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  1. Mathematical Gettier Cases and Their Implications.Neil Barton - manuscript
    Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...)
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  2. A Two-Dimensionalist Solution to the Access Problem.Hasen Khudairi - manuscript
    I argue that the two-dimensional intensions of epistemic two-dimensional semantics provide a compelling solution to the access problem.
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  3. Making Mathematics Visible: Mathematical Knowledge and How It Differs From Mathematical Understanding.Anne Newstead - manuscript
    This is a grant proposal for a research project conceived and written as a Research Associate at UNSW in 2011. I have plans to spin it into an article.
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  4. A Theory of Implicit Commitment for Mathematical Theories.Mateusz Łełyk & Carlo Nicolai - manuscript
    The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains so far an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still (...)
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  5. 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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  6. Bishop's Mathematics: A Philosophical Perspective.Laura Crosilla - forthcoming - In Handbook of Bishop's Mathematics. CUP.
    Errett Bishop's work in constructive mathematics is overwhelmingly regarded as a turning point for mathematics based on intuitionistic logic. It brought new life to this form of mathematics and prompted the development of new areas of research that witness today's depth and breadth of constructive mathematics. Surprisingly, notwithstanding the extensive mathematical progress since the publication in 1967 of Errett Bishop's Foundations of Constructive Analysis, there has been no corresponding advances in the philosophy of constructive mathematics Bishop style. The aim of (...)
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  7. What is Mathematical Rigor?John Burgess & Silvia De Toffoli - 2022 - Aphex 25:1-17.
    Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.
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  8. How Does Hands-On Making Attitude Predict Epistemic Curiosity and Science, Technology, Engineering, and Mathematics Career Interests? Evidence From an International Exhibition of Young Inventors.Yuting Cui, Jon-Chao Hong, Chi-Ruei Tsai & Jian-Hong Ye - 2022 - Frontiers in Psychology 13:859179.
    Whether the hands-on experience of creating inventions can promote Students’ interest in pursuing a science, technology, engineering, and mathematics (STEM) career has not been extensively studied. In a quantitative study, we drew on the attitude-behavior-outcome framework to explore the correlates between hands-on making attitude, epistemic curiosities, and career interest. This study targeted students who joined the selection competition for participating in the International Exhibition of Young Inventors (IEYI) in Taiwan. The objective of the invention exhibition is to encourage young students (...)
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  9. Dialogue Types, Argumentation Schemes, and Mathematical Practice: Douglas Walton and Mathematics.Andrew Aberdein - 2021 - Journal of Applied Logics 8 (1):159-182.
    Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.
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  10. Critique of Impure Reason: Horizons of Possibility and Meaning.Steven James Bartlett - 2021 - Salem, USA: Studies in Theory and Behavior.
    This is a second Philpapers record for this book which links only to HAL's downloadable copies of the work. Please refer to the main Philpapers entry for this book which can be found by searching under the book's title. ●●●●● PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make (...)
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  11. Wittgenstein, Peirce, and Paradoxes of Mathematical Proof.Sergiy Koshkin - 2021 - Analytic Philosophy 62 (3):252-274.
    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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  12. 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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  13. 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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  14. 私は奇妙なループです」のレビュー(I am a Strange Loop) by Douglas Hofstadter (2007) (レビュー改訂2019).Michael Richard Starks - 2020 - In 地獄へようこそ 赤ちゃん、気候変動、ビットコイン、カルテル、中国、民主主義、多様性、ディスジェニックス、平等、ハッカー、人権、イスラム教、自由主義、繁栄、ウェブ、カオス、飢餓、病気、暴力、人工知能、戦争. Las Vegas, NV, USA: Reality Press. pp. 102-118.
    ホフスタッター牧師による原理主義自然主義教会からの最新の説教。彼のはるかに有名な(または容赦ない哲学的誤りで悪名高い)作品ゴーデル、エッシャー、バッハのように、それは表面的な妥当性を持っていますが、こ れが哲学的なものと実際の科学的問題を混ぜ合わせた横行するサイエンティズムであることを理解すれば(つまり、唯一の本当の問題は、私たちがプレイすべき言語ゲームです)、その後、ほとんどすべての関心が消えます 。進化心理学とヴィトゲンシュタインの仕事に基づく分析のフレームワークを提供しています(最近の著作で更新されて以来)。 現代の2つのシス・エムスの見解から人間の行動のための包括的な最新の枠組みを望む人は、私の著書「ルートヴィヒ・ヴィトゲンシュタインとジョン・サールの第2回(2019)における哲学、心理学、ミンと言語の論 理的構造」を参照することができます。私の著作の多くにご興味がある人は、運命の惑星における「話す猿--哲学、心理学、科学、宗教、政治―記事とレビュー2006-2019 第3回(2019)」と21世紀4日(2019年)の自殺ユートピア妄想st Century 4th ed (2019)などを見ることができます .
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  15. 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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  16. 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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  17. ¿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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  18. 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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  19. 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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  20. 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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  21. 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.
    Comprehensive resource for indispensability research.
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  22. ‘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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  23. 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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  24. 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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  25. 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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  26. 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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  27. 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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  28. 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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  29. 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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  30. 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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  31. 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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  32. 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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  33. Mathematical Symbols as Epistemic Actions.Johan De Smedt & Helen De Cruz - 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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  34. 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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  35. 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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  36. 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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  37. 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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  38. Fictionalism and Mathematical Objectivity.Iulian D. Toader - 2012 - In Metaphysics and Science. University of Bucharest Press. pp. 137-158.
    This paper, written in Romanian, compares fictionalism, nominalism, and neo-Meinongianism as responses to the problem of objectivity in mathematics, and then motivates a fictionalist view of objectivity as invariance.
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  39. 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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  40. 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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  41. The Paradox of Infinite Given Magnitude: Why Kantian Epistemology Needs Metaphysical Space.Lydia Patton - 2011 - Kant Studien 102 (3):273-289.
    Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately oriented, constructed (...)
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  42. Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism.Iulian D. Toader - 2011 - Dissertation, University of Notre Dame
    A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected.
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  43. 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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  44. 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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  45. The Reliability Challenge and the Epistemology of Logic.Joshua Schechter - 2010 - Philosophical Perspectives 24 (1):437-464.
    We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...)
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  46. 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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  47. 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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  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 of Peano’s (...)
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  49. What Does It Mean That PRIMES is in P: Popularization and Distortion Revisited.Boaz Miller - 2009 - Social Studies of Science 39 (2):257-288.
    In August 2002, three Indian computer scientists published a paper, ‘PRIMES is in P’, online. It presents a ‘deterministic algorithm’ which determines in ‘polynomial time’ if a given number is a prime number. The story was quickly picked up by the general press, and by this means spread through the scientific community of complexity theorists, where it was hailed as a major theoretical breakthrough. This is although scientists regarded the media reports as vulgar popularizations. When the paper was published in (...)
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  50. 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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