Philosophy of Mathematics

Edited by Øystein Linnebo (University of Oslo)
Assistant editor: Sam Roberts (Universität Konstanz)
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268 found
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  1. added 2023-09-23
    The insubstantiality of mathematical objects as positions in structures.Bahram Assadian - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 20.
    The realist versions of mathematical structuralism are often characterized by what I call ‘the insubstantiality thesis’, according to which mathematical objects, being positions in structures, have no non-structural properties: they are purely structural objects. The thesis has been criticized for being inconsistent or descriptively inadequate. In this paper, by implementing the resources of a real-definitional account of essence in the context of Fregean abstraction principles, I offer a version of structuralism – essentialist structuralism – which validates a weaker version of (...)
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  2. added 2023-09-23
    Mathematical logic.Alan Turing - 2001 - New York: Elsevier Science. Edited by R. O. Gandy & C. E. M. Yates.
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  3. added 2023-09-22
    On Philomatics and Psychomatics for Combining Philosophy and Psychology with Mathematics.Benyamin Ghojogh & Morteza Babaie - manuscript
    We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy, proposing science of philosophy, justifying mathematical algorithms by philosophy, and abstraction in both philosophy and mathematics. We enumerate various examples for philomatics and psychomatics, some of which are explained in more depth. The first example is the analysis of relation between the context principle, semantic holism, and the usage (...)
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  4. added 2023-09-22
    What makes a `good' modal theory of sets?Neil Barton - manuscript
    I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...)
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  5. added 2023-09-22
    No Easy Road to Impredicative Definabilism.Øystein Linnebo & Sam Roberts - forthcoming - Philosophia Mathematica:nkad013.
    Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that (...)
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  6. added 2023-09-22
    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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  7. added 2023-09-22
    Deductivism in the Philosophy of Mathematics.Alexander Paseau & Fabian Pregel - 2023 - Stanford Encyclopedia of Philosophy 2023.
  8. added 2023-09-22
    Not So Simple.Colin R. Caret - 2023 - Asian Journal of Philosophy 2 (2):1-16.
    In a recent series of articles, Beall has developed the view that FDE is the formal system most deserving of the honorific “Logic”. The Simple Argument for this view is a cost-benefit analysis: the view that FDE is Logic has no drawbacks and it has some benefits when compared with any of its rivals. In this paper, I argue that both premises of the Simple Argument are mistaken. I use this as an opportunity to further reflect on how such arguments (...)
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  9. added 2023-09-22
    Descartes et ses mathématiques.Olivia Chevalier (ed.) - 2022 - Paris: Classiques Garnier.
    Dans cet ouvrage, il s'agira non seulement d'aborder différentes facettes de l'activité mathématique de Descartes, assez peu connues, mais également diverses dimensions de sa pensée mathématique.
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  10. added 2023-09-22
    An introduction to proof via inquiry-based learning.Dana C. Ernst - 2022 - Providence, Rhode Island: MAA Press, an imprint of the American Mathematical Society.
    An Introduction to Proof via Inquiry-Based Learning is a textbook for the transition to proof course for mathematics majors. Designed to promote active learning through inquiry, the book features a highly structured set of leading questions and explorations. The reader is expected to construct their own understanding by engaging with the material. The content ranges over topics traditionally included in transitions courses: logic, set theory including cardinality, the topology of the real line, a bit of number theory, and more. The (...)
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  11. added 2023-09-22
    Ludwig Wittgenstein: writings on mathematics and logic, 1937-1944.Ludwig Wittgenstein - 2022 - New York, NY: Cambridge University Press. Edited by Victor Rodych & Timothy F. Pope.
    This five-volume German-English edition presents, for the first time, new translations of all of Wittgenstein's mature 1937-1944 writings on mathematics and logic. The first (1956) and third (1978) editions of Wittgenstein's Remarks on the Foundations of Mathematics omitted, unsystematically, more than half of Wittgenstein's later writings on mathematics; for that reason, the reader will here read some entire manuscripts for the first time, and other manuscripts for the first time as unabridged, sustained pieces of writing. Philosophers and other interested readers (...)
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  12. added 2023-09-22
    The story of proof: logic and the history of mathematics.John Stillwell - 2022 - Princeton, New Jersey: Princeton University Press.
    How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the (...)
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  13. added 2023-09-22
    Metamathematics: foundations & physicalization.Stephen Wolfram - 2022 - [Champaign]: Wolfram Media.
    "What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question-showing through the concept of the physicalization of metamathematics how both mathematics and physics as experienced by humans can be seen to emerge from the unique underlying computational structure of the recently formulated ruliad. Written with Stephen Wolfram's characteristic expositional flair and richly illustrated with remarkable algorithmic diagrams, the book takes the reader on a unprecedented intellectual journey to (...)
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  14. added 2023-09-22
    The psychology of mathematics: a journey of personal mathematical empowerment for educators and curious minds.Anderson Norton - 2022 - New York, NY: Routledge.
    This book offers an innovative introduction to the psychological basis of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. Through accessible and engaging writing, award-winning mathematician and educator Anderson Norton reframes mathematics as something that exists first in the minds of students, rather than something that exists first in a textbook. By exploring the psychological basis for mathematics at every level - including geometry, algebra, calculus, (...)
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  15. added 2023-09-22
    Mathematical logic through Python.Yannai A. Gonczarowski - 2022 - New York, NY: Cambridge University Press. Edited by Noam Nisan.
    An introduction to Mathematical Logic using a unique pedagogical approach in which the students implement the underlying conceps as well as almost all the mathematical proofs in the Python programming language. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. The covered mathematical material includes Propositional Logic and first-order Predicate Logic, culminating in a proof of Gödel's Completeness Theorem. A "sneak peak" into Gödel's Incompleteness Theorem is also provided.
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  16. added 2023-09-22
    The meaning of proofs: mathematics as storytelling.Gabriele Lolli - 2022 - Cambridge, Massachusetts: The MIT Press. Edited by Bonnie McClellan-Broussard & Matilde Marcolli.
    This book introduces readers to the narrative structure of mathematical proofs and why mathematicians communicate that way, drawing examples from classic literature and employing metaphors and imagery.
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  17. added 2023-09-22
    Stress-free math: a visual guide to acing math in grades 4-9.Theresa Fitzgerald - 2020 - Waco, TX: Prufrock Press Inc. ;.
    Quick reference guide includes illustrated explanations of the most common terms used in general math classes. Discusses how students can use manipulatives and basic math tools to improve their understanding. With measurement conversion tables, guides to geometric shapes, and more.
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  18. added 2023-09-22
    Dedekind's Logicism†.Ansten Mørch Klev - 2015 - Philosophia Mathematica 25 (3):341-368.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  19. added 2023-09-22
    A beginner's guide to mathematical logic.Raymond M. Smullyan - 2014 - Mineola, New York: Dover Publications.
    Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate (...)
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  20. added 2023-09-22
    The origin of symbolic mathematics and the end of the science of quantity.Sören Stenlund - 2014 - Uppsala: Uppsala Universitet.
  21. added 2023-09-22
    Algorithm theory - SWAT 2014: 14th Scandinavian Symposium and Workshops, Copenhagen, Denmark, July 2-4, 2014: proceedings.R. Ravi & Inge Li Gørtz (eds.) - 2014 - New York: Springer.
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  22. added 2023-09-22
    Report on some ramified-type assignment systems and their model-theoretic semantics.Harold Hodes - 2013 - In Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan.
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  23. added 2023-09-22
    Principia mathematica : versus.Gregory Llandini - 2013 - In Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan.
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  24. added 2023-09-22
    Theory of fuzzy computation.Apostolos Syropoulos - 2013 - New York: Springer.
    The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. Ideas for future research (...)
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  25. added 2023-09-22
    Why there is no Frege-Russell definition of number.Jolen Galaugher - 2013 - In Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan.
  26. added 2023-09-22
    The logic of classes and the no-class theory.Byeong-Uk Yi - 2013 - In Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan.
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  27. added 2023-09-22
    Proofs of the Cantor-Bernstein theorem in Principia mathematica.Arie Hinkis - 2013 - In Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan.
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  28. added 2023-09-22
    Principia mathematica, the multiple-relation theory of judgment and molecular facts.James Levine - 2013 - In Nicholas Griffin & Bernard Linsky (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan.
  29. added 2023-09-22
    Toward "Principia Mathematica" 1905-08.Bertrand Russell - 1983 - London: Routledge. Edited by Alfred North Whitehead & Gregory H. Moore.
    This volume of Bertrand Russell's Collected Papers finds Russell focused on writing Principia Mathematica during 1905-08. The volume's 80-page introduction covers the evolution of his logic from 1896 until 1909, when volume I of Principia went to the printer.
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  30. added 2023-09-22
    Éléments de logique mathématique.Georg Kreisel - 1967 - Paris,: Dunod. Edited by J. L. Krivine.
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  31. added 2023-09-22
    Qué es la lógica matemática.Alberto Moreno - 1967 - [Buenos Aires]: Editorial Columba.
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  32. added 2023-09-22
    L'algèbre logique et ses rapports avec la théorie des relations.Roland Fraïssé - 1967 - Montréal,: les Presses de l'Université de Montréal.
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  33. added 2023-09-22
    Métamathématique.Paul Lorenzen - 1967 - Paris,: Mouton.
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  34. added 2023-09-22
    Logique mathématique, éléments de base: calcul propositionnel, calcul des prédicats.Daniel Ponasse - 1967 - Paris,: O.C.D.L..
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  35. added 2023-09-22
    Sur les algèbres de Hilbert..A. Diego - 1966 - Paris,: Gauthier-Villars, Louvain, E. Nauwelaerts.
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  36. added 2023-09-22
    Il teorema e il corollario di Gödel.Francesca Rivetti Barbò - 1964 - Milano,: Società editrice Vita e pensiero.
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  37. added 2023-09-22
    Almene begreber fra logik, mængdelære og algebra.Bent Christiansen - 1964 - [Copenhagen]: Munksgaard. Edited by Jonas Lichtenberg, Pedersen, Johs & [From Old Catalog].
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  38. added 2023-09-22
    Sur la clarté des démonstrations mathématiques.François Rostand - 1962 - Paris,: J. Vrin.
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  39. added 2023-09-22
    Beweistheorie.K. Schütte - 1960 - Berlin,: Springer.
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  40. added 2023-09-22
    Einführung in die mathematische Logik.Günter Asser - 1959 - Leipzig,: Teubner.
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  41. added 2023-09-22
    Structure et objet de l'analyse mathématique.Eloi Lefebvre - 1958 - Paris,: Gauthier-Villars.
  42. added 2023-09-22
    Metod matematicheskoĭ indukt︠s︡ii.Iman I︠A︡kovlevich Depman - 1957
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  43. added 2023-09-22
    Les limitations internes des formalismes.Jean Ladrière - 1957 - Louvain,: E. Nauwelaerts.
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  44. added 2023-09-22
    Mavo le-torat-ha-higayon.Alfred Tarski - 1954 - [Tel-Aviv]:
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  45. added 2023-09-22
    La recherche scientifique en mathématiques.Paul Antonin Montel - 1953 - [Alençon,: Impr. alençonnaise.
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  46. added 2023-09-22
    Les trois étapes du problème pythagore-fermat, la récurrence, l'art des réciproques.Alphonse Louis Maroger - 1951 - Paris,: Vuibert.
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  47. added 2023-09-22
    Philosophie und Mathematik.Alfred North Whitehead - 1949 - [Wien]: Humboldt-Verlag.
  48. added 2023-09-22
    Les mathématiques et la vie.Paul Montel - 1947 - Paris,: Tirany. Edited by Pierre Collot.
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  49. added 2023-09-22
    Das Leben der Mathematiker.Max Bense - 1944 - Köln,: Staufen-Verlag.
    Vorwort über das Leben der Mathematiker.--Die Bernoullis.--Leonhard Euler und die Phantasie in der Mathematik.--Gauss und die Mathematik.--Geist und Character d'Alemberts.--Evariste Galois.--über Niels Henrik Abels.--Bernard Bolzanos Grösse.--Felix Klein, der Systematiker der Geometrie.--David Hilbert.
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  50. added 2023-09-22
    Essai sur la signification du langage de la géométrie (acribologie géométrique)..Marcel Prot - 1940 - Paris,: Hermann & cie.
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1 — 50 / 268