Philosophy of Mathematics

Edited by Øystein Linnebo (University of Oslo)
Assistant editor: Sam Roberts (Birkbeck College, University of Oslo)
29 found
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  1. added 2018-06-20
    Robert Lorne Victor Hale FRSE May 4, 1945 – December 12, 2017.Roy T. Cook & Stewart Shapiro - 2018 - Philosophia Mathematica 26 (2):266-274.
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  2. added 2018-06-20
    Fitting Feelings and Elegant Proofs: On the Psychology of Aesthetic Evaluation in Mathematics†.Cain Todd - 2018 - Philosophia Mathematica 26 (2):211-233.
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  3. added 2018-06-19
    Physical Foundations of Mathematics (In Russian).Andrey Smirnov - manuscript
    The physical foundations of mathematics in the theory of emergent space-time-matter were considered. It is shown that mathematics, including logic, is a consequence of equation which describes the fundamental field. If the most fundamental level were described not by mathematics, but something else, then instead of mathematics there would be consequences of this something else.
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  4. added 2018-06-14
    Modal Structuralism and Reflection.Sam Roberts - forthcoming - Review of Symbolic Logic:1-38.
    Modal structuralism promises an interpretation of set theory that avoids commitment to abstracta. This article investigates its underlying assumptions. In the first part, I start by highlighting some shortcomings of the standard axiomatisation of modal structuralism, and propose a new axiomatisation I call MSST (for Modal Structural Set Theory). The main theorem is that MSST interprets exactly Zermelo set theory plus the claim that every set is in some inaccessible rank of the cumulative hierarchy. In the second part of the (...)
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  5. added 2018-06-13
    Einführung in die Philosophie der Mathematik.Jörg Neunhäuserer - forthcoming - Wiesbaden, Deutschland: Springer Spektrum.
    Inhaltsverzeichnis (vorläufig) 1 Einführung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 -/- 2 Pythagorismus . . . . . . . . . . . . . . . . . . . . . . . . . (...)
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  6. added 2018-06-12
    Execution of the Universal Dream.Sergey Kljujkov - manuscript
    Even the ancient Greeks defined the Dream as a happy πόλις, Heraclitus - κόσμοπόλις, Socrates - ethical anthropology, Plato - Good, Hegel - absolute idea, Marx - communism... All of Humanity has made a lot of its survival experience for the realization of Dreams. Without any plan, to the touch to, only by the method of "trial and error" it aspired the Dream on unknown roads, which often stymied deadlocks. Among the many achieved results of Humanity by Plato's prompts, the (...)
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  7. added 2018-06-08
    Note on the Significance of the New Logic.Frederique Janssen-Lauret - 2018 - The Reasoner 6 (12):47-48.
    Brief note explaining the content, importance, and historical context of my joint translation of Quine's The Significance of the New Logic with my single-authored historical-philosophical essay 'Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s'.
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  8. added 2018-06-07
    Lautman on Problems as the Conditions of Existence of Solutions.Simon B. Duffy - 2018 - Angelaki 23 (2):79-93.
    Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...)
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  9. added 2018-06-06
    Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  10. added 2018-05-30
    Syntax Meets Semantics During Brain Logical Computations.Arturo Tozzi, James F. Peters, Andrew And Alexander Fingelkurts & Leonid Perlovsky - forthcoming - Progress in Biophysics and Molecular Biology (in-press).
    The discrepancy between syntax and semantics is a painstaking issue that hinders a better comprehension of the underlying neuronal processes in the human brain. In order to tackle the issue, we at first describe a striking correlation between Wittgenstein's Tractatus, that assesses the syntactic relationships between language and world, and Perlovsky's joint language-cognitive computational model, that assesses the semantic relationships between emotions and “knowledge instinct”. Once established a correlation between a purely logical approach to the language and computable psychological activities, (...)
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  11. added 2018-05-29
    Kondratieff Waves in the Global Studies Perspective.Leonid Grinin & Andrey Korotayev - 2014 - In Leonid Grinin, Ilya V. Ilyin & Andrey V. Korotayev (eds.), Globalistics and Globalization Studies. Volgograd: Uchitel Publishing House. pp. 65-98.
    The analysis of long economic cycles allows us to understand long-term worldsystem dynamics, to develop forecasts, to explain crises of the past, as well as the current global economic crisis. The article offers a historical sketch of research on K-waves; it analyzes the nature of Kondratieff waves that are considered as a special form of cyclical dynamics that emerged in the industrial period of the World System history. It offers a historical and theoretical analysis of K-wave dynamics in the World (...)
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  12. added 2018-05-11
    What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscript
    Introduction to mathematical logic, part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.
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  13. added 2018-05-09
    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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  14. added 2018-05-03
    The Significance of the New Logic.Walter Carnielli, Frederique Janssen-Lauret & William Pickering (eds.) - 2018 - Cambridge University Press.
    W. V. Quine was one of the most influential figures of twentieth-century American analytic philosophy. Although he wrote predominantly in English, in Brazil in 1942 he gave a series of lectures on logic and its philosophy in Portuguese, subsequently published as the book O Sentido da Nova Lógica. The book has never before been fully translated into English, and this volume is the first to make its content accessible to Anglophone philosophers. Quine would go on to develop revolutionary ideas about (...)
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  15. added 2018-05-01
    The Significance of the New Logic.W. V. Quine, Frederique Janssen-Lauret, Walter Carnielli & William Pickering - 2018 - Cambridge: Cambridge University Press.
    W. V. Quine was one of the most influential figures of twentieth-century American analytic philosophy. Although he wrote predominantly in English, in Brazil in 1942 he gave a series of lectures on logic and its philosophy in Portuguese, subsequently published as the book O Sentido da Nova Lógica. The book has never before been fully translated into English, and this volume is the first to make its content accessible to Anglophone philosophers. Quine would go on to develop revolutionary ideas about (...)
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  16. added 2018-04-30
    Tuples All the Way Down?Simon Thomas Hewitt - forthcoming - Thought: A Journal of Philosophy.
  17. added 2018-04-30
    The Because of Because Without Cause†.Daniele Molinini - 2018 - Philosophia Mathematica 26 (2):275-286.
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  18. added 2018-04-30
    World to Word: Nomenclature Systems of Color and Species.Tanya Kelley - 2017 - Dissertation, University Of Missouri
    As the digitization of information accelerates, the push to encode our surrounding numerically instead of linguistically increases. The role that language has traditionally played in the nomenclature of an integrative taxonomy is being replaced by the numeric identification of one or few quantitative characteristics. Nineteenth-century scientific systems of color identification divided, grouped, and named colors according to multiple characteristics. Now color identification relies on numeric values applied to spectrographic readings. This means of identification of color lacks the taxonomic rigor of (...)
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  19. added 2018-04-29
    Definition in Mathematics.Carlo Cellucci - forthcoming - European Journal for Philosophy of Science:1-25.
    In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.
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  20. added 2018-04-28
    A Role for Representation Theorems.Emiliano Ippoliti - forthcoming - Philosophia Mathematica:nky007.
    I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into (...)
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  21. added 2018-04-18
    Aristoteles’in Matematik Felsefesi ve Matematik Soyut­lama.Murat Kelikli - 2017 - Beytulhikme An International Journal of Philosophy 7 (2):33-49.
    Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea­ son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the (...)
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  22. added 2018-04-12
    An ‘I’ for an I, a Truth for a Truth.Mary Leng - forthcoming - Philosophia Mathematica:nky005.
    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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  23. added 2018-04-03
    Existence, Mathematical Nominalism, and Meta-Ontology: An Objection to Azzouni on Criteria for Existence.Farbod Akhlaghi-Ghaffarokh - 2018 - Philosophia Mathematica 26 (2):251-265.
    Jody Azzouni argues that whilst it is indeterminate what the criteria for existence are, there is a criterion that has been collectively adopted to use ‘exist’ that we can employ to argue for positions in ontology. I raise and defend a novel objection to Azzouni: his view has the counterintuitive consequence that the facts regarding what exists can and will change when users of the word ‘exist’ change what criteria they associate with its usage. Considering three responses, I argue Azzouni (...)
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  24. added 2018-04-02
    Between Witches, Angels and Unicorns. The Possibility of Expanding Russell´s Existential Analysis.Olga Ramirez Calle - 2018 - E-Logos Electronic Journal for Philosophy 25 (1):4-15.
    This paper attempts to be a contribution to the epistemological project of explaining complex conceptual structures departing from more basic ones. The central thesis of the paper is that there are what I call “functionally structured concepts”, these are non-harmonic concepts in Dummett’s sense that might be legitimized if there is a function that justifies the tie between the inferential connection the concept allows us to trace. Proving this requires enhancing the russellian existential analysis of definite descriptions to apply to (...)
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  25. added 2018-03-31
    Our Incorrigible Ontological Relations and Categories of Being.Julian M. Galvez Bunge (ed.) - 2017 - Buenos Aires: Amazon.
    The object of this book is to present a radical novel conception of the ontological categories, their nature and epistemic importance. A conception that constitutes a challenge to the prevailing tenets, if not paradigms, of ontology today. The arguments and observations are given without addressing nor directly contesting the current theories on the subject. However, its author emphasises some of the main conclusions that entail from the new perspective, in particular regarding the role of philosophy among the sciences. Departing from (...)
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  26. added 2018-03-29
    Research Habits in Financial Modelling: The Case of Non-Normativity of Market Returns in the 1970s and the 1980s.Boudewijn De Bruin & Christian Walter - 2017 - In Emiliano Ippoliti & Ping Chen (eds.), Methods and Finance: A Unifying View on Finance, Mathematics, and Philosophy. Cham: Springer. pp. 73-93.
    In this chapter, one considers finance at its very foundations, namely, at the place where assumptions are being made about the ways to measure the two key ingredients of finance: risk and return. It is well known that returns for a large class of assets display a number of stylized facts that cannot be squared with the traditional views of 1960s financial economics (normality and continuity assumptions, i.e. Brownian representation of market dynamics). Despite the empirical counterevidence, normality and continuity assumptions (...)
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  27. added 2018-03-27
    Conversational Exculpature.Daniel Hoek - 2018 - Philosophical Review 127 (2):151-196.
    Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say “Rob is six feet tall” without implying that Rob is between 5'0.99" and 6'0.01" tall, and why we can say “Ellen has a hat like the one Sherlock Holmes always wears” without implying Holmes exists or has a hat. This article presents a simple formalism for understanding this pragmatic mechanism, specifying how, (...)
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  28. added 2018-03-26
    Iconicity and Abduction.Rocco Gangle & Gianluca Caterina - 2016 - New York, USA: Springer.
  29. added 2018-03-25
    Categories and Language.Jesús Gerardo Martínez del Castillo - 2015 - International Journal of Language and Linguistics 3 (6-1):96-104.
    Language exists because human subjects define themselves in the circumstance they are in. This is possible because they are able to know, not directly through their senses only, but adding something new to the construct they create in their conscience. The main thing they add to the construct created is categories, something invented or fabricated by the human subject at the moment of speaking.
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