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  1. Mathematical Explanations of Physical Phenomena.Sorin Bangu - forthcoming - Tandf: Australasian Journal of Philosophy:1-14.
    Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.
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  2. Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
  3. Structuralism and the Applicability of Mathematics.Jairo José Silvdaa - forthcoming - Axiomathes.
    In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
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  4. The Reasonable Effectiveness of Mathematics in the Natural Sciences.László Tisza - forthcoming - Boston Studies in the Philosophy of Science.
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  5. Mathematics as a Science of Non-Abstract Reality: Aristotelian Realist Philosophies of Mathematics.James Franklin - 2021 - Foundations of Science 26:1-18.
    There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...)
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  6. A Dilemma for Mathematical Constructivism.Samuel Kahn - 2021 - Axiomathes 31 (1):63-72.
    In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...)
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  7. Is Mathematics Unreasonably Effective?Daniel Waxman - 2021 - Australasian Journal of Philosophy 99 (1):83-99.
    Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural science is mysterious. This paper sharpens and responds to a challenge to this effect. I argue that the aesthetic considerations used to evaluate and motivate mathematics are much more closely connected with the physical world than one might presume, and (with reference to case-studies within Galois theory and probabilistic number theory) show that they are correlated with (...)
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  8. Formal Semantics and Applied Mathematics: An Inferential Account.Ryan M. Nefdt - 2020 - Journal of Logic, Language and Information 29 (2):221-253.
    In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan : 345–374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying indirectly to linguistic (...)
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  9. The Principle of Equivalence as a Criterion of Identity.Ryan Samaroo - 2020 - Synthese 197 (8):3481-3505.
    In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...)
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  10. असंभव, अपूर्णता, अपूर्णता, झूठा विरोधाभास, सिद्धांतवाद, गणना की सीमा, एक गैर-क्वांटम यांत्रिक अनिश्चितता सिद्धांत और कंप्यूटर के रूप में ब्रह्मांड पर Wolpert, Chaitin और Wittgenstein ट्यूरिंग मशीन थ्योरी में अंतिम प्रमेय --Wolpert, Chaitin and Wittgenstein on impossibility, incompleteness, the liar paradox, theism, the limits of computation, a non-quantum mechanical uncertainty principle and the universe as computer—the ultimate theorem in Turing Machine Theory (संशोधित 2019).Michael Richard Starks - 2020 - In पृथ्वी पर नर्क में आपका स्वागत है: शिशुओं, जलवायु परिवर्तन, बिटकॉइन, कार्टेल, चीन, लोकतंत्र, विविधता, समानता, हैकर्स, मानव अधिकार, इस्लाम, उदारवाद, समृद्धि, वेब, अराजकता, भुखमरी, बीमारी, हिंसा, कृत्रिम बुद्धिमत्ता, युद्ध. Las Vegas, NV, USA: Reality Press. pp. 215-220.
    मैं कंप्यूटर के रूप में गणना और ब्रह्मांड की सीमा के कई हाल ही में चर्चा पढ़ लिया है, polymath भौतिक विज्ञानी और निर्णय सिद्धांतकार डेविड Wolpert के अद्भुत काम पर कुछ टिप्पणी खोजने की उम्मीद है, लेकिन एक भी प्रशस्ति पत्र नहीं मिला है और इसलिए मैं यह बहुत संक्षिप्त मौजूद सारांश. Wolpert कुछ आश्चर्यजनक असंभव या अधूरापन प्रमेयों साबित कर दिया (1992 से 2008-देखें arxiv dot org) अनुमान के लिए सीमा पर (कम्प्यूटेशन) कि इतने सामान्य वे गणना कर (...)
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  11. Supertasks and Arithmetical Truth.Jared Warren & Daniel Waxman - 2020 - Philosophical Studies 177 (5):1275-1282.
    This paper discusses the relevance of supertask computation for the determinacy of arithmetic. Recent work in the philosophy of physics has made plausible the possibility of supertask computers, capable of running through infinitely many individual computations in a finite time. A natural thought is that, if supertask computers are possible, this implies that arithmetical truth is determinate. In this paper we argue, via a careful analysis of putative arguments from supertask computations to determinacy, that this natural thought is mistaken: supertasks (...)
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  12. Infinity and the Foundations of Linguistics.Ryan Nefdt - 2019 - Synthese 196 (5):1671-1711.
    The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal apparatus of (...)
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  13. Revisão de ' Os Limites Exteriores da Razão ' (The Outer Limits of Reason)Por Noson Yanofsky 403p (2013) (Revisão Revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 188-202.
    Eu dou uma revisão detalhada de "os limites exteriores da razão" por Noson Yanofsky de uma perspectiva unificada de Wittgenstein e psicologia evolutiva. Eu indico que a dificuldade com tais questões como paradoxo na linguagem e matemática, incompletude, undecidabilidade, computabilidade, o cérebro eo universo como computadores, etc., todos surgem a partir da falta de olhar atentamente para o nosso uso da linguagem no apropriado contexto e, consequentemente, a falta de separar questões de fato científico a partir de questões de como (...)
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  14. The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic Oscillator.Sorin Bangu & Robert H. C. Moir - 2018 - Foundations of Physics 48 (5):507-525.
    The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of (...)
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  15. Filosofia Aplicabilitatii Matematicii: Intre Irational si Rational.Catalin Barboianu - 2018 - Târgu Jiu, Romania: Infarom.
    Lucrarea tratează unul dintre “misterele” filosofiei analitice şi ale raţionalităţii însăşi, anume aplicabilitatea matematicii în ştiinţe şi în investigarea matematică a realităţii înconjurătoare, a cărei filosofie este dezvoltată în jurul sintagmei – de acum paradigmatice – ‘eficacitatea iraţională a matematicii’, aparţinând fizicianului Eugene Wigner, problemă filosofică etichetată în literatură drept “puzzle-ul lui Wigner”. Odată intraţi în profunzimea acestei probleme, investigaţia nu trebuie limitată la căutarea unor răspunsuri explicative la întrebări precum “Ce este de fapt aplicabilitatea matematicii?”, “Cum explicăm prezenţa în (...)
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  16. Scientific Explanation, Unifying Mathematics, and Indispensability Arguments.Patrick Dieveney - 2018 - Synthese 198 (1):57-77.
    Indispensability arguments occupy a prominent role in discussions of mathematical realism. While different versions of these arguments are discussed in the literature, their general structure remains the same. These arguments contend that insofar as reference to mathematical objects is indispensable to science, we are committed to the existence of these ‘objects’. Unsurprisingly, much of the debate concerning indispensability arguments focuses on the crucial contention that mathematical objects are indispensable to science. For these arguments to provide support for mathematical realism, what (...)
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  17. Applicability Problems Generalized.Michele Ginammi - 2018 - In Gabriele Pulcini & Mario Piazza (eds.), Truth, Existence and Explanation. Springer Verlag. pp. 209-224.
    In this paper, I will do preparatory work for a generalized account of applicability, that is, for an account which works for math-to-physics, math-to-math, and physics-to-math application. I am going to present and discuss some examples of these three kinds of application, and I will confront them in order to see whether it is possible to find analogies among them and whether they can be ultimately considered as instantiations of a unique pattern. I will argue that these analogies can be (...)
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  18. Reconstruction in Philosophy of Mathematics.Davide Rizza - 2018 - Dewey Studies 2 (2):31-53.
    Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...)
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  19. Mathematics and Explanatory Generality.Alan Baker - 2017 - Philosophia Mathematica 25 (2):194-209.
    According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that (...)
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  20. Mathematical Spandrels.Alan Baker - 2017 - Australasian Journal of Philosophy 95 (4):779-793.
    The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on (...)
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  21. Rolul constitutiv al matematicii in stiinta structurala.Catalin Barboianu - 2017 - Târgu Jiu, Romania: Infarom.
    Problemele filosofie sensibile pe care le pune aplicabilitatea matematicii în ştiinţe şi viaţa de zi cu zi au conturat, pe un fond interdisciplinar, o nouă “ramură” a filosofiei ştiinţei, anume filosofia aplicabilităţii matematicii. Aplicarea cu succes a matematicii de-a lungul istoriei ştiinţei necesită reprezentare, încadrare, explicaţie, dar şi o justificare de ordin metateoretic a aplicabilităţii. Între rolurile matematicii în practica ştiinţifică, rolul constitutiv teoriilor ştiinţifice este cel a cărui analiză poate contribui esenţial la această justificare. În lucrarea de faţă, am (...)
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  22. The Applicability of Mathematics to Physical Modality.Nora Berenstain - 2017 - Synthese 194 (9):3361-3377.
    This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal structure of (...)
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  23. 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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  24. Early Modern Mathematical Principles and Symmetry Arguments.James Franklin - 2017 - In The Idea of Principles in Early Modern Thought Interdisciplinary Perspectives. New York, USA: Routledge. pp. 16-44.
    The leaders of the Scientific Revolution were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.
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  25. On The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Sorin Bangu - 2016 - In Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science. Springer. pp. 11-29.
    I present a reconstruction of Eugene Wigner’s argument for the claim that mathematics is ‘unreasonable effective’, together with six objections to its soundness. I show that these objections are weaker than usually thought, and I sketch a new objection.
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  26. Mathematical Explanation and Epistemology: Please Mind the Gap.Sam Baron - 2016 - Ratio 29 (2):149-167.
    This paper draws together two strands in the debate over the existence of mathematical objects. The first strand concerns the notion of extra-mathematical explanation: the explanation of physical facts, in part, by facts about mathematical objects. The second strand concerns the access problem for platonism: the problem of how to account for knowledge of mathematical objects. I argue for the following conditional: if there are extra-mathematical explanations, then the core thesis of the access problem is false. This has implications for (...)
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  27. Fundamentality, Effectiveness, and Objectivity of Gauge Symmetries.Aldo Filomeno - 2016 - International Studies in the Philosophy of Science 30 (1):19-37.
    Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully satisfactory. This is (...)
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  28. Creating a New Mathematics.Arran Gare - 2016 - In Ronny Desmet (ed.), Intuition in Mathematics and Physics. Anoka, MN, USA: pp. 146-164.
    The focus of this chapter is on efforts to create a new mathematics, with my prime interest being the role of mathematics in comprehending a world consisting first and foremost of processes, and examining what developments in mathematics are required for this. I am particularly interested in developments in mathematics able to do justice to the reality of life. Such mathematics could provide the basis for advancing ecology, human ecology and ecological economics and thereby assist in the transformation of society (...)
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  29. Avoiding Reification: Heuristic Effectiveness of Mathematics and the Prediction of the Omega Minus Particle.Michele Ginammi - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:20-27.
    According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne׳eman׳s prediction of the Ω− particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on (...)
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  30. The Applicability of Mathematics and the Indispensability Arguments.Michele Ginammi - 2016 - Lato Sensu, Revue de la Société de Philosophie des Sciences 3 (1).
    In this paper I will take into examination the relevance of the main indispensability arguments for the comprehension of the applicability of mathematics. I will conclude not only that none of these indispensability arguments are of any help for understanding mathematical applicability, but also that these arguments rather require a preliminary analysis of the problems raised by the applicability of mathematics in order to avoid some tricky difficulties in their formulations. As a consequence, we cannot any longer consider the applicability (...)
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  31. A Match Not Made in Heaven: On the Applicability of Mathematics in Physics.Arezoo Islami - 2016 - Synthese:1-23.
    In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been entirely overlooked due to an exclusive concern with solving Wigner’s problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner’s unjustified conclusion—that mathematics is unreasonably effective in the natural sciences—to his formalist views on mathematics. My goal is to show (...)
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  32. Applied Mathematics in the World of Complexity.V. P. Kazaryan - 2016 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 5 (1):3.
    In modern mathematics the value of applied research increases, for this reason, modern mathematics is initially focused on resolving the situation actually arose in this respect on a par with other disciplines. Using a new tool - computer systems, applied mathematics appealed to the new object: not to nature, not to society or the practical activity of man. In fact, the subject of modern applied mathematics is a problem situation for the actor-person, and the study is aimed at solving the (...)
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  33. Divergent Mathematical Treatments in Utility Theory.Davide Rizza - 2016 - Erkenntnis 81 (6):1287-1303.
    In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection (...)
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  34. Logic, Physics and Intuition.Peter Clark - 2015 - Philosophical Inquiry 39 (1):38-48.
    This paper is addressed to the problem of how is applied mathematics possible?
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  35. Numerical Methods, Complexity, and Epistemic Hierarchies.Nicolas Fillion & Sorin Bangu - 2015 - Philosophy of Science 82 (5):941-955.
    Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a (...)
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  36. Proof Phenomenon as a Function of the Phenomenology of Proving.Inês Hipólito - 2015 - Progress in Biophysics and Molecular Biology 119:360-367.
    Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...)
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  37. Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on M-Adic Trees.Giuseppe Iurato & Andrei Khrennikov - 2015 - P-Adic Numbers, Ultrametric Analysis, and Applications 7 (4):312-321.
    In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers.
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  38. From Mathematics to Quantum Mechanics - On the Conceptual Unity of Cassirer’s Philosophy of Science.Thomas Mormann - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 31-64.
  39. Abstract Explanations in Science.Christopher Pincock - 2015 - British Journal for the Philosophy of Science 66 (4):857-882.
    This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations.explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to unify (...)
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  40. Nonstandard Utilities for Lexicographically Decomposable Orderings.Davide Rizza - 2015 - Journal of Mathematical Economics 1 (60):105-109.
    Using a basic theorem from mathematical logic, I show that there are field-extensions ofRon which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the lexicographic ordering (...)
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  41. Are There Genuine Physical Explanations of Mathematical Phenomena?Bradford Skow - 2015 - British Journal for the Philosophy of Science 66 (1):69-93.
    There are lots of arguments for, or justifications of, mathematical theorems that make use of principles from physics. Do any of these constitute explanations? On the one hand, physical principles do not seem like they should be explanatorily relevant; on the other, some particular examples of physical justifications do look explanatory. In this article, I defend the idea that physical justifications can and do explain mathematical facts. 1 Physical Arguments for Mathematical Truths2 Preview3 Mathematical Facts4 Purity5 Doubts about Purity: I6 (...)
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  42. Global and Local.James Franklin - 2014 - Mathematical Intelligencer 36 (4).
    The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...)
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  43. Applicability, Indispensability, and Underdetermination: Puzzling Over Wigner’s ‘Unreasonable Effectiveness of Mathematics’.Axel Gelfert - 2014 - Science & Education 23 (5):997-1009.
    In his influential 1960 paper ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts—mathematics—should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has developed ‘Wigner’s puzzle’ in two different directions: First, in relation to the supposed indispensability of mathematical facts to particular scientific explanations and, secondly, in connection with the idea that aesthetic criteria track (...)
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  44. Mathematical Representation: Playing a Role.Kate Hodesdon - 2014 - Philosophical Studies 168 (3):769-782.
    The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead explains the (...)
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  45. The Application of Mathematics in Science: Sorin Bangu: The Applicability of Mathematics in Science: Indispensability and Ontology. London: Palgrave Macmillan, 2012, Xii+252pp, £55 HB.Alex Koo - 2014 - Metascience 23 (2):263-268.
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  46. Abstract Expressionism and the Communication Problem.David Liggins - 2014 - British Journal for the Philosophy of Science 65 (3):599-620.
    Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...)
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  47. Mindful Physics — A NEW ACCOUNT OF WHAT HAPPENS.Desmond Sander - 2014 - AENESIDEMUS PRESS.
    A physics that fails to take account of minds, or account for them, cannot be quite right; a physics that accounts so beautifully and so powerfully for so much of what we observe cannot be quite wrong. This book had that conundrum as its starting point, and resolves it. The mindful physics we need is complementary to the compelling and successful but mind-ignoring physics of today. It is the physics that life, especially human life, has made and is making here (...)
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  48. The Mystery of Applied Mathematics?: A Case Study in Mathematical Development Involving the Fractional Derivative†: Articles.Sheldon R. Smith - 2014 - Philosophia Mathematica 22 (1):35-69.
    I discuss the applicability of mathematics via a detailed case study involving a family of mathematical concepts known as ‘fractional derivatives.’ Certain formulations of the mystery of applied mathematics would lead one to believe that there ought to be a mystery about the applicability of fractional derivatives. I argue, however, that there is no clear mystery about their applicability. Thus, via this case study, I think that one can come to see more clearly why certain formulations of the mystery of (...)
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  49. Critical Review of Mathematics and Scientific Representation. [REVIEW]Sean Walsh, Eleanor Knox & Adam Caulton - 2014 - Philosophy of Science 81 (3):460-469.
  50. Chris Pincock , Mathematics and Scientific Representation . Reviewed By. [REVIEW]Sam Baron - 2013 - Philosophy in Review 33 (1):63-66.