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  1. Ancient Greek Mathematical Proofs and Metareasoning.Mario Bacelar Valente - 2024 - In Maria Zack (ed.), Research in History and Philosophy of Mathematics. Annals of the Canadian Society for History and Philosophy of Mathematics. pp. 15-33.
    We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we go (...)
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  2. Frege’s Theory of Types.Bruno Bentzen - 2023 - Manuscrito 46 (4):2022-0063.
    It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types. This claim roughly states that Frege presupposes a type of functions in the sense of simple type theory in the expository language of Grundgesetze. However, this view makes it hard to accommodate function names of two arguments and view functions as incomplete entities. I propose and defend an alternative interpretation of first-level (...)
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  3. Scientific Platonism.Alexander Paseau - 2007 - In Mary Leng, Alexander Paseau & Michael Potter (eds.), Mathematical Knowledge. Oxford University Press. pp. 123-149.
    Does natural science give us reason to believe that mathematical statements are true? And does natural science give us reason to believe in some particular metaphysics of mathematics? These two questions should be firmly distinguished. My argument in this chapter is that a negative answer to the second question is compatible with an affirmative answer to the first. Loosely put, even if science settles the truth of mathematics, it does not settle its metaphysics.
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  4. Fair equality of chances for prediction-based decisions.Michele Loi, Anders Herlitz & Hoda Heidari - forthcoming - Economics and Philosophy:1-24.
    This article presents a fairness principle for evaluating decision-making based on predictions: a decision rule is unfair when the individuals directly impacted by the decisions who are equal with respect to the features that justify inequalities in outcomes do not have the same statistical prospects of being benefited or harmed by them, irrespective of their socially salient morally arbitrary traits. The principle can be used to evaluate prediction-based decision-making from the point of view of a wide range of antecedently specified (...)
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  5. 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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  6. Towards a Computational Ontology for the Philosophy of Wittgenstein: Representing Aspects of the Tractarian Philosophy of Mathematics.Jakub Gomułka - 2023 - Analiza I Egzystencja 63:27-54.
    The present paper concerns the Wittgenstein ontology project: an attempt to create a Semantic Web representation of Ludwig Wittgenstein’s philosophy. The project has been in development since 2006, and its current state enables users to search for information about Wittgenstein-related documents and the documents themselves. However, the developers have much more ambitious goals: they attempt to provide a philosophical subject matter knowledge base that would comprise the claims and concepts formulated by the philosopher. The current knowledge representation technology is not (...)
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  7. Reference Fixing and the Paradoxes.Mario Gomez-Torrente - forthcoming - In Mattia Petrolo & Giorgio Venturi (eds.), Paradoxes between Truth and Proof. Springer.
    I defend the hypothesis that the semantic paradoxes, the paradoxes about collections, and the sorites paradoxes, are all paradoxes of reference fixing: they show that certain conventionally adopted and otherwise functional reference-fixing principles cannot provide consistent assignments of reference to certain relevant expressions in paradoxical cases. I note that the hypothesis has interesting implications concerning the idea of a unified account of the semantic, collection and sorites paradoxes, as well as about the explanation of their “recalcitrance”. I also note that (...)
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  8. The Empirical and the Formal – Tensions in Scientific Knowledge (Centaurus 50/3).Gregor Schiemann & Friedrich Steinle (eds.) - 2008
  9. 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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  10. Abhandlungen zur Philosophie der Mathematik.Paul Bernays - 1976 - Darmstadt: Wissenschaftliche Buchgesellschaft, [Abt. Verl.].
  11. Graṅs rig bsam bloʾi thabs lam rnam bśad.Śa-bo Tshe-riṅ, Dpal-Chen-Rdo-Rje & Jianjun Ma (eds.) - 1998 - [Lanzhou]: Kan-suʾu mi rigs dpe skrun khaṅ.
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  12. Copernicus and Axiomatics.Alberto Bardi - 2021 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Springer.
    The debate about the foundations of mathematical sciences traces back to Greek antiquity, with Euclid and the foundations of geometry. Through the flux of history, the debate has appeared in several shapes, places, and cultural contexts. Remarkably, it is a locus where logic, philosophy, and mathematics meet. In mathematical astronomy, Nicolaus Copernicus’s axiomatic approach toward a heliocentric theory of the universe has prompted questions about foundations among historians who have studied Copernican axioms in their terminological and logical aspects but never (...)
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  13. Research in History and Philosophy of Mathematics. The CSHPM 2019-2020 Volume.Maria Zack & Dirk Schlimm (eds.) - 2022 - Birkhäuser.
    J. S. Silverberg, The Most Obscure and Inconvenient Tables ever Constructed.- D. J. Melville, Commercializing Arithmetic: The Case of Edward Hatton.- C. Baltus, Leading to Poncelet: A Story of Collinear Points.- R. Godard, Cauchy, Le Verrier et Jacobi sur le problème algébrique des valeurs propres et les inégalités séculaires des mouvements des planètes.- A. Ackerberg-Hastings, Mathematics in Astronomy at Harvard College Before 1839 as a Case Study for Teaching Historical Writing in Mathematics Courses.- J. J. Tattersall, S. L. McMurran, "Lectures (...)
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  14. Naturalism and Its Challenges.Ali Hossein Khani & Gary Kemp (eds.) - forthcoming - New York: Routledge.
    This volume features new essays on the application and role of naturalism in philosophical inquiry. It serves as an important update on current controversies about naturalism.
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  15. On Gödel's way in : the influence of Rudolf Carnap.Warren Goldfarb - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: essays for his centennial. Association for Symbolic Logic.
  16. Matrix models and poetic verses of the human mind.Matthew He - 2023 - New Jersey: World Scientific Publishing Co. Pte..
    In this multidisciplinary book, mathematician Matthew He provides integrative perspectives of algebraic biology, cognitive informatics, and poetic expressions of the human mind. Using classical Pythagorean Theorem and contemporary Category Theory, the proposed matrix models of the human mind connect three domains of the physical space of objective matters, mental space of subjective meanings, and emotional space of bijective modes; draws the connections between neural sparks and idea points, between synapses and idea lines, and between action potentials and frequency curves.
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  17. La «matemática situada» como propuesta de reflexión epistémica en clave histórico-social sobre la práctica matemática.Héctor Horacio Gerván - 2021 - Culturas Cientificas 2 (2):01-25.
    La presente investigación tiene como propósito general asumir un posicionamiento filosófico en clave histórico-social y de tipo anti-relativista para analizar el desarrollo histórico de la matemática, el cual aplicaremos a un caso en particular: la matemática del antiguo Egipto. Para ello se discutirán y criticarán, en primera instancia, determinadas posiciones filosóficas afines al cuasi-empirismo en matemática que, siendo relativistas, permitirán delinear nuestro propio posicionamiento en contraste: la existencia de una «matemática situada». Esta categoría filosófica tendrá como sustento teórico la noción (...)
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  18. Euclides entre los árabes.Norma Ivonne Ortega Zarazúa - 2021 - Culturas Cientificas 2 (1):76-105.
    Es común escuchar que el mundo Occidental debe a los árabes el descubrimiento del álgebra. No obstante, el desarrollo de esta disciplina puede interpretarse como un crisol de distintas tradiciones científicas que fue posible gracias a la clasificación, traducción y crítica tanto de los clásicos como de las obras que los árabes obtuvieron de los pueblos que conquistaron. Entre estos trabajos se encontraba Los Elementos de Euclides. Los Elementos fueron cuidadosamente traducidos durante el califato de Al-Ma’mūn por el matemático Mohammed (...)
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  19. Artistic Mediation in Mathematized Phenomenology.Robert Prentner & Shanna Dobson - manuscript
    Mathematics has a long track record of refining the concepts by which we make sense of the world. For example, mathematics allows one to speak about different senses of "sameness", depending on the larger context. Phenomenology is the name of a philosophical discipline that tries to systematically investigate the first-personal perspective on reality and how it is constituted. Together, mathematics and phenomenology seem to be a good fit to derive statements about our experience that are, at the same time, well-defined, (...)
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  20. Advances in Experimental Philosophy of Logic and Mathematics: A. Aberdein and M. Inglis, editors, London: Bloomsbury Academic, 2019. 291 pp. $28.76. ISBN 978-1-3500-3902-5.Yuri Sato - 2021 - History and Philosophy of Logic 43 (3):305-307.
    This book is a collection of articles on research that attempts to connect logic and mathematics with empirical and cognition. There have been various such a...
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  21. Salvatore Florio* and Øystein Linnebo**. The Many and the One. A Philosophical Study of Plural Logic.Francesca Boccuni - 2022 - Philosophia Mathematica 30 (3):369-381.
    Several natural languages such as English contain prima facie different kinds of referential and quantificational expressions. In particular, natural languages.
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  22. Algunos tópicos de Lógica matemática y los Fundamentos de la matemática.Franklin Galindo - manuscript
    En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...)
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  23. El Programa original de David Hilbert y el Problema de la Decibilidad.Franklin Galindo & Ricardo Da Silva - 2017 - Episteme NS: Revista Del Instituto de Filosofía de la Universidad Central de Venezuela 37 (1):1-23.
    En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...)
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  24. Critical Studies/Book Reviews.Juliette Kennedy - forthcoming - Philosophia Mathematica.
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  25. Critical Studies/Book Reviews.Chris Scambler - forthcoming - Philosophia Mathematica.
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  26. The Curious Neglect of Geometry in Modern Philosophies of Mathematics.Siavash Shahshahani - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 379-389.
    From ancient times to 19th century geometryGeometry symbolized the essence of mathematical thinking and method, but modern philosophy of mathematics seems to have marginalized the philosophical status of geometryGeometry. The roots of this transformation will be sought in the ascendance of logical foundations in place of intuitive primacy as the cornerstone of mathematical certainty in the late 19th century. Nevertheless, geometry and geometrical thinking, in multiple manifestations, have continued to occupy a central place in the practice of mathematics proper. We (...)
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  27. Resolving Frege’s Other Puzzle.Eric Snyder, Richard Samuels & Stewart Shapiro - 2022 - Philosophica Mathematica 30 (1):59-87.
    Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...)
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  28. Applying Mathematics: Immersion, Inference, Interpretation.Otávio Bueno & Steven French - 2018 - Oxford, England: Oxford University Press. Edited by Steven French.
    How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otavio Bueno and Steven French offer a middle way, which focuses on the moves that have to be made (...)
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  29. Counting Composites.Jonathan D. Payton - 2022 - Australasian Journal of Philosophy 100 (4):695-710.
    I defend the thesis that Composition Entails Identity (CEI): that is, a whole is identical to all of its parts, taken together. CEI seems to be inconsistent, since it seems to require that the parts of a whole possess incompatible number properties (for instance, being one thing and being many things). I show that these number properties are, in fact, compatible.
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  30. Philosophische Notizbücher, Band 2: Zeiteinteilung (Maximen) I und II / Philosophical Notebooks, Volume 2: Time Management (Maxims) I and II, edited by Eva-Maria Engelen, translated by Merlin Carl, Berlin (De Gruyter) 2020.Kurt Gödel (ed.) - 2020 - Berlin: De Gruyter.
    Volume 2 contains both notebooks of "Time Management (Max) I and II" and thereby Gödel’s applied individual ethics, which he received among others through his teacher Heinrich Gomperz. Gödel thus incorporates the ethical ideal of self-perfection into his opus. The volume is prefaced by an introduction to relevant considerations from the ethics of the Stoics as well as ancient dietetics, which provide the philosophical background to understand Gödel’s approach. In addition, editor Eva-Maria Engelen presents how this fits into the context (...)
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  31. Review of Andrew Aberdein and Matthew Inglis (eds), Advances in Experimental Philosophy of Logic and Mathematics: New York: Bloomsbury Academic Publishers, 2019, 296 pages, $114. [REVIEW]Mark Zelcer - 2020 - Philosophia 48 (3):1283-1287.
  32. The Language Essence of Rational Cognition with some Philosophical Consequences.Boris Culina - 2021 - Tesis (Lima) 14 (19):631-656.
    The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.
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  33. Математизирането на историята: число и битие.Vasil Penchev - 2013 - Sofia: BAS: ISSk (IPR).
    The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.
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  34. Hale and Wright on the Metaontology of Neo-Fregeanism.Matti Eklund - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford, England: Oxford University Press UK.
  35. Demostraciones «tópicamente puras» en la práctica matemática: un abordaje elucidatorio.Guillermo Nigro Puente - 2020 - Dissertation, Universidad de la República Uruguay
  36. গণিত দর্শন Gonit Dorshon.Avijit Lahiri - manuscript
    This article, written in Bengali ('Gonit Dorshon' means `philosophy of mathematics' ), briefly reviews a few of the major points of view toward mathematics and the world of mathematical entities, and interprets the philosophy of mathematics as an interaction between these. The existence of these different points of view is indicative that mathematics, in spite of being of universal validity, can nevertheless accommodate alternatives. In particular, I review the alternative viewpoints of Platonism and Intuitionism and present the case that in (...)
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  37. 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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  38. Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium.Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.) - 2019 - Berlin, Boston: De Gruyter.
    The volume deals with the history of logic, the question of the nature of logic, the relation of logic and mathematics, modal or alternative logics (many-valued, relevant, paraconsistent logics) and their relations, including translatability, to classical logic in the Fregean and Russellian sense, and, more generally, the aim or aims of philosophy of logic and mathematics. Also explored are several problems concerning the concept of definition, non-designating terms, the interdependence of quantifiers, and the idea of an assertion sign. The contributions (...)
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  39. 关于在柴廷、维特根斯坦、霍夫施塔特、沃尔珀特、多里亚、达科斯塔、戈德尔、西尔、罗迪赫、贝托、弗洛伊德、贝托、弗洛伊德、莫亚尔-沙罗克和亚诺夫斯基.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    人们普遍认为,不可能性、不完整性、不一致性、不可度、随机性、可预见性、悖论、不确定性和理性极限是完全不同的科学物理或数学问题,在常见。我认为,它们主要是标准的哲学问题(即语言游戏),这些问题大多在80 多年前由维特根斯坦解决。 -/- "在这种情况下,我们'想说'当然不是哲学,而是它的原材料。因此,例如,数学家倾向于对数学事实的客观性和现实性说的,不是数学哲学,而是哲学处理的东西。维特根斯坦 PI 234 -/- "哲学家们经常看到科学的方法,他们不可抗拒地试图以科学的方式提问和回答问题。这种倾向是形而上学的真正源泉,将哲学家带入完全的黑暗之中。 维特根斯坦 -/- 我简要地总结了现代两位最杰出的学生路德维希·维特根斯坦和约翰·西尔关于故意的逻辑结构(思想、语言、行为)的一些主要发现,作为我的起点Wittgenstein 的基本发现——所有真正的"哲学"问题都是相同的——关于在特定上下文中如何使用语言的困惑,因此所有解决方案都是一样的——研究如何在相关上下文中使用语言,使其真实性条件(满意度或 COS 条件)是明确的。基本问题是,人们可以说什么,但一个人不能意味着(状态明确COS)任何任意的话语和意义只有在非常具体的上下文中才可能。 -/- 在两种思想体系的现代视角(被推广为"思维快,思维慢")的框架内,我从维特根斯坦人的角度剖析了一些主要评论员关于这些问题的一些著作,并采用了一个新的表意向性和新的双系统命名法。 我表明,这是一个强大的启发式描述这些假定的科学,物理或数学问题的真实性质,这是真正最好的处理作为标准哲学问题,如何使用语言(语言游戏在维特根斯坦的术语)。 -/- 我的论点是,这里突出特征的意向表(理性、思想、思想、语言、个性等)或多或少地准确地描述了,或者至少作为启发式,我们思考和行为的方式,所以它包含不只是哲学和心理学,但其他一切(历史,文学,数学,政治等) 。特别要注意,我(以及西尔、维特根斯坦和其他人)认为,故意和理性包括有意识的审议语言系统2和无意识的自动预语言系统1行为或反射。 .
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  40. Kurt Vogel: Kleinere Schriften zur Geschichte der Mathematik (ed. Menso Folkerts). (Boethius, Texte und Abhandlungen zur Geschichte der exakten Wissenschaften, 20.) Pp. xlvii + 413; vii + 414–884; illustrations. Stuttgart: Franz Steiner, 1988. Paper, DM 150. [REVIEW]Ivor Bulmer-Thomas - 1990 - The Classical Review 40 (1):190-190.
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  41. James Robert Brown. Philosophy of mathematics, an introduction to the world of proofs and pictures. Routledge, 1999, vii + 215 pp. [REVIEW]Janet Folina - 2003 - Bulletin of Symbolic Logic 9 (4):504-506.
  42. Visualization, Explanation and Reasoning Styles in Mathematics.Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.) - 2005 - Springer.
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  43. Concept and Formalization of Constellatory Self-Unfolding: A Novel Perspective on the Relation between Quantum and Relativistic Physics.Albrecht von Müller & Elias Zafiris - 2018 - Cham: Springer. Edited by Elias Zafiris.
    This volume develops a fundamentally different categorical framework for conceptualizing time and reality. The actual taking place of reality is conceived as a “constellatory self-unfolding” characterized by strong self-referentiality and occurring in the primordial form of time, the not yet sequentially structured “time-space of the present.” Concomitantly, both the sequentially ordered aspect of time and the factual aspect of reality appear as emergent phenomena that come into being only after reality has actually taken place. In this new framework, time functions (...)
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  44. Deleuze and the conceptualizable character of mathematical theories.Simon B. Duffy - 2017 - In Nathalie Sinclair & Alf Coles Elizabeth de Freitas (ed.), What is a Mathematical Concept? Cambridge University Press.
    To make sense of what Gilles Deleuze understands by a mathematical concept requires unpacking what he considers to be the conceptualizable character of a mathematical theory. For Deleuze, the mathematical problems to which theories are solutions retain their relevance to the theories not only as the conditions that govern their development, but also insofar as they can contribute to determining the conceptualizable character of those theories. Deleuze presents two examples of mathematical problems that operate in this way, which he considers (...)
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  45. Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective.Lawrence Sklar & Jan von Plato - 1994 - Journal of Philosophy 91 (11):622.
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  46. The Modern Aspect of Mathematics. Lucienne Félix, Julius H. Hlavaty, Francille H. Hlavaty. [REVIEW]Karl Menger - 1962 - Philosophy of Science 29 (1):95-96.
  47. The Rainbow, from Myth to Mathematics. Carl B. Boyer. [REVIEW]Oystein Ore - 1960 - Philosophy of Science 27 (2):207-208.
  48. Essay Review: Islamic Mathematics: The Muslim Contribution to Mathematics.David A. King - 1979 - History of Science 17 (4):295-296.
  49. Revisiting the reliability of published mathematical proofs: where do we go next?Joachim Frans & Laszlo Kosolosky - 2014 - Theoria 29 (3):345-360.
    Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians all too often believe that this type of argumentation leaves no room for errors or unclarity. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature is also more reliable is too naive. We will discuss several (...)
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  50. Jiri Hudecek, Reviving Ancient Chinese Mathematics: Mathematics, History and Politics in the Work of Wu Wen-Tsun. New York: Routledge, 2014. Pp. xii + 210. ISBN 978-0-4157-0296-6. £90.00. [REVIEW]Ubiratan D'Ambrosio - 2016 - British Journal for the History of Science 49 (1):143-144.
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