Philosophy of Mathematics

Edited by Øystein Linnebo (University of Oslo)
Assistant editor: Sam Roberts (Universität Konstanz)
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  1. Knowledge, Number and Reality: Encounters with the Work of Keith Hossack.Nils Kürbis, Bahram Assadian & Jonathan Nassim (eds.) - forthcoming - London: Bloomsbury.
    Centered around our knowledge of mathematical, modal, and a priori truths, this is a collection that celebrates the work of Keith Hossack, who, throughout his career, has made outstanding contributions to the theory of knowledge, metaphysics, and the philosophy of mathematics. Starting with a focus on our knowledge of abstract entities such as mathematical objects and the source of the necessity of mathematical truths, attention moves to the notion of necessity and its interaction with a priori knowledge: Is it the (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  2. On the Buck-Stopping Identification of Numbers.Dongwoo Kim - forthcoming - Philosophia Mathematica.
    Kripke observes that the decimal numerals have the buck-stopping property: when a number is given in decimal notation, there is no further question of what number it is. What makes them special in this way? According to Kripke, it is because of structural revelation: each decimal numeral represents the structure of the corresponding number. Though insightful, I argue, this account has some counterintuitive consequences. Then I sketch an alternative account of the buck-stopping property in terms of how we specify the (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  3. William Boos. Metamathematics and the Philosophical Tradition.Brendan Larvor - forthcoming - Philosophia Mathematica.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  4. Rainer Stuhlmann-Laeisz.* Gottlob Freges Grundgesetze der Arithmetik: Ein Kommentar des Vorworts, des Nachworts Und der Einleitenden Paragraphen. [Gottlob Frege’s Basic Laws of Arithmetic: A Commentary on the Foreword, the Afterword and the Introductory Paragraphs].Matthias Wille - forthcoming - Philosophia Mathematica.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  5. How Do We Semantically Individuate Natural Numbers?†.Stefan Buijsman - forthcoming - Philosophia Mathematica.
    ABSTRACT How do non-experts single out numbers for reference? Linnebo has argued that they do so using a criterion of identity based on the ordinal properties of numerals. Neo-logicists, on the other hand, claim that cardinal properties are the basis of individuation, when they invoke Hume’s Principle. I discuss empirical data from cognitive science and linguistics to answer how non-experts individuate numbers better in practice. I use those findings to develop an alternative account that mixes ordinal and cardinal properties to (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  6. Definition in Frege's Foundations of Arithmetic.David Hunter - 1996 - Pacific Philosophical Quarterly 77:88-107.
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  7. A Validation of Knowledge: A New, Objective Theory of Axioms, Causality, Meaning, Propositions, Mathematics, and Induction.Ronald Pisaturo - 2020 - Norwalk, Connecticut: Prime Mover Press.
    This book seeks to offer original answers to all the major open questions in epistemology—as indicated by the book’s title. These questions and answers arise organically in the course of a validation of the entire corpus of human knowledge. The book explains how we know what we know, and how well we know it. The author presents a positive theory, motivated and directed at every step not by a need to reply to skeptics or subjectivists, but by the need of (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  8. Intrinsic Justifications for Large-Cardinal Axioms.Rupert McCallum - forthcoming - Philosophia Mathematica:nkaa038.
    ABSTRACT The aim of the paper is to answer some arguments raised against mathematical structuralism developed by Michael Resnik. These arguments stress the abstractness of mathematical objects, especially their causal inertness, and conclude that mathematical objects, the structures posited by Resnik included, are inaccessible to human cognition. In the paper I introduce a distinction between abstract and ideal objects and argue that mathematical objects are primarily ideal. I reconstruct some aspects of the instrumental practice of mathematics, such as symbolic manipulations (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  9. Strict Finitism and the Logic of Mathematical Applications, Synthese Library, Vol. 355.Feng Ye - 2011 - Springer.
    This book intends to show that, in philosophy of mathematics, radical naturalism (or physicalism), nominalism and strict finitism (which does not assume the reality of infinity in any format, not even potential infinity) can account for the applications of classical mathematics in current scientific theories about the finite physical world above the Planck scale. For that purpose, the book develops some significant applied mathematics in strict finitism, which is essentially quantifier-free elementary recursive arithmetic (with real numbers encoded as elementary recursive (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
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  10. Studies in No-Self Physicalism.Feng Ye - manuscript
    This book develops and defends a version of physicalism in contemporary philosophy of mind, called ‘No-Self Physicalism’. No-Self Physicalism emphasizes that a subject of cognition is itself a physical entity, a human brain (and body). -/- The book first argues (in Chapters 1 and 2) that many contemporary philosophers who openly accept physicalism in fact (though perhaps unconsciously and/or implicitly) take the stance of a non-physical Subject in understanding and using core philosophical notions, such as conceptual representation, truth, analyticity, modality, (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
     Revisability in Mathematics
     Visualization in Mathematics
     Phenomenology of Mathematics
     Mathematical Methodology
     Nondeductive Methods in Mathematics
     Debunking Arguments about Mathematics
     Epistemology of Mathematics, Misc
    Ontology of Mathematics
     Mathematical Fictionalism
     Mathematical Nominalism
     Mathematical Platonism
     Mathematical Psychologism
     Mathematical Structuralism
     Mathematical Neo-Fregeanism
     Indeterminacy in Mathematics
     Debunking Arguments about Mathematics
     Indispensability Arguments in Mathematics
     Numbers
     The Nature of Sets
    Mathematical Cognition
     Mathematical Intuition
     Visualization in Mathematics
     Mathematical Cognition, Misc
     Phenomenology of Mathematics
     Numerical Cognition
    Mathematical Truth
     Analyticity in Mathematics
     Axiomatic Truth
     Objectivity Of Mathematics
     Mathematical Truth, Misc
    Set Theory
     The Nature of Sets
     Axioms of Set Theory
     Cardinals and Ordinals
     Set Theory as a Foundation
    Areas of Mathematics
     Algebra
     Analysis
     Category Theory
     Geometry
     Logic and Phil of Logic
     Number Theory
     Set Theory
     Topology
     Areas of Mathematics, Misc
    Theories of Mathematics
     Logicism in Mathematics
     Formalism in Mathematics
     Intuitionism and Constructivism
     Predicativism in Mathematics
     Mathematical Naturalism
     Mathematical Finitism
     Theories of Mathematics, Misc
    History: Philosophy of MathematicsPhil of Mathematics, Miscellaneous
     Explanation in Mathematics
     The Infinite
     The Application of Mathematics
     History of Mathematics
     Mathematical Practice
     Phil of Mathematics, General Works
     Mathematical Explanation
     Phil of Mathematics, Misc
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  11. Kreisel's Interests. On the Foundations of Logic and Mathematics.Paul Weingartner & Hans-Peter Leeb (eds.) - 2020 - London, Vereinigtes Königreich: College Publications.
    The contributions to this volume are from participants of the international conference "Kreisel's Interests - On the Foundations of Logic and Mathematics", which took place from 13 to 14 2018 at the University of Salzburg in Salzburg, Austria. The contributions have been revised and partially extended. Among the contributors are Akihiro Kanamori, Göran Sundholm, Ulrich Kohlenbach, Charles Parsons, Daniel Isaacson, and Kenneth Derus. The contributions cover the discussions between Kreisel and Wittgenstein on philosophy of mathematics, Kreisel's Dictum, proof theory, the (...)
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    Epistemology of Mathematics
     Apriority in Mathematics
     Mathematics and the Causal Theory of Knowledge
     Mathematical Intuition
     Mathematical Proof
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  12. Set Theory INC# Based on Intuitionistic Logic with Restricted Modus Ponens Rule (Part. I).Jaykov Foukzon - 2021 - Journal of Advances in Mathematics and Computer Science 36 (2):73-88.
    In this article Russell’s paradox and Cantor’s paradox resolved successfully using intuitionistic logic with restricted modus ponens rule.
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  13. The Future of Science.Hossein Shirkhani - manuscript
    This article has been written about the explanation of the scientific affair. There are the philosophical circles that a philosopher must consider their approaches. Postmodern thinkers generally refuse the universality of the rational affair. They believe that the experience cannot reach general knowledge. They emphasize on the partial and plural knowledge. Any human being has his knowledge and interpretation. The world is always becoming. Diversity is an inclusive epistemological principle. Naturally, in such a state, the scientific activity is a non-sense (...)
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  14. The Josephson Junction.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
    What the Josephson Junction proves. The Josephson-Yardley 'connection.'.
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  15. Natural Cybernetics of Time, or About the Half of Any Whole.Vasil Penchev - 2021 - Information Systems eJournal (Elsevier: SSRN) 4 (28):1-55.
    Norbert Wiener’s idea of “cybernetics” is linked to temporality as in a physical as in a philosophical sense. “Time orders” can be the slogan of that natural cybernetics of time: time orders by itself in its “screen” in virtue of being a well-ordering valid until the present moment and dividing any totality into two parts: the well-ordered of the past and the yet unordered of the future therefore sharing the common boundary of the present between them when the ordering is (...)
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  16. The Equivalence of Definitions of Algorithmic Randomness†.Christopher Porter - forthcoming - Philosophia Mathematica:nkaa039.
    ABSTRACT In this paper, I evaluate the claim that the equivalence of multiple intensionally distinct definitions of random sequence provides evidence for the claim that these definitions capture the intuitive conception of randomness, concluding that the former claim is false. I then develop an alternative account of the significance of randomness-theoretic equivalence results, arguing that they are instances of a phenomenon I refer to as schematic equivalence. On my account, this alternative approach has the virtue of providing the plurality of (...)
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  17. There May Be Many Arithmetical Gödel Sentences.Kaave Lajevardi & Saeed Salehi - forthcoming - Philosophia Mathematica:nkaa041.
    We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.
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  18. Leonard Nelson: Mathematische Erkenntnis als synthetisches Apriori. In: Mathematik in der Tradition des Neukantianismus: Siegener Beiträge zur Geschichte und Philosophie der Mathematik, Ralf Krömer, Georg Nickel (Hrsg.). Bd. 11 (2019), S. 17–33.Kay Herrmann - 2019 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 11:17–33.
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  19. Three Letters on the Foundations of Mathematics by Frank Plumpton Ramsey†.Paolo Mancosu - forthcoming - Philosophia Mathematica.
    Summary This article presents three hitherto unpublished letters by Frank Plumpton Ramsey on the foundations of mathematics with commentary. One of the letters was sent to Abraham Fraenkel and the other two letters to Heinrich Behmann. The transcription of the letters is preceded by an account that details the extent of Ramsey's known contacts with mathematical logicians on the Continent.
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  20. Should Mathematicians Play Dice?Don Berry - 2019 - Logique Et Analyse 246 (62):135-160.
    It is an established part of mathematical practice that mathematicians demand -/- deductive proof before accepting a new result as a theorem. However, a wide -/- variety of probabilistic methods of justification are also available. Though such -/- procedures may endorse a false conclusion even if carried out perfectly, their -/- robust structure may mean they are actually more reliable in practice once implementation -/- errors are taken into account. Can mathematicians be rational -/- in continuing to reject these probabilistic (...)
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  21. Numerical Infinities Applied for Studying Riemann Series Theorem and Ramanujan Summation.Yaroslav Sergeyev - 2018 - In AIP Conference Proceedings 1978. AIP. pp. 020004.
    A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional methodologies studying (...)
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  22. Conceptual and Computational Mathematics†.Nicolas Fillion - 2019 - Philosophia Mathematica 27 (2):199-218.
    ABSTRACT This paper examines consequences of the computer revolution in mathematics. By comparing its repercussions with those of conceptual developments that unfolded in the nineteenth century, I argue that the key epistemological lesson to draw from the two transformative periods is that effective and successful mathematical practices in science result from integrating the computational and conceptual styles of mathematics, and not that one of the two styles of mathematical reasoning is superior. Finally, I show that the methodology deployed by applied (...)
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  23. Intuitive and Regressive Justifications†.Michael Potter - 2020 - Philosophia Mathematica 28 (3):385-394.
    In his recent book, Quine, New Foundations, and the Philosophy of Set Theory, Sean Morris attempts to rehabilitate Quine’s NF as a possible foundation for mathematics. I explain why he does not succeed.
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  24. Emily Rolfe* Great Circles: The Transits of Mathematics and Poetry.Jean Paul Van Bendegem & Bart Van Kerkhove - 2020 - Philosophia Mathematica 28 (3):431-441.
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  25. Structuralism and Mathematical Practice in Felix Klein’s Work on Non-Euclidean Geometry†.Biagioli Francesca - 2020 - Philosophia Mathematica 28 (3):360-384.
    It is well known that Felix Klein took a decisive step in investigating the invariants of transformation groups. However, less attention has been given to Klein’s considerations on the epistemological implications of his work on geometry. This paper proposes an interpretation of Klein’s view as a form of mathematical structuralism, according to which the study of mathematical structures provides the basis for a better understanding of how mathematical research and practice develop.
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  26. Gerhard Jäger* and Wilfried Sieg.** Feferman on Foundations: Logic, Mathematics, Philosophy.Reinhard Kahle - 2020 - Philosophia Mathematica 28 (3):421-425.
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  27. Erich Reck* and Georg Schiemer.** The Prehistory of Mathematical Structuralism.Jean-Pierre Marquis - 2020 - Philosophia Mathematica 28 (3):416-420.
    _Erich Reck* * and Georg Schiemer.** ** The Prehistory of Mathematical Structuralism. _Oxford University Press, 2020. Pp. 454. ISBN: 978-0-19-064122-1 ; 978-0-19-064123-8. doi: 10.1093/oso/9780190641221.001.0001.
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  28. Introduction to Special Issue: Foundations of Mathematical Structuralism.Georg Schiemer & John Wigglesworth - 2020 - Philosophia Mathematica 28 (3):291-295.
    Structuralism, the view that mathematics is the science of structures, can be characterized as a philosophical response to a general structural turn in modern mathematics. Structuralists aim to understand the ontological, epistemological, and semantical implications of this structural approach in mathematics. Theories of structuralism began to develop following the publication of Paul Benacerraf’s paper ‘What numbers could not be’ in 1965. These theories include non-eliminative approaches, formulated in a background ontology of sui generis structures, such as Stewart Shapiro’s ante rem (...)
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  29. Justin Clarke-Doane* Morality and Mathematics.Michael Bevan & A. C. Paseau - 2020 - Philosophia Mathematica 28 (3):442-446.
    _Justin Clarke-Doane* * Morality and Mathematics. _ Oxford University Press, 2020. Pp. xx + 208. ISBN: 978-0-19-882366-7 ; 978-0-19-2556806.† †.
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  30. Tim Button and Sean Walsh* Philosophy and Model Theory.Brice Halimi - 2020 - Philosophia Mathematica 28 (3):404-415.
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  31. Luca Incurvati* Conceptions of Set and the Foundations of Mathematics.Burgess John - 2020 - Philosophia Mathematica 28 (3):395-403.
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  32. Matthias Wille.* ›Largely unknown‹ Gottlob Frege und der posthume Ruhm ›alles in den Wind geschrieben‹ Gottlob Frege wider den Zeitgeist.Ansten Klev - 2020 - Philosophia Mathematica 28 (3):426-430.
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  33. Structuralist Neologicism†.Francesca Boccuni & Jack Woods - 2020 - Philosophia Mathematica 28 (3):296-316.
    Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all properties of the numbers, achieving a key (...)
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  34. On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A†.Hannes Leitgeb - 2020 - Philosophia Mathematica 28 (3):317-346.
    This is Part A of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of non-eliminative structuralism. Afterwards, it motivates an understanding of unlabeled graphs as structures sui generis and develops a corresponding axiomatic theory of unlabeled graphs. As the theory demonstrates, graph theory can be developed consistently without eliminating unlabeled graphs in favour of sets; and the usual structuralist criterion of identity can (...)
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  35. An ‘I’ for an I, a Truth for a Truth†.Mary Leng - 2020 - Philosophia Mathematica 28 (3):347-359.
    Stewart Shapiro’s ante rem structuralism recognizes the structural or ‘algebraic’ aspects of mathematical practice while still offering a face-value semantics. Fictionalism, as a purely ‘algebraic’ approach, is held to be at a disadvantage, as compared with Shapiro’s structuralism, in not interpreting mathematics at face value. However, the face-value reading of mathematical singular terms has difficulty explaining how we can use such terms to pick out a unique referent in cases where the relevant mathematical structures admit non-trivial automorphisms. Shapiro offers a (...)
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  36. Frege, Hankel, and Formalism in the Foundations.Richard Lawrence - forthcoming - Journal for the History of Analytical Philosophy.
    Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program ``could be called formal'' but is ``completely different'' from the view he has just criticized. This essay examines Frege's relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege's foundational program actually has quite a lot in common with Hankel's. This undercuts Frege's claim that (...)
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  37. Infinite Lotteries, Spinners, Applicability of Hyperreals†.Emanuele Bottazzi & Mikhail G. Katz - forthcoming - Philosophia Mathematica.
    We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fields can be avoided by working in the Kanovei–Shelah model or in saturated models. We argue that some of the objections to hyperreal probabilities arise from hidden biases that favor Archimedean models. We discuss the advantage of the hyperreals over transferless fields with infinitesimals. In Paper II we analyze two underdetermination theorems by Pruss and (...)
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  38. Internality, Transfer, and Infinitesimal Modeling of Infinite Processes†.Emanuele Bottazzi & Mikhail G. Katz - forthcoming - Philosophia Mathematica.
    ABSTRACTA probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson’s transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields may have advantages over hyperreals in probabilistic modeling. (...)
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  39. Conscious Experience and Designing User Experiences.Venkata Rayudu Posina - manuscript
    Neuroscientific discourse on consciousness often resorts to "collection of elements", notwithstanding the Gestalt demonstrations against representing conscious experience as a collection of sensory elements. Here I show that defining conscious experience as an object of the category of conscious experiences, instead of as cohesion-less set of structure-less elements, provides the conceptual repertoire—basic shapes, figures, and incidence relations—needed to reason about the essence of conscious experiences and the essence-preserving transformations of conscious experiences. Viewed in light of the category of conscious experiences, (...)
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  40. Objective Logic of Consciousness.Venkata Rayudu Posina & Sisir Roy - forthcoming - In 14th Nalanda Dialogue.
    We define consciousness as the category of all conscious experiences. This immediately raises the question: What is the essence in which every conscious experience in the category of conscious experiences partakes? We consider various abstract essences of conscious experiences as theories of consciousness. They are: (i) conscious experience is an action of memory on sensation, (ii) conscious experience is experiencing a particular as an exemplar of a general, (iii) conscious experience is an interpretation of sensation, (iv) conscious experience is referring (...)
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  41. Truth Through Nonviolence.Venkata Rayudu Posina - 2016 - GITAM Journal of Gandhian Studies 5 (1):143-150.
    What is reality? How do we know? Answers to these fundamental questions of ontology and epistemology, based on Mahatma Gandhi's "experiments with truth", are: reality is nonviolent (in the sense of not-inconsistent), and nonviolence (in the sense of respecting-meaning) is the only means of knowing (Gandhi, 1940). Be that as it may, science is what we think of when we think of reality and knowing. How does Gandhi's nonviolence, discovered in his spiritual quest for Truth, relate to the scientific pursuit (...)
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  42. Persi Diaconis and Brian Skyrms. Ten Great Ideas About Chance.Christian Hennig - 2020 - Philosophia Mathematica 28 (2):282-285.
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  43. Reflections on Frege’s Theory of Real Numbers†.Peter Roeper - 2020 - Philosophia Mathematica 28 (2):236-257.
    ABSTRACT Although Frege’s theory of real numbers in Grundgesetze der Arithmetik, Vol. II, is incomplete, it is possible to provide a logicist justification for the approach he is taking and to construct a plausible completion of his account by an extrapolation which parallels his theory of cardinal numbers.
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  44. Geoffrey Hellman* and Stewart Shapiro.**Mathematical Structuralism. Cambridge Elements in the Philosophy of Mathematics, Penelope Rush and Stewart Shapiro, Eds.Andrea Sereni - 2020 - Philosophia Mathematica 28 (2):277-281.
    HellmanGeoffrey ** and ShapiroStewart. **** Mathematical Structuralism. Cambridge Elements in the Philosophy of Mathematics, RushPenelope and ShapiroStewart, eds. Cambridge University Press, 2019. Pp. iv + 94. ISBN 978-1-108-45643-2, 978-1-108-69728-6. doi: 10.1017/9781108582933.
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