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  1. Logical Akrasia.Frederik J. Andersen - forthcoming - Episteme.
    The aim of this paper is threefold. Firstly, §1 and §2 introduce the novel concept logical akrasia by analogy to epistemic akrasia. If successful, the initial sections will draw attention to an interesting akratic phenomenon which has not received much attention in the literature on akrasia (although it has been discussed by logicians in different terms). Secondly, §3 and §4 present a dilemma related to logical akrasia. From a case involving the consistency of Peano Arithmetic and Gödel’s Second Incompleteness Theorem (...)
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  2. Numerical Cognition and the Epistemology of Arithmetic.Markus Pantsar - 2024 - Cambridge University Press.
    Arithmetic is one of the foundations of our educational systems, but what exactly is it? Numbers are everywhere in our modern societies, but what is our knowledge of numbers really about? This book provides a philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition. It explains how humans have developed arithmetic from humble origins to its modern status as an almost universally possessed knowledge and skill. Central to the account is the realisation that, (...)
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  3. Abstract Objects.David Liggins - 2024 - Cambridge: Cambridge University Press.
    Philosophers often debate the existence of such things as numbers and propositions, and say that if these objects exist, they are abstract. But what does it mean to call something 'abstract'? And do we have good reason to believe in the existence of abstract objects? This Element addresses those questions, putting newcomers to these debates in a position to understand what they concern and what are the most influential considerations at work in this area of metaphysics. It also provides advice (...)
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  4. Rules to Infinity: The Normative Role of Mathematics in Scientific Explanation.Mark Povich - 2024 - Oxford University Press USA.
    [EDIT: This book will be published open access. Production is taking longer than expected but I will post the whole book sometime this summer.] One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science (...)
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  5. Essai sur les principes des sciences mathématiques.Louis Delegue - 1908 - Paris,: Vuibert et Nony.
    Excerpt from Essai sur les Principes des Sciences Mathematiques A Briancon, dans le calme des longues soirees d'hiver, j'ai trouve a ces etudes un interet passionnant. En occupant mes loisirs, elles m'ont permis d'echapper au desoeuvrement et a l'ennui. Aussi, meme si la theorie a laquelle elles m'ont con duit ne devait pas recevoir la consecration officielle du succes, je leur en saurai toujours un gre infini. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. (...)
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  6. Distinctively generic explanations of physical facts.Erik Weber, Kristian González Barman & Thijs De Coninck - 2024 - Synthese 203 (4):1-30.
    We argue that two well-known examples (strawberry distribution and Konigsberg bridges) generally considered genuine cases of distinctively _mathematical_ explanation can also be understood as cases of distinctively _generic_ explanation. The latter answer resemblance questions (e.g., why did neither person A nor B manage to cross all bridges) by appealing to ‘generic task laws’ instead of mathematical necessity (as is done in distinctively mathematical explanations). We submit that distinctively generic explanations derive their explanatory force from their role in ontological unification. Additionally, (...)
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  7. Evolutionary Debunking Arguments: Ethics, Philosophy of Religion, Philosophy of Mathematics, Metaphysics, and Epistemology, edited by Diego E. Machuca.Peter Königs - 2023 - International Journal for the Study of Skepticism 14 (1):73-78.
  8. Defectiveness of formal concepts.Carolin Antos - manuscript
    It is often assumed that concepts from the formal sciences, such as mathematics and logic, have to be treated differently from concepts from non-formal sciences. This is especially relevant in cases of concept defectiveness, as in the empirical sciences defectiveness is an essential component of lager disruptive or transformative processes such as concept change or concept fragmentation. However, it is still unclear what role defectiveness plays for concepts in the formal sciences. On the one hand, a common view sees formal (...)
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  9. Dominique Pradelle.*Être et genèse des idéalités. Un ciel sans éternité.Bruno Leclercq - 2024 - Philosophia Mathematica 32 (1):128-136.
    In Intuition et idéalités: Phénoménologie des objets mathématiques (2020), Dominique Pradelle questioned the nature of mathematical knowledge–the status of math.
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  10. Theorem proving in artificial neural networks: new frontiers in mathematical AI.Markus Pantsar - 2024 - European Journal for Philosophy of Science 14 (1):1-22.
    Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...)
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  11. Why do numbers exist? A psychologist constructivist account.Markus Pantsar - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...)
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  12. La mathématisation comme problème.Hugues Chabot & Sophie Roux (eds.) - 2011 - Paris (France): Édiitons des Archives contemporaines.
    L'histoire des sciences suffit à réfuter la thèse de la mathématisation impossible, selon laquelle la mathématisation procéderait d'un formalisme abstrait manquant les choses mêmes ou la spécificité d'un domaine d'objets. Cette histoire montre en effet qu'on n'a pas cessé de mathématiser des choses dont il avait été longtemps dit qu'elles devaient, étant donné leur nature, éternellement résister à la mathématisation. À la thèse de la mathématisation impossible, il est dès lors tentant d'opposer la thèse de la mathématisation inéluctable, selon laquelle (...)
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  13. A Conventionalist Account of Distinctively Mathematical Explanation.Mark Povich - 2023 - Philosophical Problems in Science 74:171–223.
    Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...)
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  14. Modelling of Generancy A Logical Solution.Deapon Biswas - 2021 - Chisinau, Republic of Moldova: Scholars’ Press. Edited by Mihaela Melnic.
    Modelling of Generancy is a book on Indian philosophy. In this book I have tried to express various problems of philosophy in mathematical language. I think mathematics is a language. Everything can be expressed in this language. With the help of mathematics, the published issues are understandable to all. No one has any objection to this. In the realm of knowledge all terms or words are considered categories. This category is again of three types: substance, quality and action. In another (...)
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  15. How not to analyse number sentences.Robert Schwartzkopff - 2022 - Philosophia Mathematica 30 (2):200 - 222.
    Number and Count Sentences like ‘The number of Martian moons is two’ and ‘Mars has two moons’ give rise to a puzzle. How can they be equivalent if only the truth of Number but not that of Count Sentences requires the existence of numbers? Proponents of Linguistic Deflationism seek to resolve this puzzle by arguing that on their correct linguistic analysis the truth of Number Sentences does not require the existence of numbers. In this paper, I argue that Katharina Felka’s (...)
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  16. The algorithmic Enlightenment.J. B. Shank - 2022 - In Morgan G. Ames & Massimo Mazzotti (eds.), Algorithmic modernity: mechanizing thought and action, 1500-2000. New York, NY: Oxford University Press.
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  17. Mathematical Explanations: An Analysis Via Formal Proofs and Conceptual Complexity.Francesca Poggiolesi - forthcoming - Philosophia Mathematica:nkad023.
    This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as having (...)
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  18. Les fondements psycho-linguistiques des mathématiques.Gerrit Mannoury - 1934 - Bussum,: Pays-Bas, F. G. Kroonder.
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  19. Internalism and the Determinacy of Mathematics.Lavinia Picollo & Daniel Waxman - 2023 - Mind 132 (528):1028-1052.
    A major challenge in the philosophy of mathematics is to explain how mathematical language can pick out unique structures and acquire determinate content. In recent work, Button and Walsh have introduced a view they call ‘internalism’, according to which mathematical content is explained by internal categoricity results formulated and proven in second-order logic. In this paper, we critically examine the internalist response to the challenge and discuss the philosophical significance of internal categoricity results. Surprisingly, as we argue, while internalism arguably (...)
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  20. Are Large Cardinal Axioms Restrictive?Neil Barton - 2023 - Philosophia Mathematica 31 (3):372-407.
    The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of (...)
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  21. A Critique of Yablo’s If-thenism.Bradley Armour-Garb & Frederick Kroon - 2023 - Philosophia Mathematica 31 (3):360-371.
    Using ideas proposed in Aboutness and developed in ‘If-thenism’, Stephen Yablo has tried to improve on classical if-thenism in mathematics, a view initially put forward by Bertrand Russell in his Principles of Mathematics. Yablo’s stated goal is to provide a reading of a sentence like ‘The number of planets is eight’ with a sort of content on which it fails to imply ‘Numbers exist’. After presenting Yablo’s framework, our paper raises a problem with his view that has gone virtually unnoticed (...)
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  22. Justified Epistemic Exclusions in Mathematics.Colin Jakob Rittberg - 2023 - Philosophia Mathematica 31 (3):330-359.
    Who gets to contribute to knowledge production of an epistemic community? Scholarship has focussed on unjustified forms of exclusion. Here I study justified forms of exclusion by investigating the phenomenon of so-called ‘cranks’ in mathematics. I argue that workload-management concerns justify the exclusion of these outsiders from mathematical knowledge-making practices. My discussion reveals three insights. There are reasons other than incorrect mathematical argument that justify exclusions from mathematical practices. There are instances in which mathematicians are justified in rejecting even correct (...)
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  23. Numbers as properties.Melisa Vivanco - 2023 - Synthese 202 (4):1-23.
    Although number sentences are ostensibly simple, familiar, and applicable, the justification for our arithmetical beliefs has been considered mysterious by the philosophical tradition. In this paper, I argue that such a mystery is due to a preconception of two realities, one mathematical and one nonmathematical, which are alien to each other. My proposal shows that the theory of numbers as properties entails a homogeneous domain in which arithmetical and nonmathematical truth occur. As a result, the possibility of arithmetical knowledge is (...)
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  24. The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics.Alain Badiou, Zachary Fraser & Tzuchien Tho - 2007 - Re.press.
    In The Concept of Model Alain Badiou establishes a new logical ’concept of model’. Translated for the first time into English, the work is accompanied by an exclusive interview with Badiou in which he elaborates on the connections between his early and most recent work-for which the concept of model remains seminal.
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  25. Is math real?: how simple questions lead us to mathematics' deepest truths.Eugenia Cheng - 2023 - New York: Basic Books.
    Where does math come from? From a textbook? From rules? From deduction? From logic? Not really, Eugenia Cheng writes in Is Math Real?: it comes from curiosity, from instinctive human curiosity, "from people not being satisfied with answers and always wanting to understand more." And most importantly, she says, "it comes from questions": not from answering them, but from posing them. Nothing could seem more at odds from the way most of us were taught math: a rigid and autocratic model (...)
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  26. Kritik der mathematischen vernunft.J. E. Gerlach - 1922 - Bonn,: F. Cohen.
    Die allgemeine anzahlenlehre.--Der araum und die grössenlehre.--Die gestaltenlehre.--Besondere gestalten.--Gleich und gleich.--Plus, minus und das irgend-i.--Anhang: Zur "gemeinverständlichen" erörterund der relativitätstheorie.
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  27. On the continuum fallacy: is temperature a continuous function?Aditya Jha, Douglas Campbell, Clemency Montelle & Phillip L. Wilson - 2023 - Foundations of Physics 53 (69):1-29.
    It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is fallacious on (...)
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  28. Die heutige Erkenntnislage in der Mathematik.Hermann Weyl - 1926 - Erlangen,: Weltkreis-Verlag.
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  29. Fiktionen in der mathematik.Christian Betsch - 1926 - Stuttgart: Fr. Frommann.
  30. La pensée et la quantité.Albert Spaier - 1927 - Paris,: F. Alcan.
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  31. Towards a critical epistemology of mathematics.David Kollosche - 2023 - Prometeica - Revista De Filosofía Y Ciencias 27:825-833.
    This essay addresses a critical epistemology of mathematics as an investigation into the epistemic limitations of mathematical thinking. After arguing for the relevance of a critical epistemology of mathematics, I discuss assumptions underlying standard arithmetic and assumptions underlying standard logic as examples for such epistemic limitations of mathematical thinking. Looking into the work of philosophically inte­res­ted scholars in mathematics education such as Alan Bishop and Ole Skovsmose, I discuss some early insights for a critical epistemology of mathematics. I conclude that (...)
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  32. De l'ordre et du hasard.Jean de La Harpe - 1936 - Neuchâtel,: Secrétariat de l'Université.
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  33. Mario Bunge's Philosophy of Mathematics: An Appraisal.Marquis Jean-Pierre - 2012 - Science & Education 21:1567-1594.
    In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.
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  34. Mathematik als Begriff und Gestalt.Max Steck - 1942 - Halle (Saale): M. Niemeyer.
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  35. Solutions to the Knower Paradox in the Light of Haack’s Criteria.Mirjam de Vos, Rineke Verbrugge & Barteld Kooi - 2023 - Journal of Philosophical Logic 52 (4):1101-1132.
    The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on (...)
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  36. Wiskunde: een deductieve wetenschap.E. J. E. Huffer - 1946 - Roermond: J. J. Romen & Zonen.
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  37. On Radical Enactivist Accounts of Arithmetical Cognition.Markus Pantsar - 2022 - Ergo: An Open Access Journal of Philosophy 9.
    Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...)
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  38. L'imagination du réel.Rolin Wavre - 1948 - Neuchâtel,: Baconnière.
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  39. Sobre la naturaleza del razonamiento matemático.Th Skolem - 1952 - Madrid,: [Instituto de Matemáticas "Jorge Juan"].
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  40. La recherche scientifique en mathématiques.Paul Antonin Montel - 1953 - [Alençon,: Impr. alençonnaise.
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  41. Vom Denken in Begriffen.Alexander Israel Wittenberg - 1957 - Basel,: Birkhäuser.
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  42. Les limitations internes des formalismes.Jean Ladrière - 1957 - Louvain,: E. Nauwelaerts.
  43. Structure et objet de l'analyse mathématique.Eloi Lefebvre - 1958 - Paris,: Gauthier-Villars.
  44. Sur la clarté des démonstrations mathématiques.François Rostand - 1962 - Paris,: J. Vrin.
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  45. Wissenschaftliche Grundlagen des Rechnens.Hans Schubart - 1966 - Frankfurt a.: M., Hamburg, Salle.
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  46. Teoría de la investigación matemática.Darío Maravall Casesnoves - 1966 - Madrid,: Editorial Dossat.
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  47. Matthew Handelman.* The Mathematical Imagination: On the Origins and Promise of Critical Theory.Mirna Džamonja - 2023 - Philosophia Mathematica 31 (2):283-285.
    This book, published in 2019 as an open-access edition of the Fordham University Press, attracts by its title. Imagination, as we mathematicians know only too w.
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  48. Szkice z epistemologii matematyki.Jarosław Ładosz - 1968 - Warszawa]: Książka i Wiedza.
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  49. Das Wissenschaftsideal der Mathematiker.Pierre Boutroux - 1927 - Wiesbaden,: M. Sändig. Edited by Hilda Geiringer.
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  50. Gnoseologicheskie problemy formalizat︠s︡ii.D. P. Gorskiĭ (ed.) - 1969 - Minsk,: ["Nauka i tekhnika"].
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1 — 50 / 1803