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  31. added 2017-01-17
    Bernd Buldt, Review of Jørgensen, Klaus Frovin: Kant and the Natural Numbers. [REVIEW]
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  32. added 2017-01-17
    Liesbeth De Mol, Looking for Busy Beavers. A Socio-Philosophical Study of a Computer-Assisted Proof.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  33. added 2017-01-17
    Bernd Buldt, Review of the Book Hermann Grassmann’s Contribution to Whitehead’s Foundations of Logic and Mathematics by J. Riche. [REVIEW]
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  34. added 2017-01-17
    Catherine Z. Elgin (2010). Touchstones of History: Anscombe, Hume, and Julius Caesar. Logos and Episteme 1 (1):39-57.
    In “Hume and Julius Caesar,” G.E.M. Anscombe argues that some historical claims, such as “Julius Caesar was assassinated,” serve as touchstones for historical knowledge. Only Cartesian doubt can call them into question. I examine her reasons for thinking that the discipline of history must be grounded in claims that it is powerless to discredit. I argue that she is right to recognize that some historical claims are harder to dislodge than others, but wrong to contend that any are invulnerable to (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  35. added 2017-01-17
    K’Odhiambo Atieno Kili & O. Gunga Samson (2010). The Impact of the Interaction Between Verbal and Mathematical Languages in Education. Thought and Practice: A Journal of the Philosophical Association of Kenya 2 (2):79-99.
    Since the methods employed during teacher-learner interchange are constrained by the internal structure of a discipline, a study of the interaction amongst verbal language, technical language and structure of disciplines is at the heart of the classic problem of transfer in teaching-learning situations. This paper utilizes the analytic method of philosophy to explore aspects of the role of language in mathematics education, and attempts to harmonize mathematical meanings exposed by verbal language and the precise meanings expressed by the mathematics register (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  36. added 2017-01-17
    Bernd Buldt & Dirk Schlimm, Loss of Vision: How Mathematics Turned Blind While It Learned to See More Clearly.
    To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a (...)
    No categories
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  37. added 2017-01-17
    Igor Žagar (2010). Topoi in Critical Discourse Analysis. Lodz Papers in Pragmatics 6 (1):3-27.
    Topoi in Critical Discourse Analysis Topos is one of the most widely-used concepts from classical argumentation theory. It found its way not only in philosophy, sociology, anthropology, and linguistics; it found its way in everyday life and everyday conversation as well.In this article, I will examine the role that topoi play in Critical Discourse Analysis. Starting with definitions from Aristotle and Cicero, contrasting them with new conceptualisations by Perelman and Toulmin, and examining the superficial use of topoi in everyday conversation, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  38. added 2017-01-17
    Vahedi Zohreh & Rahimian Jalal (2010). The Semantic-Pragmatic Analysis of Persian Modal Verbs Based on Papafragou's Model. Lodz Papers in Pragmatics 6 (1):67-116.
    The Semantic-Pragmatic Analysis of Persian Modal Verbs Based on Papafragou's Model This paper aims at analyzing the semantics and pragmatics of Persian modal verbs based on Papafragou's relevance-theoretic model. Persian modals are defined in terms of logical relations and propositional domains. According to the findings of the research, two of the three modals, namely, šodan and tavân express the logical relation of compatibility with respect to different propositional domains: the three forms mišavad, mišod and mišode are unspecified with respect to (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  39. added 2017-01-17
    Meyer Olaf & Janssen André (2009). Macro-Systematic Interpretation of Uniform Commercial Law: The Interrelation of the CISG and Other Uniform Sources. In Olaf Meyer & André Janssen (eds.), Cisg Methodology. Sellier de Gruyter.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  40. added 2017-01-17
    M. Hutton Jeremy (2009). 1. Echoes of the Past and Topos as Text: The Transjordanian Motif and Landscape Criticism. In Jeremy M. Hutton (ed.), The Transjordanian Palimpsest: The Overwritten Texts of Personal Exile and Transformation in the Deuteronomistic History. Walter de Gruyter.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  41. added 2017-01-17
    Greenberg Robert (2008). Chapter 11 – Derivations of the Real Modalities. In Robert Greenberg (ed.), Real Existence, Ideal Necessity: Kant's Compromise, and the Modalities Without the Compromise. Walter de Gruyter.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  42. added 2017-01-17
    C. Dimitracopoulos, L. Newelski & D. Normann (eds.) (2007). Logic Colloquium 2005. Cambridge: Cambridge University Press.
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  43. added 2017-01-17
    Pierre Cassou-Nogués (2006). Signs, Figures and Time. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 21 (1):89-104.
    This paper is concerned with Cavaillès’ account of “intuition” in mathematics. Cavaillès starts from Kant’s theory of constructions in intuition and then relies on various remarks by Hilbert to apply it tomodern mathematics. In this context, “intuition” includes the drawing of geometrical figures, the use of algebraic or logical signs and the generation of numbers as, for example, described by Brouwer. Cavaillès argues that mathematical practice can indeed be described as “constructions in intuition” but that these constructions are not imbedded (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  44. added 2017-01-17
    Charles Sayward (2005). Steiner Versus Wittgenstein. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (3):347-352.
    Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  45. added 2017-01-17
    Robles Gemma & M. Méndez José (2005). Two Versions of Minimal Intuitionism with the CAP. A Note. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (2):183-190.
    Two versions of minimal intuitionism are defined restricting Contraction. Both are defined by means of a falsity constant F. The first one follows the historical trend, the second is the result of imposing specialconstraints on F. RelationaI ternary semantics are provided.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  46. added 2017-01-17
    Juan José Acero (2003). Conceptions of the Mind... That Do Not Loose Sight of Logic. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 18 (1):17-25.
    Which is the relation between logic and philosophy of mind? This work tries to answer that question by shortly examining, first, the place that is assigned to logic in three current views of the mind: Computationalism, Interpretativism and Naive Naturalism. Secondly, the classical debate between psychologism and antipsychologism is reviewed -the question about whether logic is or not a part of psychology- and it is indicated in which place of such debate the three mentioned conceptions of mind are located.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  47. added 2017-01-17
    H. Hanson William (2003). Logic, the A Priori, and the Empirical. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 18 (2):171-177.
    The time-honored view that logic is a non-empirical enterprise is still widely accepted, but it is not always recognized that there are two distinct ways in which this view can be made precise. One way focuses on the knowledge we can have of logical matters, the other on the nature of the logical consequence relation itself. More specifically; the first way embodies the claim that knowledge of whether the logical consequence relation holds in a particular case is knowledge that can (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  48. added 2017-01-17
    Sayward (2002). Is an Unpictorial Mathematical Platonism Possible? Journal of Philosophical Research 27:201-214.
    In his book Wittgenstein on the Foundations of Mathematics, Crispin Wright notes that remarkably little has been done to provide an unpictorial, substantial account of what mathematical platonism comes to. Wright proposes to investigate whether there is not some more substantial doctrine than the familiar images underpinning the platonist view. He begins with the suggestion that the essential platonist claim is that mathematical truth is objective. Although he does not demarcate them as such, Wright proposes several different tests for objectivity. (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  49. added 2017-01-17
    Donald Gillies & Yuxin Zheng (2001). Dynamic Interactions with the Philosophy of Mathematics. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 16 (3):437-459.
    Dynamic interaction is said to occur when two significanrly different fields A and B come into relation, and their interaction is dynamic in the sense that at first the flow of ideas is principally from A to B, but later ideas from B come to influence A. Two examples are given of dynamic interactions with the philosophy of mathematics. The first is with philosophy of scicnce, and thc sccond with computer science. Theanalysis cnables Lakatos to be charactcrised as thc first (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  50. added 2017-01-17
    Hale Bob (2000). Reals by Abstraction. The Proceedings of the Twentieth World Congress of Philosophy 6:197-207.
    While Frege’s own attempt to provide a purely logical foundation for arithmetic failed, Hume’s principle suffices as a foundation for elementary arithmetic. It is known that the resulting system is consistent—or at least if second-order arithmetic is. Some philosophers deny that HP can be regarded as either a truth of logic or as analytic in any reasonable sense. Others—like Crispin Wright and I—take the opposed view. Rather than defend our claim that HP is a conceptual truth about numbers, I explain (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
1 — 50 / 122