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  1. added 2019-12-19
    Einführung in die Philosophie der Mathematik.Jörg Neunhäuserer - 2019 - Wiesbaden, Deutschland: Springer Spektrum.
    Welche Art von Gegenständen untersucht die Mathematik und in welchem Sinne existieren diese Gegenstände? Warum dürfen wir die Aussagen der Mathematik zu unserem Wissen zählen und wie lassen sich diese Aussagen rechtfertigen? Eine Philosophie der Mathematik versucht solche Fragen zu beantworten. In dieser Einführung stellen wir maßgeblichen Positionen in der Philosophie der Mathematik vor und formulieren die Essenz dieser Positionen in möglichst einfachen Thesen. Der Leser erfährt, auf welche Philosophen eine Position zurückgeht und in welchem historischen Kontext diese entstand. Ausgehend (...)
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  2. added 2019-06-06
    Rationality and Logic. [REVIEW]Joseph Ulatowski - 2008 - Polish Journal of Philosophy 2 (2):148-152.
    In this brief article, I review the main argument's of Robert Hanna's <em>Rationality and Logic</em>.
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  3. added 2019-06-06
    The Fundamental Laws of Arithmetic: Psychological Logic.Gottlob Frege - 1916 - The Monist 26 (2):182-199.
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  4. added 2018-06-06
    Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  5. added 2017-10-21
    Mathematics and Its Applications, A Transcendental-Idealist Perspective.Jairo Da Silva - 2017 - Springer.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...)
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  6. added 2017-04-13
    Mathematics and Aesthetics in Kantian Perspectives.Wenzel Christian Helmut - 2016 - In Peter Cassaza, Steven G. Krantz & Randi R. Ruden (eds.), I, Mathematician II. Further Introspections on the Mathematical Life. The Consortium of Mathematics and its Applications. pp. 93-106.
    This essay will inform the reader about Kant’s views on mathematics and aesthetics. It will also critically discuss these views and offer further suggestions and personal opinions from the author’s side. Kant (1724-1804) was not a mathematician, nor was he an artist. One must even admit that he had little understanding of higher mathematics and that he did not have much of a theory that could be called a “philosophy of mathematics” either. But he formulated a very influential aesthetic theory (...)
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  7. added 2016-04-17
    Frege, the Complex Numbers, and the Identity of Indiscernibles.Wenzel Christian Helmut - 2010 - Logique Et Analyse 53 (209):51-60.
    There are mathematical structures with elements that cannot be distinguished by the properties they have within that structure. For instance within the field of complex numbers the two square roots of −1, i and −i, have the same algebraic properties in that field. So how do we distinguish between them? Imbedding the complex numbers in a bigger structure, the quaternions, allows us to algebraically tell them apart. But a similar problem appears for this larger structure. There seems to be always (...)
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  8. added 2015-03-26
    Mill's System of Logic.David Godden - 2014 - In W. J. Mander (ed.), Oxford handbook of British philosophy in the nineteenth century. Oxford University Press. pp. 44-70.
    This chapter situates Mill’s System of Logic (1843/1872) in the context of some of the meta-logical themes and disputes characteristic of the 19th century as well as Mill’s empiricism. Particularly, by placing the Logic in relation to Whately’s (1827) Elements of Logic and Mill’s response to the “great paradox” of the informativeness of syllogistic reasoning, the chapter explores the development of Mill’s views on the foundation, function, and the relation between ratiocination and induction. It provides a survey of the Mill-Whewell (...)
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  9. added 2015-03-26
    Psychologism in the Logic of John Stuart Mill: Mill on the Subject Matter and Foundations of Ratiocinative Logic.David M. Godden - 2005 - History and Philosophy of Logic 26 (2):115-143.
    This paper considers the question of whether Mill's account of the nature and justificatory foundations of deductive logic is psychologistic. Logical psychologism asserts the dependency of logic on psychology. Frequently, this dependency arises as a result of a metaphysical thesis asserting the psychological nature of the subject matter of logic. A study of Mill's System of Logic and his Examination reveals that Mill held an equivocal view of the subject matter of logic, sometimes treating it as a set of psychological (...)
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  10. added 2014-06-20
    Husserl's Psychology of Arithmetic.Carlo Ierna - 2012 - Bulletin d'Analyse Phénoménologique 8 (1):97-120.
    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) in its simplest and (...)
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  11. added 2014-04-02
    Pretense, Mathematics, and Cognitive Neuroscience.Jonathan Tallant - 2013 - British Journal for the Philosophy of Science 64 (4):axs013.
    A pretense theory of a given discourse is a theory that claims that we do not believe or assert the propositions expressed by the sentences we token (speak, write, and so on) when taking part in that discourse. Instead, according to pretense theory, we are speaking from within a pretense. According to pretense theories of mathematics, we engage with mathematics as we do a pretense. We do not use mathematical language to make claims that express propositions and, thus, we do (...)
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  12. added 2014-03-29
    What is Mathematics, Really?Reuben Hersh - 1997 - Oxford University Press.
    Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist (...)
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  13. added 2013-09-02
    Frege on the Relations Between Logic and Thought.Simon Evnine - manuscript
    Frege's diatribes against psychologism have often been taken to imply that he thought that logic and thought have nothing to do with each other. I argue against this interpretation and attribute to Frege a view on which the two are tightly connected. The connection, however, derives not from logic's being founded on the empirical laws of thought but rather from thought's depending constitutively on the application to it of logic. I call this view 'psycho-logicism.'.
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  14. added 2013-09-02
    Frege on Truth, Beauty and Goodness.Simon Evnine - 2003 - Manuscrito 26 (2):315-330.
    The paper attempts to shed light on Frege's views on the relation of logic to truth by looking at several passages in which he compares it to the relation of ethics to the good and aesthetics to the beautiful. It turns out that Frege makes four distinct points by means of these comparisons only one of which both concerns truth and makes use of distinctive features of ethics and aesthetics. This point is that logic is about reaching truth in the (...)
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  15. added 2013-03-19
    Co łączy umysł z teorią liczb?Paweł Stacewicz - 2012 - Filozofia Nauki 20 (3).
    According to the methodology of cognitive science we consider a hypothesis (justified partially by cognitive applications of computer science), that the mind functions similarly to a computer. Philosophical consequences of this thesis are as follows: (1) there exists a mental code (similar to the code of computer program); (2) this code can be represented as one unique number; (3) this number can be computable or non-computable.
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  16. added 2013-03-19
    O przedmiocie matematycznym.Piotr Błaszczyk - 2004 - Filozofia Nauki 2 (1):45-59.
    In this paper we show that the field of the real numbers is an intentional object in the sense specified by Roman Ingarden in his Das literarische Kunstwer and Der Streit um die Existenz der Welt. An ontological characteristics of a classic example of an intentional object, i.e. a literary character, is developed. There are three principal elements of such an object: the author, the text and the entity in which the literary character forms the content. In the case of (...)
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  17. added 2013-03-19
    Mózg I Matematyka [Recenzja] Stanislas Dehaene, The Number Sense - How the Mind Creates Mathematics?, 1997.Michał Heller - 2000 - Zagadnienia Filozoficzne W Nauce 26.
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  18. added 2013-02-28
    The Status of Consciousness in Nature.Berit Brogaard - forthcoming - In Steven Miller (ed.), The Constitution of Consciousness, Volume 2. John Benjamins.
    The most central metaphysical question about phenomenal consciousness is that of what constitutes phenomenal consciousness, whereas the most central epistemic question about consciousness is that of whether science can eventually provide an explanation of phenomenal consciousness. Many philosophers have argued that science doesn't have the means to answer the question of what consciousness is (the explanatory gap) but that consciousness nonetheless is fully determined by the physical facts underlying it (no metaphysical gap). Others have argued that the explanatory gap in (...)
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  19. added 2013-01-05
    Psychologism, Logic, and Mr. Myhill.N. L. Wilson - 1964 - Philosophia Mathematica 1:1-4.
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  20. added 2012-09-10
    Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics.Julian C. Cole - 2013 - Philosophia Mathematica 21 (1):9-36.
    I contend that mathematical domains are freestanding institutional entities that, at least typically, are introduced to serve representational functions. In this paper, I outline an account of institutional reality and a supporting metaontological perspective that clarify the content of this thesis. I also argue that a philosophy of mathematics that has this thesis as its central tenet can account for the objectivity, necessity, and atemporality of mathematics.
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  21. added 2012-09-10
    Mathematical Domains: Social Constructs?Julian C. Cole - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematics Association of America. pp. 109--128.
    I discuss social constructivism in the philosophy of mathematics and argue for a novel variety of social constructivism that I call Practice-Dependent Realism.
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  22. added 2012-09-10
    The Nature of Sociocultural Existence: A Prologue.J. Fang - 1974 - Philosophia Mathematica (1-2):127-144.
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  23. added 2011-08-15
    In General and in Prospect: 'The Psychology of Science' (a Sum-Up).Abraham H. Maslow - 1980 - Philosophia Mathematica (1):39-49.
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