Epistemology of Mathematics

Edited by Alan Baker (Swarthmore College)
Assistant editor: Sam Roberts (University of Sheffield)
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  1. Notes and remarks on information-seeking.Besim Karakadılar - manuscript
    By asking questions and seeking information with an eye on the logical implications of the answers of one's questions, one can become a lifelong seeker. However, one cannot become so, if one does not pay enough attention to the boundaries of logical inquiry. It holds true in all types of information-seeking that some lines of thought may turn out to be pointless, unnecessary, or at most a waste of time. Some lines of thought, on the other hand, may turn out (...)
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  2. Knowledge and the Philosophy of Number. [REVIEW]Richard Lawrence - 2022 - History and Philosophy of Logic 43 (4):404-406.
    Hossack’s project in this book is to provide a new foundation for the philosophy of number inspired by the traditional idea that numbers are magnitudes.
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  3. A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$ ε -operator.Nicola Bonatti - 2022 - Synthese 200 (5):1-26.
    Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first (...)
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  4. The Quasi-Empirical Epistemology of Mathematics.Ellen Yunjie Shi - 2022 - Kriterion – Journal of Philosophy 36 (2):207-226.
    This paper clarifies and discusses Imre Lakatos’ claim that mathematics is quasi-empirical in one of his less-discussed papers A Renaissance of Empiricism in the Recent Philosophy of Mathematics. I argue that Lakatos’ motivation for classifying mathematics as a quasi-empirical theory is epistemological; what can be called the quasi-empirical epistemology of mathematics is not correct; analysing where the quasi-empirical epistemology of mathematics goes wrong will bring to light reasons to endorse a pluralist view of mathematics.
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  5. Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist.Fabio Sterpetti - 2021 - Foundations of Science 27 (3):1073-1105.
    This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...)
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  6. Grundlagen §64: An Alternative Strategy to Account for Second-Order Abstraction.Vincenzo Ciccarelli - 2022 - Principia: An International Journal of Epistemology 26 (2):183-204.
    A famous passage in Section 64 of Frege’s Grundlagen may be seen as a justification for the truth of abstraction principles. The justification is grounded in the procedureofcontent recarvingwhich Frege describes in the passage. In this paper I argue that Frege’sprocedure of content recarving while possibly correct in the case of first-order equivalencerelations is insufficient to grant the truth of second-order abstractions. Moreover, I propose apossible way of justifying second-order abstractions by referring to the operation of contentrecarving and I show (...)
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  7. The Justificatory Force of Experiences: From a Phenomenological Epistemology to the Foundations of Mathematics and Physics.Philipp Berghofer - 2022 - Springer (Synthese Library).
  8. Moral dynamics: Grounding moral judgment in intuitive physics and intuitive psychology.Felix A. Sosa, Tomer Ullman, Joshua B. Tenenbaum, Samuel J. Gershman & Tobias Gerstenberg - 2021 - Cognition 217 (C):104890.
  9. Neutrality and Force in Field's Epistemological Objection to Platonism.Ylwa Sjölin Wirling - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...)
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  10. Truth, Reflection, and Commitment.Leon Horsten & Matteo Zicchetti - 2021 - In Johannes Stern & Carlo Nicolai (eds.), Modes of Truth: The Unified Approach to Truth, Modality, and Paradox. pp. 69-87.
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  11. Human Thought, Mathematics, and Physical Discovery.Gila Sher - forthcoming - In Yemima Ben Menahem & Carl Posy (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner. Berlin: Springer Nature.
    In this paper I discuss Mark Steiner's view of the contribution of mathematics to physics and take up some of the questions it raises. In particular, I take up the question of discovery and explore two aspects of this question ‒ a metaphysical aspect and a related epistemic aspect. The metaphysical aspect concerns the formal structure of the physical world. Does the physical world have mathematical or formal features or constituents, and what is the nature of these constituents? The related (...)
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  12. Quine vs. Quine: Abstract Knowledge and Ontology.Gila Sher - 2020 - In Frederique Janssen-Lauret (ed.), Quine, Structure, and Ontology. Oxford: Oxford. pp. 230-252.
    How does Quine fare in the first decades of the twenty-first century? In this paper I examine a cluster of Quinean theses that, I believe, are especially fruitful in meeting some of the current challenges of epistemology and ontology. These theses offer an alternative to the traditional bifurcations of truth and knowledge into factual and conceptual-pragmatic-conventional, the traditional conception of a foundation for knowledge, and traditional realism. To make the most of Quine’s ideas, however, we have to take an active (...)
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  13. The Quasi-Empirical Epistemology of Mathematics.Ellen Shi - forthcoming - Kriterion - Journal of Philosophy.
    This paper clarifies and discusses Imre Lakatos’ claim that mathematics is quasi-empirical in one of his less-discussed papers A Renaissance of Empiricism in the Recent Philosophy of Mathematics. I argue that (1) Lakatos’ motivation for classifying mathematics as a quasi-empirical theory is epistemological; (2) what can be called the quasi-empirical epistemology of mathematics is not correct; (3) analysing where the quasi-empirical epistemology of mathematics goes wrong will bring to light reasons to endorse a pluralist view of mathematics.
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  14. Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf.P. Dybjer, Sten Lindström, Erik Palmgren & G. Sundholm (eds.) - 2012 - Dordrecht, Netherland: Springer.
    This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...)
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  15. Du Châtelet’s Philosophy of Mathematics.Aaron Wells - forthcoming - In The Bloomsbury Companion to Du Châtelet. Bloomsbury.
    I begin by outlining Du Châtelet’s ontology of mathematical objects: she is an idealist, and mathematical objects are fictions dependent on acts of abstraction. Next, I consider how this idealism can be reconciled with her endorsement of necessary truths in mathematics, which are grounded in essences that we do not create. Finally, I discuss how mathematics and physics relate within Du Châtelet’s idealism. Because the primary objects of physics are partly grounded in the same kinds of acts as yield mathematical (...)
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  16. Grasping Mathematical Reality.Catherine Legg - 2015 - CUADERNOS DE SISTEMÁTICA PEIRCEANA 7.
    This paper presents a Peircean take on Wittgenstein's famous rule-following problem as it pertains to 'knowing how to go on in mathematics'. I argue that McDowell's advice that the philosophical picture of 'rules as rails' must be abandoned is not sufficient on its own to fully appreciate mathematics' unique blend of creativity and rigor. Rather, we need to understand how Peirce counterposes to the brute compulsion of 'Secondness', both the spontaneity of 'Firstness' and also the rational intelligibility of 'Thirdness'. This (...)
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  17. "Cała matematyka to właściwie geometria". Poglądy Gottloba Fregego na podstawy matematyki po upadku logicyzmu.Krystian Bogucki - 2019 - Hybris. Internetowy Magazyn Filozoficzny 44:1 - 20.
    Gottlob Frege abandoned his logicist program after Bertrand Russell had discovered that some assumptions of Frege’s system lead to contradiction (so called Russell’s paradox). Nevertheless, he proposed a new attempt for the foundations of mathematics in two last years of his life. According to this new program, the whole of mathematics is based on the geometrical source of knowledge. By the geometrical source of cognition Frege meant intuition which is the source of an infinite number of objects in arithmetic. In (...)
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  18. Building blocks for a cognitive science-led epistemology of arithmetic.Stefan Buijsman - 2021 - Philosophical Studies 179 (5):1-18.
    In recent years philosophers have used results from cognitive science to formulate epistemologies of arithmetic :5–18, 2001). Such epistemologies have, however, been criticised, e.g. by Azzouni, for interpreting the capacities found by cognitive science in an overly numerical way. I offer an alternative framework for the way these psychological processes can be combined, forming the basis for an epistemology for arithmetic. The resulting framework avoids assigning numerical content to the Approximate Number System and Object Tracking System, two systems that have (...)
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  19. Intersubjective Propositional Justification.Silvia De Toffoli - forthcoming - In Luis R. G. Oliveira & Paul Silva Jr (eds.), Propositional and Doxastic Justification. Routledge.
    The distinction between propositional and doxastic justification is well-known among epistemologists. Propositional justification is often conceived as fundamental and characterized in an entirely apsychological way. In this chapter, I focus on beliefs based on deductive arguments. I argue that such an apsychological notion of propositional justification can hardly be reconciled with the idea that justification is a central component of knowledge. In order to propose an alternative notion, I start with the analysis of doxastic justification. I then offer a notion (...)
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  20. Aritmética e conhecimento simbólico: notas sobre o Tractatus Logico-Philosophicus e o ensino de filosofia da matemática.Gisele Dalva Secco - 2020 - Perspectiva Filosófica 47 (2):120-149.
    Departing from and closing with reflections on issues regarding teaching practices of philosophy of mathematics, I propose a comparison between the main features of the Leibnizian notion of symbolic knowledge and some passages from the Tractatus on arithmetic. I argue that this reading allows (i) to shed a new light on the specificities of the Tractarian definition of number, compared to those of Frege and Russell; (ii) to highlight the understanding of the nature of mathematical knowledge as symbolic or formal (...)
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  21. A Neglected Chapter in the History of Philosophy of Mathematical Thought Experiments: Insights from Jean Piaget’s Reception of Edmond Goblot.Marco Buzzoni - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):282-304.
    Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot’s account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today’s debate: (1) the relationship between empirical and (...)
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  22. Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups.Joshua Habgood-Coote & Fenner Stanley Tanswell - forthcoming - Episteme.
    In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...)
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  23. A general framework for a Second Philosophy analysis of set-theoretic methodology.Carolin Antos & Deborah Kant - manuscript
    Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...)
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  24. Mathematical Selves and the Shaping of Mathematical Modernism: Conflicting Epistemic Ideals in the Emergence of Enumerative Geometry.Nicolas Michel - 2021 - Isis 112 (1):68-92.
  25. Foucault, Deleuze, and Nietzsche.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  26. Hiromi's Voice (Multi-Channel Mathematics).Ilexa Yardley - 2021 - Https://Medium.Com/Musical-Notes/.
    Using Hiromi’s ‘Voice’ to understand ‘physics.’ (The underlying relationship between mind and music.) (The relationship between mind and mathematics.) The relationship between the arithmetic numbers 'two' and 'three.' The relationship between light (an infinite line) and sound (an infinite circle) (where it is impossible to have one without the other).
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  27. Bootstrapping of integer concepts: the stronger deviant-interpretation challenge.Markus Pantsar - 2021 - Synthese 199 (3-4):5791-5814.
    Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...)
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  28. Universal Circularity.Ilexa Yardley - 2019 - Intelligent Design Center: Intelligent Design Center.
    Universal Circularity answers the most important question on every person’s mind: what is the core dynamic in Nature? It’s a short, easily digestible read that anyone can understand, targeted to the intellectually curious of any age, background, and-or cultural group. Why will people read it? It untangles, finally, the relationship between religion and science (biology and technology) (philosophy and physics) at the perfect time in a digital age, when we all need a shortcut to work through the cognitive dissonance called (...)
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  29. A Neglected Chapter in the History of Philosophy of Mathematical Thought Experiments: Insights from Jean Piaget’s Reception of Edmond Goblot.Marco Buzzoni - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):282-304.
    Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot’s account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today’s debate: (1) the relationship between empirical and (...)
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  30. Modal Cognitivism and Modal Expressivism.Hasen Khudairi - manuscript
    This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual engineering for intensions and (...)
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  31. Assessing the “Empirical Philosophy of Mathematics”.Markus Pantsar - 2015 - Discipline filosofiche. 25 (1):111-130.
    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” 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 sociological (...)
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  32. Rigour and Proof.Oliver Tatton-Brown - forthcoming - Review of Symbolic Logic:1-29.
    This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to. The account is used to address two current questions in the literature: that of how mathematicians are so good at resolving disputes about validity, and that of whether rigorous proofs are necessarily formalizable.
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  33. Science of Knowing: Mathematics.Venkata Rayudu Posina - manuscript
    The 'Science of Knowing: Mathematics' textbook is the first book to put forward and substantiate the thesis that the mathematical understanding of mathematics, as exemplified in F. William Lawvere's Functorial Semantics, constitutes the science of knowing i.e. cognitive science.
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  34. Set-theoretic pluralism and the Benacerraf problem.Justin Clarke-Doane - 2020 - Philosophical Studies 177 (7):2013-2030.
    Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper is (...)
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  35. Ce este matematica: Ghidul şcolar al înţelegerii conceptuale a matematicii.Catalin Barboianu - 2020 - Targu Jiu: PhilScience Press.
    Aceasta nu este o carte de matematică, ci una despre matematică, care se adresează elevului sau studentului, dar şi dascălului său, cu un scop cât se poate de practic, anume acela de a iniţia şi netezi calea către înţelegerea completă a matematicii predate în şcoală. Tradiţia predării matematicii într-o abordare preponderent procedural-formală a avut ca efect o viziune deformată a elevilor asupra matematicii, ca fiind ceva strict formal, instrumental şi calculatoriu. Pierzând contactul cu baza conceptuală a matematicii, elevii dezvoltă pe (...)
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  36. How Can Mathematical Objects Be Real but Mind-Dependent?Hazhir Roshangar - forthcoming - In Jakub Mácha & Herbert Hrachovec (eds.), Platonism: Proceedings of the 43rd International Ludwig Wittgenstein Symposium. De Gruyter.
    Taking mathematics as a language based on empirical experience, I argue for an account of mathematics in which its objects are abstracta that describe and communicate the structure of reality based on some of our ancestral interactions with their environment. I argue that mathematics as a language is mostly invented. Nonetheless, in being a general description of reality it cannot be said that it is fictional; and as an intersubjective reality, mathematical objects can exist independent of any one person’s mind.
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  37. Book Review of “Numbers and the Making of Us: Counting and the Course of Human Cultures” by Caleb Everett.Paula Quinon & Markus Pantsar - 2018 - Journal of Numerical Cognition 4 (2).
  38. The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - Metafizika 2 (8):p. 87-100.
    The concept of ‘ideas’ plays central role in philosophy. The genesis of the idea of continuity and its essential role in intellectual history have been analyzed in this research. The main question of this research is how the idea of continuity came to the human cognitive system. In this context, we analyzed the epistemological function of this idea. In intellectual history, the idea of continuity was first introduced by Leibniz. After him, this idea, as a paradigm, formed the base of (...)
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  39. Francesca Biagioli: Space, Number, and Geometry from Helmholtz to Cassirer: Springer, Dordrecht, 2016, 239 pp, $109.99 , ISBN: 978-3-319-31777-9. [REVIEW]Lydia Patton - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (2):311-315.
    Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. The book provides a bracing and painstakingly researched re-appreciation of the work of Hermann von Helmholtz and Ernst Cassirer, and of their place in the tradition, and is worth study for that alone. The contributions of the book go far beyond that, however. (...)
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  40. Mathematical cognition and enculturation: introduction to the Synthese special issue.Markus Pantsar - 2020 - Synthese 197 (9):3647-3655.
  41. Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  42. Forms of Structuralism: Bourbaki and the Philosophers.Jean-Pierre Marquis - 2020 - Structures Meres, Semantics, Mathematics, and Cognitive Science.
    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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  43. What is Field's Epistemological Objection to Platonism?Ylwa Sjölin Wirling - 2019 - In Robin Stenwall & Tobias Hansson Wahlberg (eds.), Maurinian Truths : Essays in Honour of Anna-Sofia Maurin on her 50th Birthday. pp. 123-133.
    This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...)
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  44. Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.) - 2019 - Springer Verlag.
    This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, (...)
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  45. Mathesis Universalis, Computability and Proof.Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...)
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  46. On the Philosophical Significance of Frege’s Constraint.Andrea Sereni - 2019 - Philosophia Mathematica 27 (2):244–275.
    Foundational projects disagree on whether pure and applied mathematics should be explained together. Proponents of unified accounts like neologicists defend Frege’s Constraint (FC), a principle demanding that an explanation of applicability be provided by mathematical definitions. I reconsider the philosophical import of FC, arguing that usual conceptions are biased by ontological assumptions. I explore more reasonable weaker variants — Moderate and Modest FC — arguing against common opinion that ante rem structuralism (and other) views can meet them. I dispel doubts (...)
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  47. Naturalizing Logico-Mathematical Knowledge: Approaches from Philosophy, Psychology and Cognitive Science.Markus Pantsar - 2019 - Philosophical Quarterly 69 (275):432-435.
    Naturalizing Logico-Mathematical Knowledge: Approaches from Philosophy, Psychology and Cognitive Science. Edited by Bangu Sorin.
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  48. Mathematical Knowledge and Naturalism.Fabio Sterpetti - 2019 - Philosophia 47 (1):225-247.
    How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize (...)
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  49. Mathematician's call for interdisciplinary research effort.Catalin Barboianu - 2013 - International Gambling Studies 13 (3):430-433.
    The article addresses the necessity of increasing the role of mathematics in the psychological intervention in problem gambling, including cognitive therapies. It also calls for interdisciplinary research with the direct contribution of mathematics. The current contributions and limitations of the role of mathematics are analysed with an eye toward the professional profiles of the researchers. An enhanced collaboration between these two disciplines is suggested and predicted.
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  50. Circularities In The Contemporary Philosophical Accounts Of The Applicability Of Mathematics In The Physical Universe.Catalin Barboianu - 2015 - Revista de Filosofie 61 (5):517-542.
    Contemporary philosophical accounts of the applicability of mathematics in physical sciences and the empirical world are based on formalized relations between the mathematical structures and the physical systems they are supposed to represent within the models. Such relations were constructed both to ensure an adequate representation and to allow a justification of the validity of the mathematical models as means of scientific inference. This article puts in evidence the various circularities (logical, epistemic, and of definition) that are present in these (...)
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