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166 found
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1 — 50 / 166
  1. added 2020-06-03
    The Epistemology of Abstract Objects: Access and Inference.David Bell & W. D. Hart - 1979 - Proceedings of the Aristotelian Society, Supplementary Volumes( 53:135-165.
  2. added 2020-05-22
    Cognitive Processing of Spatial Relations in Euclidean Diagrams.Yacin Hamami, Milan N. A. van der Kuil, Ineke J. M. van der Ham & John Mumma - 2020 - Acta Psychologica 205:1--10.
    The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first part, we (...)
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  3. added 2020-04-17
    Towards an Account of Epistemic Luck for Necessary Truths.James Collin - 2018 - Acta Analytica 33 (4):483-504.
    Modal epistemologists parse modal conditions on knowledge in terms of metaphysical possibilities or ways the world might have been. This is problematic. Understanding modal conditions on knowledge this way has made modal epistemology, as currently worked out, unable to account for epistemic luck in the case of necessary truths, and unable to characterise widely discussed issues such as the problem of religious diversity and the perceived epistemological problem with knowledge of abstract objects. Moreover, there is reason to think that this (...)
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  4. added 2020-03-10
    Die sogenannte Analytizität der Mathematik: Für eine Radikalisierung der Theorie Hintikkas.J. P. Dubucs - 1988 - Grazer Philosophische Studien 32 (1):83-112.
    Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.
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  5. added 2020-02-17
    Wittgenstein, Peirce, and Paradoxes of Mathematical Proof.Sergiy Koshkin - forthcoming - Analytic Philosophy.
    Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic (...)
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  6. added 2020-01-28
    Ptolemy’s Philosophy: Mathematics as a Way of Life. By Jacqueline Feke. Princeton: Princeton University Press, 2018. Pp. Xi + 234. [REVIEW]Nicholas Danne - 2020 - Metaphilosophy 51 (1):151-155.
  7. added 2019-12-04
    Reseña de ‘I am a Strange Loop’ (Soy un Lazo Extraño) de Douglas Hofstadter (2007) (revisión revisada 2019).Michael Richard Starks - 2019 - In Delirios Utópicos Suicidas en el Siglo 21 La filosofía, la naturaleza humana y el colapso de la civilización Artículos y reseñas 2006-2019 4a Edición. Las Vegas, NV USA: Reality Press. pp. 205-221.
    Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...)
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  8. added 2019-11-29
    ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de la Manera de Godel: explota en un mundo indecible (Godel’s Way: exploits into an undecidable world) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160P (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 44-63.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  9. added 2019-11-15
    Wigner’s Puzzle on Applicability of Mathematics: On What Table to Assemble It?Cătălin Bărboianu - 2019 - Axiomathes 1:1-30.
    Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...)
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  10. added 2019-09-14
    Quantity and Number.James Franklin - 2014 - In Daniel D. Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. New York, USA: Routledge. pp. 221-244.
    Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.
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  11. added 2019-09-09
    Alain Badiou : un philosophe face au concept de modèle.Franck Varenne - 2008 - Natures Sciences Sociétés 16 (3):252-257.
    In 1969, the influent French philosopher Alain Badiou published a book called "The concept of Model: An Introduction to the Materialist Epistemology of Mathematics". A recent reprint gives the opportunity to trace back and analyze its main arguments. This paper essentially aims to present and explain Badiou's arguments against the representationalist vision of models in empirical sciences and for a materialist interpretation of formal systems coupled with semantic models in mathematics. Now that the practices of scientific modeling and simulation have (...)
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  12. added 2019-08-14
    Mathematical and Moral Disagreement.Silvia Jonas - 2020 - Philosophical Quarterly 70 (279):302-327.
    The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I argue (...)
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  13. added 2019-08-14
    Iterated Reflection Over Full Disquotational Truth.Fischer Martin, Nicolai Carlo & Horsten Leon - 2017 - Journal of Logic and Computation 27 (8):2631-2651.
    Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by iterated reflection at strong compositional truth theories. In the context of classical logic, it is incoherent to adopt an initial truth theory in which A and ‘A is truen’ are inter-derivable. In this article, we show how in the context (...)
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  14. added 2019-07-19
    Modal Security.Justin Clarke‐Doane & Dan Baras - forthcoming - Philosophy and Phenomenological Research.
    Modal Security is an increasingly discussed proposed necessary condition on undermining defeat. Modal Security says, roughly, that if evidence undermines (rather than rebuts) one’s belief, then one gets reason to doubt the belief's safety or sensitivity. The primary interest of the principle is that it seems to entail that influential epistemological arguments, including Evolutionary Debunking Arguments against moral realism and the Benacerraf-Field Challenge for mathematical realism, are unsound. The purpose of this paper is to critically examine Modal Security in detail. (...)
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  15. added 2019-06-06
    The Growth of Mathematical Knowledge—Introduction of Convex Bodies.Tinne Hoff Kjeldsen & Jessica Carter - 2012 - Studies in History and Philosophy of Science Part A 43 (2):359-365.
  16. added 2019-06-06
    Jody Azzouni. Tracking Reason: Proof, Consequence and Truth: Critical Studies/Book Reviews.Conrad Asmus - 2009 - Philosophia Mathematica 17 (3):369-377.
    (No abstract is available for this citation).
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  17. added 2019-06-06
    From Bayesianism to the Epistemic View of Mathematics: Review of R. Jeffrey, Subjective Probability: The Real Thing[REVIEW]Jon Williamson - 2006 - Philosophia Mathematica 14 (3):365-369.
    Subjective Probability: The Real Thing is the last book written by the late Richard Jeffrey, a key proponent of the Bayesian interpretation of probability.Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consider 7:3 to be fair odds for a bet on rain. There are two extreme Bayesian (...)
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  18. added 2019-06-05
    Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism.Hasen Khudairi - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer.
    This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity correspond to those of (...)
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  19. added 2019-06-05
    Russell on Logicism and Coherence.Conor Mayo-Wilson - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1):89-106.
    According to Quine, Charles Parsons, Mark Steiner, and others, Russell's logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as a prioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell's explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent (...)
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  20. added 2019-06-05
    Mathematical Knowledge.Mary Leng, Alexander Paseau & Michael Potter (eds.) - 2007 - Oxford University Press.
    What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions.
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  21. added 2019-04-26
    Gentzen's Anti-Formalist Ideas.Michael Detlefsen - 2015 - In Reinhard Kahle & Michael Rathjen (eds.), Gentzen's Centenary: The Quest for Consistency. New York: Springer. pp. 25-44.
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  22. added 2019-04-26
    Discovery, Invention and Realism: Gödel and Others on the Reality of Concepts.Michael Detlefsen - 2011 - In John Polkinghorne (ed.), Mathematics and its Significance. Oxford: Oxford University Press. pp. 73-96.
    The general question considered is whether and to what extent there are features of our mathematical knowledge that support a realist attitude towards mathematics. I consider, in particular, reasoning from claims such as that mathematicians believe their reasoning to be part of a process of discovery (and not of mere invention), to the view that mathematical entities exist in some mind-independent way although our minds have epistemic access to them.
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  23. added 2019-04-26
    Proof: Its Nature and Significance.Michael Detlefsen - 2009 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. MAA. pp. 3-32.
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  24. added 2019-04-18
    The Ethics–Mathematics Analogy.Justin Clarke‐Doane - 2020 - Philosophy Compass 15 (1).
    Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind and languages. (...)
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  25. added 2019-03-30
    Evidence, Proofs, and Derivations.Andrew Aberdein - 2019 - ZDM 51 (5):825-834.
    The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...)
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  26. added 2019-03-26
    Thin Objects.Øystein Linnebo - 2018 - Oxford: Oxford University Press.
    Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the (...)
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  27. added 2019-03-21
    Uncertain Foundations.José Ferreirós - 2004 - Metascience 13 (1):79-82.
    Review of M. Giaquinto, The Search for Certainty: A Philosophical Account of Foundations of Mathematics (Osford, 2002).
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  28. added 2019-03-07
    Seeing is Reasoning.Kathryn Mann & James Robert Brown - 2007 - Metascience 16 (1):131-135.
  29. added 2019-03-07
    El infinito y el continuo en el sistema numérico.Eduardo Dib - 1995 - Dissertation, Universidad Nacional de Rio Cuarto
    This monography provides an overview of the conceptual developments that leads from the traditional views of infinite (and their paradoxes) to the contemporary view in which those old paradoxes are solved but new problems arise. Also a particular insight in the problem of continuity is given, followed by applications in theory of computability.
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  30. added 2019-01-10
    Quine and the Incoherence of the Indispensability Argument.Michael J. Shaffer - 2019 - Logos and Episteme 10 (2):207-213.
    It is an under-appreciated fact that Quine's rejection of the analytic/synthetic distinction, when coupled with some other plausible and related views, implies that there are serious difficulties in demarcating empirical theories from pure mathematical theories within the Quinean framework. This is a serious problem because there seems to be a principled difference between the two disciplines that cannot apparently be captured in the orthodox Quienan framework. For the purpose of simplicity let us call this Quine's problem of demarcation. In this (...)
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  31. added 2018-11-01
    Hypatia's Silence. Truth, Justification, and Entitlement.Martin Fischer, Leon Horsten & Carlo Nicolai - manuscript
    Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment.
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  32. added 2018-09-29
    Philosophy of Mathematics.Øystein Linnebo - 2017 - Princeton, NJ: Princeton University Press.
    Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of mathematics. Readers are (...)
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  33. added 2018-09-19
    The Principle of Equivalence as a Criterion of Identity.Ryan Samaroo - forthcoming - Synthese:1-25.
    In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...)
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  34. added 2018-09-04
    Mathematical Shortcomings in a Simulated Universe.Samuel Alexander - 2018 - The Reasoner 12 (9):71-72.
    I present an argument that for any computer-simulated civilization we design, the mathematical knowledge recorded by that civilization has one of two limitations. It is untrustworthy, or it is weaker than our own mathematical knowledge. This is paradoxical because it seems that nothing prevents us from building in all sorts of advantages for the inhabitants of said simulation.
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  35. added 2018-02-17
    On Field’s Epistemological Argument Against Platonism.Ivan Kasa - 2010 - Studia Logica 96 (2):141-147.
    Hartry Field's formulation of an epistemological argument against platonism is only valid if knowledge is constrained by a causal clause. Contrary to recent claims (e.g. in Liggins (2006), Liggins (2010)), Field's argument therefore fails the very same criterion usually taken to discredit Benacerraf's earlier version.
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  36. added 2018-02-17
    Purity as an Ideal of Proof.Michael Detlefsen - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 179-197.
    Various ideals of purity are surveyed and discussed. These include the classical Aristotelian ideal, as well as certain neo-classical and contemporary ideals. The focus is on a type of purity ideal I call topical purity. This is purity which emphasizes a certain symmetry between the conceptual resources used to prove a theorem and those needed for the clarification of its content. The basic idea is that the resources of proof ought ideally to be restricted to those which determine its content.
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  37. added 2018-01-17
    Wittgenstein Und Die Philosophie der Mathematik.Bromand Joachim & Reichert Bastian (eds.) - forthcoming - Mentis Verlag.
    Ludwig Wittgenstein selbst hielt seine Überlegungen zur Mathematik für seinen bedeutendsten Beitrag zur Philosophie. So beabsichtigte er zunächst, dem Thema einen zentralen Teil seiner Philosophischen Untersuchungen zu widmen. Tatsächlich wird kaum irgendwo sonst in Wittgensteins Werk so deutlich, wie radikal die Konsequenzen seines Denkens eigentlich sind. Vermutlich deshalb haben Wittgensteins Bemerkungen zur Mathematik unter all seinen Schriften auch den größten Widerstand provoziert: Seine Bemerkungen zu den Gödel’schen Unvollständigkeitssätzen bezeichnete Gödel selbst als Nonsens, und Alan Turing warf Wittgenstein vor, dass aufgrund (...)
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  38. added 2017-12-19
    The Eleatic and the Indispensabilist.Russell Marcus - 2015 - Theoria : An International Journal for Theory, History and Fundations of Science 30 (3):415-429.
    The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist’s criterion. I show that Colyvan’s argument is not (...)
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  39. added 2017-12-14
    Forms and Roles of Diagrams in Knot Theory.Silvia De Toffoli & Valeria Giardino - 2014 - Erkenntnis 79 (4):829-842.
    The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must (...)
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  40. added 2017-11-20
    Autonomy Platonism and the Indispensability Argument. By Russell Marcus. Lanham, Md.: Lexington Books, 2015. Pp. Xii + 247. [REVIEW]Nicholas Danne - 2017 - Metaphilosophy 48 (4):591-594.
  41. added 2017-09-28
    Mathematics.Larry W. Miller - 1976 - Tulane Studies in Philosophy 25:41-53.
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  42. added 2017-08-23
    ‘Chasing’ the Diagram—the Use of Visualizations in Algebraic Reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  43. added 2017-07-14
    Reductionism and the Universal Calculus.Gopal Sarma - 2016 - Arxiv Preprint Arxiv:1607.06725.
    In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to model its behavior with the symbolic language of mathematics. In this essay, I examine an ambitious 16th and 17th-century intellectual agenda from the perspective of Wigner's question, namely, what historian Paolo Rossi calls "the quest to create a universal language." While many elite thinkers pursued related ideas, the (...)
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  44. added 2017-06-14
    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 EPM as a case study of (...)
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  45. added 2017-06-14
    Mitä Gödelin epätäydellisyysteoreemoista voidaan päätellä filosofiassa?Markus Pantsar - 2011 - Ajatus 68.
    Tutkin tässä artikkelissa Kurt Gödelin epätäydellisyysteoreemojen tulkintoja filosofiassa. Aihepiiri kattaa valtavan määrän eri tulkintoja tekoälystä fysiikkaan ja runouteen asti. Osoitan, että kriittisesti tarkasteltuna kaikki radikaalit epätäydellisyysteoreemojen sovellukset ovat virheellisiä.
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  46. added 2017-03-20
    Introduction to Abstractionism.Philip A. Ebert & Marcus Rossberg - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford: Oxford University Press. pp. 3-33.
  47. added 2017-03-20
    A Framework for Implicit Definitions and the A Priori.Philip A. Ebert - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford: Oxford University Press. pp. 133--160.
  48. added 2017-03-15
    Cold Turkey - Kicking the Habit of Justification (Review of Critical Rationalism: A Restatement and Defence). [REVIEW]Ray Scott Percival - 1994 - New Scientist (1939).
  49. added 2017-03-06
    Referring to Mathematical Objects Via Definite Descriptions.Stefan Buijsman - 2017 - Philosophia Mathematica 25 (1):128-138.
    Linsky and Zalta try to explain how we can refer to mathematical objects by saying that this happens through definite descriptions which may appeal to mathematical theories. I present two issues for their account. First, there is a problem of finding appropriate pre-conditions to reference, which are currently difficult to satisfy. Second, there is a problem of ensuring the stability of the resulting reference. Slight changes in the properties ascribed to a mathematical object can result in a shift of reference (...)
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  50. added 2017-02-15
    Picturability and Mathematical Ideals of Knowledge.Stephen Gaukroger - 2011 - In Desmond M. Clarke & Catherine Wilson (eds.), The Oxford Handbook of Philosophy in Early Modern Europe. Oxford University Press.
    This article examines the role of picturability in mathematical demonstration in the seventeenth and eighteenth centuries and draws attention to the general question of the role that picturability places in cognitive grasp. It suggests that mathematical demonstration is particularly applicable in cognitive grasp it allows the problematic to be identified with some precision. It also discusses infinitesimal analysis and the question of direct proof and evaluates the role of picturability in the analysis of human cognitive capacities.
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