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  1. added 2019-08-14
    Mathematical and Moral Disagreement.Silvia Jonas - forthcoming - Philosophical Quarterly.
    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 mathemat- ical and moral disagreement is not as straightforward as those arguments present it. In particular, I (...)
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  2. 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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  3. 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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  4. 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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  5. added 2019-04-18
    The Ethics-Mathematics Analogy.Justin Clarke-Doane - forthcoming - Philosophy Compass.
    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 (moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind and languages. I (...)
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  6. added 2019-03-30
    Evidence, Proofs, and Derivations.Andrew Aberdein - forthcoming - ZDM 51 (4).
    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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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).
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  16. added 2017-02-12
    Logicism, Interpretability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Review of Symbolic Logic 7 (1):84-119.
    A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of representation (...)
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  17. added 2017-01-02
    Whitehead's Unique Approach to the Topic of Consciousness.Anderson Weekes - 2010 - In Michel Weber & Anderson Weekes (eds.), Process Approaches to Consciousness in Psychology, Neuroscience, and Philosophy of Mind. Albany: State University of New York Press. pp. 137-172.
    Conventional approaches to consciousness assume that our current science tells us within tolerable limits what physical nature is. Because nature so understood cannot explain consciousness as we seem to experience it ourselves, explaining consciousness becomes a problem. One solution is to rethink what consciousness is so that it becomes the sort of thing our current natural science could in principle explain. Whitehead takes the opposite approach, using the existence of consciousness as a clue to what nature must be if it (...)
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  18. added 2016-12-15
    Review of The Art of the Infinite by R. Kaplan, E. Kaplan 324p(2003).Michael Starks - 2016 - In Suicidal Utopian Delusions in the 21st Century: Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2017 2nd Edition Feb 2018. Michael Starks. pp. 619.
    This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don´t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don´t know any and don´t (...)
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  19. added 2016-11-04
    Fictionalism and Mathematical Objectivity.Iulian D. Toader - 2012 - In Metaphysics and Science. Festschrift for Professor Ilie Pârvu. University of Bucharest Press. pp. 137-158.
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  20. added 2016-06-28
    On the History of Differentiable Manifolds.Giuseppe Iurato - 2012 - International Mathematical Forum 7 (10):477-514.
    We discuss central aspects of history of the concept of an affine differentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.
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  21. added 2016-06-02
    Revisiting the Efficacy of Constructivism in Mathematics Education.Mdutshekelwa Ndlovu - 2013 - Philosophy of Mathematics Education Journal 27 (April):1-13.
    The purpose of this paper is to critically analyse and discuss the views of constructivism, on the teaching and learning of mathematics. I provide a background to the learning of mathematics as constructing and reconstructing knowledge in the form of new conceptual networks; the nature, role and possibilities of constructivism as a learning theoretical framework in Mathematics Education. I look at the major criticisms and conclude that it passes the test of a learning theoretical framework but there is still a (...)
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  22. added 2016-01-08
    Debunking Arguments: Mathematics, Logic, and Modal Security.Justin Clarke-Doane - forthcoming - In Robert Richards and Michael Ruse (ed.), The Cambridge Handbook of Evolutionary Ethics. Cambridge University Press.
    I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...)
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  23. added 2015-12-07
    The Role of Virtual Work in Levi-Civita’s Parallel Transport.Giuseppe Iurato & Giuseppe Ruta - 2015 - Proceedings of Applied Mathematics and Mechanics 15:705-706.
    According to current history of science, Levi-Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi-Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport.
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  24. added 2015-09-08
    Formalizing Darwinism, Naturalizing Mathematics.Fabio Sterpetti - 2015 - Paradigmi. Rivista di Critica Filosofica 33 (2):133-160.
    In the last decades two different and apparently unrelated lines of research have increasingly connected mathematics and evolutionism. Indeed, on the one hand different attempts to formalize darwinism have been made, while, on the other hand, different attempts to naturalize logic and mathematics have been put forward. Those researches may appear either to be completely distinct or at least in some way convergent. They may in fact both be seen as supporting a naturalistic stance. Evolutionism is indeed crucial for a (...)
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  25. added 2015-08-28
    Against Mathematical Convenientism.Seungbae Park - 2016 - Axiomathes 26 (2):115-122.
    Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘ mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that it demolishes the Quine-Putnam (...)
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  26. added 2015-08-25
    Are Evolutionary Debunking Arguments Really Self-Defeating?Fabio Sterpetti - 2015 - Philosophia 43 (3):877-889.
    Evolutionary Debunking Arguments are defined as arguments that appeal to the evolutionary genealogy of our beliefs to undermine their justification. Recently, Helen De Cruz and her co-authors supported the view that EDAs are self-defeating: if EDAs claim that human arguments are not justified, because the evolutionary origin of the beliefs which figure in such arguments undermines those beliefs, and EDAs themselves are human arguments, then EDAs are not justified, and we should not accept their conclusions about the fact that human (...)
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  27. added 2015-04-22
    Mathematics as Make-Believe: A Constructive Empiricist Account.Sarah Elizabeth Hoffman - 1999 - Dissertation, University of Alberta (Canada)
    Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered and rejected. Constructive empiricism (...)
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  28. added 2014-10-10
    Evolutionary Genetics and Cultural Traits in a 'Body of Theory' Perspective.Emanuele Serrelli - 2016 - In Fabrizio Panebianco & Emanuele Serrelli (eds.), Understanding cultural traits. A multidisciplinary perspective on cultural diversity. Springer. pp. 179-199.
    The chapter explains why evolutionary genetics – a mathematical body of theory developed since the 1910s – eventually got to deal with culture: the frequency dynamics of genes like “the lactase gene” in populations cannot be correctly modeled without including social transmission. While the body of theory requires specific justifications, for example meticulous legitimations of describing culture in terms of traits, the body of theory is an immensely valuable scientific instrument, not only for its modeling power but also for the (...)
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  29. added 2013-05-29
    Modal-Epistemic Arithmetic and the Problem of Quantifying In.Jan Heylen - 2013 - Synthese 190 (1):89-111.
    The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of logical (...)
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  30. added 2013-03-18
    Simulation informatique et pluriformalisation des objets composites.Franck Varenne - 2009 - Philosophia Scientiae 13 (1):135-154.
    A recent evolution of computer simulations has led to the emergence of complex computer simulations. In particular, the need to formalize composite objects (those objects that are composed of other objects) has led to what the author suggests to call pluriformalizations, i.e. formalizations that are based on distinct sub-models which are expressed in a variety of heterogeneous symbolic languages. With the help of four case-studies, he shows that such pluriformalizations enable to formalize distinctly but simultaneously either different aspects or different (...)
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  31. added 2012-12-12
    Mathematical Symbols as Epistemic Actions.De Cruz Helen & De Smedt Johan - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...)
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  32. added 2012-11-03
    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 of Peano’s (...)
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  33. added 2012-10-23
    Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism.Iulian D. Toader - 2011 - Dissertation, University of Notre Dame
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  34. added 2012-10-23
    Experimental Mathematics in the 1990s: A Second Loss of Certainty?Henrik Kragh Sørensen - 2010 - Oberwolfach Reports (12):601--604.
    In this paper, I describe some aspects of the phenomenon of "experimental mathematics" in order to discuss whether it constitutes a subdiscipline or a particular style of mathematics. My conclusion is that neither of these notions accurately capture the complex culture of experimental mathematics.
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  35. added 2012-10-10
    Descriptions and Unknowability.Jan Heylen - 2010 - Analysis 70 (1):50-52.
    In a recent paper Horsten embarked on a journey along the limits of the domain of the unknowable. Rather than knowability simpliciter, he considered a priori knowability, and by the latter he meant absolute provability, i.e. provability that is not relativized to a formal system. He presented an argument for the conclusion that it is not absolutely provable that there is a natural number of which it is true but absolutely unprovable that it has a certain property. The argument depends (...)
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  36. added 2011-04-11
    The Vicissitudes of Mathematical Reason in the 20th Century. [REVIEW]Thomas Mormann - 2012 - Metascience 21 (2):295-300.
    The vicissitudes of mathematical reason in the 20th century Content Type Journal Article Pages 1-6 DOI 10.1007/s11016-011-9556-y Authors Thomas Mormann, Department of Logic and Philosophy of Science, University of the Basque Country UPV/EPU, Donostia-San Sebastian, Spain, Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  37. added 2010-09-02
    Matemáticas y Platonismo(S).J. Ferreiros - 1999 - Gaceta de la Real Sociedad Matemática Española 2 (446):473.
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  38. added 2010-05-07
    The Epistemology of Geometry I: The Problem of Exactness.Anne Newstead & Franklin James - 2010 - Proceedings of the Australasian Society for Cognitive Science 2009.
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...)
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