Results for 'philosophy of mathematics'

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  1.  28
    Redrawing Kant's Philosophy of Mathematics.Joshua M. Hall - 2013 - South African Journal of Philosophy 32 (3):235-247.
    This essay offers a strategic reinterpretation of Kant’s philosophy of mathematics in Critique of Pure Reason via a broad, empirically based reconception of Kant’s conception of drawing. It begins with a general overview of Kant’s philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant’s constructivism takes up these issues, largely inspired by Hintikka’s unorthodox conception (...)
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  2.  79
    Assessing the “Empirical Philosophy of Mathematics”.Markus Pantsar - 2015 - Discipline Filosofiche:111-130.
    Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of (...)
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  3.  41
    Math by Pure Thinking: R First and the Divergence of Measures in Hegel's Philosophy of Mathematics.Ralph M. Kaufmann & Christopher Yeomans - 2017 - European Journal of Philosophy 25 (4):985-1020.
    We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, (...)
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  4. Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
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  5. Spinoza and the Philosophy of Science: Mathematics, Motion, and Being.Eric Schliesser - manuscript
    This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in (...)
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  6. Lakatos’ Quasi-Empiricism in the Philosophy of Mathematics.Michael J. Shaffer - 2015 - Polish Journal of Philosophy 9 (2):71-80.
    Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and (...)
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  7.  90
    Fourteen Arguments in Favour of a Formalist Philosophy of Real Mathematics.Karlis Podnieks - 2015 - Baltic Journal of Modern Computing 3 (1):1-15.
    The formalist philosophy of mathematics (in its purest, most extreme version) is widely regarded as a “discredited position”. This pure and extreme version of formalism is called by some authors “game formalism”, because it is alleged to represent mathematics as a meaningless game with strings of symbols. Nevertheless, I would like to draw attention to some arguments in favour of game formalism as an appropriate philosophy of real mathematics. For the most part, these arguments have (...)
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  8. Mario Bunge’s Philosophy of Mathematics: An Appraisal.Jean-Pierre Marquis - 2012 - Science & Education 21 (10):1567-1594.
    In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.To Mario, with gratitude.
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  9. Walter Dubislav’s Philosophy of Science and Mathematics.Nikolay Milkov - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):96-116.
    Walter Dubislav (1895–1937) was a leading member of the Berlin Group for scientific philosophy. This “sister group” of the more famous Vienna Circle emerged around Hans Reichenbach’s seminars at the University of Berlin in 1927 and 1928. Dubislav was to collaborate with Reichenbach, an association that eventuated in their conjointly conducting university colloquia. Dubislav produced original work in philosophy of mathematics, logic, and science, consequently following David Hilbert’s axiomatic method. This brought him to defend formalism in these (...)
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  10.  93
    Review of Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics[REVIEW]Chris Smeenk - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):194-199.
    Book Review for Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, La Salle, IL: Open Court, 2002. Edited by David Malament. This volume includes thirteen original essays by Howard Stein, spanning a range of topics that Stein has written about with characteristic passion and insight. This review focuses on the essays devoted to history and philosophy of physics.
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  11. Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio (...)
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  12.  35
    Reconstruction in Philosophy of Mathematics.Davide Rizza - 2018 - Dewey Studies 2 (2):31-53.
    Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...)
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  13.  66
    Review of D. Corfield's Toward A Philosophy Of Real Mathematics[REVIEW]Andrew Arana - 2007 - Mathematical Intelligencer 29 (2).
    When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject (...)
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  14. The connection between mathematics and philosophy on the discrete–structural plane of thinking: the discrete–structural model of the world.Eldar Amirov - 2017 - Гілея: Науковий Вісник 126 (11):266-270.
    The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. (...)
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  15. Topology as an Issue for History of Philosophy of Science.Thomas Mormann - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer. pp. 423--434.
    Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, (...)
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  16. Leibniz on Mathematics, Methodology, and the Good: A Reconsideration of the Place of Mathematics in Leibniz's Philosophy.Christia Mercer - 2006 - Early Science and Medicine 11 (4):424-454.
    Scholars have long been interested in the relation between Leibniz, the metaphysician-theologian, and Leibniz, the logician-mathematician. In this collection, we consider the important roles that rhetoric and the "art of thinking" have played in the development of mathematical ideas. By placing Leibniz in this rhetorical tradition, the present essay shows the extent to which he was a rhetorical thinker, and thereby answers the question about the relation between his work as a logician-mathematician and his other work. It becomes clear that (...)
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  17. From Mathematics to Quantum Mechanics - On the Conceptual Unity of Cassirer’s Philosophy of Science.Thomas Mormann - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 31-64.
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  18.  63
    Dummett and Wittgenstein's Philosophy of Mathematics.Carlo Penco - 1994 - In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer Academic Publishers. pp. 113--136.
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  19.  47
    Review of O. Linnebo Philosophy of Mathematics[REVIEW]Fraser MacBride - 2018 - Notre Dame Philosophical Reviews.
    In this review, as well as discussing the pedagogical of this text book, I also discuss Linnebo's approach to the Caesar problem and the use of metaphysical notions to explicate mathematics.
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  20. 'Explanatory Indispensability Arguments in Metaethics and Philosophy of Mathematics'.Debbie Roberts - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford University Press.
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  21. Models, Mathematics and Deleuze's Philosophy: Some Remarks on Simon Duffy's Deleuze and the History of Mathematics: In Defence of the New.James Williams - 2017 - Deleuze and Guatarri Studies 11 (3):475-481.
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  22. The Philosophy of Mathematics and the Independent 'Other'.Penelope Rush - unknown
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  23. Philosophy of Logic. Hilary Putnam.John Corcoran - 1973 - Philosophy of Science 40 (1):131-133.
    Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) (...)
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  24.  98
    On the Reality of the Continuum Discussion Note: A Reply to Ormell, ‘Russell's Moment of Candour’, Philosophy: Anne Newstead and James Franklin.Anne Newstead - 2008 - Philosophy 83 (1):117-127.
    In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding (...)
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  25. Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics.Jean-Pierre Marquis - 2013 - Review of Symbolic Logic 6 (1):51-75.
    Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.
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  26. Normativity and Mathematics: A Wittgensteinian Approach to the Study of Number.J. Robert Loftis - 1999 - Dissertation, Northwestern University
    I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...)
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  27. What Isn’T Obvious About ‘Obvious’: A Data-Driven Approach to Philosophy of Logic.Moti Mizrahi - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Press. pp. 201-224.
    It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically (...)
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  28.  92
    1983 Review in Mathematical Reviews 83e:03005 Of: Cocchiarella, Nino “The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy: Bertrand Russell's Early Philosophy, Part I”. Synthese 45 (1980), No. 1, 71-115.John Corcoran - 1983 - MATHEMATICAL REVIEWS 83:03005.
    CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .
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  29. Volume Introduction – Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy.Scott Edgar - 2018 - Journal for the History of Analytical Philosophy 6 (3):1-10.
    Introduction to the Special Volume, “Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy,” edited by Scott Edgar and Lydia Patton. At its core, analytic philosophy concerns urgent questions about philosophy’s relation to the formal and empirical sciences, questions about philosophy’s relation to psychology and the social sciences, and ultimately questions about philosophy’s place in a broader cultural landscape. This picture of analytic philosophy shapes this collection’s focus on the history of the philosophy (...)
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  30. On the Logical Form of Educational Philosophy and Theory: Herbart, Mill, Frankena, and Beyond.Berislav Žarnić - 2016 - Encyclopedia of Educational Philosophy and Theory: Living Reference Work.
    The investigation into logical form and structure of natural sciences and mathematics covers a significant part of contemporary philosophy. In contrast to this, the metatheory of normative theories is a slowly developing research area in spite of its great predecessors, such as Aristotle, who discovered the sui generis character of practical logic, or Hume, who posed the “is-ought” problem. The intrinsic reason for this situation lies in the complex nature of practical logic. The metatheory of normative educational (...) and theory inherits all the difficulties inherent in the general metatheory but has also significantly contributed to its advancement. In particular, the discussion on its mixed normative-descriptive character and complex composition has remained an important part of research in educational philosophy and theory. The two points seem to be indisputable. First, the content of educational philosophy and theory is a complex one, connecting different disciplines. Second, these disciplines are integrated within the logical form of practical inference or means-end reasoning. On the other hand, the character of consequence relation in this field, although generally recognized as specific, represents an unresolved prob- lem, a solution of which requires a sophisticated logical theory and promises to influence the self- understanding of educational philosophy and theory. (shrink)
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  31. Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.
    I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the (...)
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  32. Avoiding Reification: Heuristic Effectiveness of Mathematics and the Prediction of the Omega Minus Particle.Michele Ginammi - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:20-27.
    According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne׳eman׳s prediction of the Ω− particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based (...)
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  33. Making Philosophy of Science Relevant for Science Students.Henrik Kragh Sørensen - 2012 - Centre for Science Studies, University of Aarhus.
    Since 2004, it has been mandated by law that all Danish undergraduate university programmes have to include a compulsory course on the philosophy of science for that particular program. At the Faculty of Science and Technology, Aarhus University, the responsibility for designing and running such courses were given to the Centre for Science Studies, where a series of courses were developed aiming at the various bachelor educations of the Faculty. Since 2005, the Centre has been running a dozen different (...)
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  34. David Lewis's Place in the History of Late Analytic Philosophy: His Conservative and Liberal Methodology.Frederique Janssen-Lauret & Fraser MacBride - 2018 - Philosophical Inquiries 5 (1):1-22.
    In 1901 Russell had envisaged the new analytic philosophy as uniquely systematic, borrowing the methods of science and mathematics. A century later, have Russell’s hopes become reality? David Lewis is often celebrated as a great systematic metaphysician, his influence proof that we live in a heyday of systematic philosophy. But, we argue, this common belief is misguided: Lewis was not a systematic philosopher, and he didn’t want to be. Although some aspects of his philosophy are systematic, (...)
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  35.  28
    Introduction.Andrew Aberdein & Matthew Inglis - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. Bloomsbury Academic. pp. 1-13.
    There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of (...)
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  36.  36
    The Changing Practices of Proof in Mathematics.Andrew Arana - 2017 - Metascience 26 (1):131-135.
    Review of Dowek, Gilles, Computation, Proof, Machine, Cambridge University Press, Cambridge, 2015. Translation of Les Métamorphoses du calcul, Le Pommier, Paris, 2007. Translation from the French by Pierre Guillot and Marion Roman.
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  37. Infinitesimals as an Issue of Neo-Kantian Philosophy of Science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.
    We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and (...)
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  38. Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08.John Corcoran - 1972 - Philosophy of Science 39 (1):106-108.
    Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08. -/- Constance Reid was an insider of the Berkeley-Stanford logic circle. Her San Francisco home was in Ashbury Heights near the homes of logicians such as Dana Scott and John Corcoran. Her sister Julia Robinson was one of the top mathematical logicians of her generation, as was Julia’s husband Raphael Robinson for whom Robinson Arithmetic was named. Julia was a Tarski PhD and, in recognition (...)
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  39. Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225-235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...)
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  40. Tools for Thought: The Case of Mathematics.Valeria Giardino - 2018 - Endeavour 2 (42):172-179.
    The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced.
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  41.  29
    Forms of Structuralism: Bourbaki and the Philosophers.Jean-Pierre Marquis - forthcoming - In Alberto Peruzzi & Silvano Zipoli Caiani (eds.), Structures Meres, Semantics, Mathematics, and Cognitive Science. New York, NY, USA:
    In this paper, we argue that, contrary to the view held by most philosophers of mathematics, Bourbaki’s technical conception of mathematical structuralism is relevant to philosophy of mathematics. In fact, we believe that Bourbaki has captured the core of any mathematical structuralism.
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  42. Hobbes on the Order of Sciences: A Partial Defense of the Mathematization Thesis.Zvi Biener - 2016 - Southern Journal of Philosophy 54 (3):312-332.
    Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomtic-deductive, with statecraft being deduced in an unbroken chain from the principles of logic and first philosophy. On the other, it is portrayed as rife with conceptual cracks and fissures, with Hobbes’s statements about its deductive structure amounting to mere window-dressing. This paper argues that a middle way is found by conceiving of Hobbes’s _Elements of Philosophy_ on the model of (...)
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  43. Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble - forthcoming - Progress in Biophysics and Molecular Biology 119 (2).
    The is the Editorial of the 2015 JPBMB Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.
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  44.  31
    Takeuti's Proof Theory in the Context of the Kyoto School.Andrew Arana - 2019 - Jahrbuch Für Philosophie Das Tetsugaku-Ronso 46:1-17.
    Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used (...)
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  45. Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
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  46. The Role of Mathematics in Deleuze’s Critical Engagement with Hegel.Simon Duffy - 2009 - International Journal of Philosophical Studies 17 (4):563 – 582.
    The role of mathematics in the development of Gilles Deleuze's (1925-95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze's interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770-1831) presents in the Science of Logic . Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal (...)
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  47.  34
    The Philosophy of Language and the Ontology of Knowledge.Jean-Louis Boucon - 2019
    Objective The relations between thought and reality are studied in many fields of philosophy and science. Examples include ontology and metaphysics in general, linguistics, neuroscience and even mathematics. Each one has its postulates, its language, its methods and its own constraints. It would be unreasonable, however, for them to ignore each other. In the pages that follow we will try to identify areas of proximity between the ideas of contemporary philosophers of language and those issued mainly by Ontology (...)
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  48. Life and Works of Giovanni Vailati.Paola Cantù & De Zan Mauro - 2009 - In Arrighi Claudia, Cantù Paola, De Zan Mauro & Suppes Patrick (eds.), Life and Works of Giovanni Vailati. CSLI Publications.
    The paper introduces Vailati’s life and works, investigating Vailati’s education, the relation to Peano and his school, and the interest for pragmatism and modernism. A detailed analysis of Vailati’s scientific and didactic activities, shows that he held, like Peano, a a strong interest for the history of science and a pluralist, anti-dogmatic and anti-foundationalist conception of definitions in mathematics, logic and philosophy of language. Vailati’s understanding of mathematical logic as a form of pragmatism is not a faithful interpretation (...)
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  49. Plato’s Philosophy of Cognition by Mathematical Modelling.Roman S. Kljujkov & Sergey Kljujkov - 2014 - Dialogue and Universalism 24 (3):110-115.
    By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long (...)
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  50. The Unreasonable Effectiveness of Abstract Metaphysics.Daniel Nolan - 2015 - Oxford Studies in Metaphysics 9:61-88.
    In Metaphysics A, Aristotle offers some objections to Plato’s theory of Forms to the effect that Plato’s Forms would not be explanatory in the right way, and seems to suggest that they might even make the explanatory project worse. One interesting historical puzzle is whether Aristotle can avoid these same objections to his own theory of universals. The concerns Aristotle raises are, I think, cousins of contemporary concerns about the usefulness and explanatoriness of abstract objects, some of which have recently (...)
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