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  1. Mathematics as an Exact and Precise Language of Nature.Dr Afsar Abbas - manuscript
    One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is offered here. This will allow us to appreciate the manner in which mathematics acts as an exact and precise language of nature. This has significant implications for Artificial Intelligence.
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  2. The Relation of Mathematics to the Other Sciences.Evandro Agazzi - 1997 - In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today. Kluwer Academic Publishers. pp. 235--259.
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  3. Methodological Problems of Mathematical Modeling in Natural Science.I. A. Akchurin, M. F. Vedenov & Iu V. Sachkov - 1966 - Russian Studies in Philosophy 5 (2):23-34.
    The constantly accelerating progress of contemporary natural science is indissolubly associated with the development and use of mathematics and with the processes of mathematical modeling of the phenomena of nature. The essence of this diverse and highly fertile interaction of mathematics and natural science and the dialectics of this interaction can only be disclosed through analysis of the nature of theoretical notions in general. Today, above all in the ranks of materialistically minded researchers, it is generally accepted that theory possesses (...)
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  4. Sameness of Age Cohorts in the Mathematics of Population Growth.Abraham Akkerman - 1994 - British Journal for the Philosophy of Science 45 (2):679-691.
    The axiom of extensionality of set theory states that any two classes that have identical members are identical. Yet the class of persons age i at time t and the class of persons age i + 1 at t + l, both including same persons, possess different demographic attributes, and thus appear to be two different classes. The contradiction could be resolved by making a clear distinction between age groups and cohorts. Cohort is a multitude of individuals, which is constituted (...)
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  5. Troubles with Indispensability: Applying Pure Mathematics in Physical Theory.Peressini Anthony - 1997 - Philosophia Mathematica 5 (3):210-227.
    Much of the current thought concerning mathematical ontology in volves in some way the Quine/Putnam indispensability argument. The indispensability approach needs to be more thoroughly specified, however, before substantive progress can be made in assessing it. To this end I examine in some detail the ways in which pure mathematics is applied to physical theory; such considerations give rise to three specific issues with which the indispensability approach must come to grips.
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  6. History and Philosophy of Modern Mathematics.William Aspray & Philip Kitcher - 1988
  7. Applying Mathematics.Jody Azzouni - 2000 - The Monist 83 (2):209-227.
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  8. Comments on Shapiro.Jody Azzouni - 1999 - Journal of Philosophy 96 (10):541-544.
  9. B. Réponses de l'Enquête Sur l'Enseignement de Mathématique Et de Physique B. Replies on the Teaching of Mathematics and Physics Reply to the Questionnaire.Kazimierz Badziag - 1967 - Dialectica 21 (1‐4):157-158.
  10. Mathematics and the Natural Sciences: The Physical Singularity of Life.Francis Bailly - 2010 - Imperial College Press.
    This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics.
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  11. Are There Genuine Mathematical Explanations of Physical Phenomena?Alan Baker - 2005 - Mind 114 (454):223-238.
    Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...)
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  12. Indexing and Mathematical Explanation.Alan Baker & Mark Colyvan - 2011 - Philosophia Mathematica 19 (3):323-334.
    We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...)
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  13. Review: Stewart Shapiro, Thinking About Mathematics. The Philosophy of Mathematics. [REVIEW]Mark Balaguer - 2002 - Bulletin of Symbolic Logic 8 (1):89-91.
  14. Do Mathematics Constitute a Scientific Continent?Aristides Baltas - 1995 - Neusis 3:97-108.
  15. Steiner on the Applicability of Mathematics and Naturalism.S. Bangu - 2006 - Philosophia Mathematica 14 (1):26-43.
    Steiner defines naturalism in opposition to anthropocentrism, the doctrine that the human mind holds a privileged place in the universe. He assumes the anthropocentric nature of mathematics and argues that physicists' employment of mathematically guided strategies in the discovery of quantum mechanics challenges scientists' naturalism. In this paper I show that Steiner's assumption about the anthropocentric character of mathematics is questionable. I draw attention to mathematicians' rejection of what Maddy calls ‘definabilism’, a methodological maxim governing the development of mathematics. I (...)
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  16. On The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Sorin Bangu - 2016 - In Ippoliti, Sterpetti & Nickles (eds.), Models and Inferences in Science. Springer. pp. 11-29.
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  17. The Applicability of Mathematics in Science: Indispensability and Ontology.Sorin Bangu - 2012 - Palgrave-Macmillan.
  18. Wigner's Puzzle for Mathematical Naturalism.Sorin Bangu - 2009 - International Studies in the Philosophy of Science 23 (3):245-263.
    I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist.
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  19. Reifying Mathematics? Prediction and Symmetry Classification.Sorin Bangu - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):239-258.
    In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. Gell-Mann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raised by (...)
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  20. Inference to the Best Explanation and Mathematical Realism.Sorin Ioan Bangu - 2008 - Synthese 160 (1):13-20.
    Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.
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  21. Philosophy of Mathematics as a Theoretical and Applied Discipline.A. G. Barabashev - 1989 - Philosophia Mathematica (2):121-128.
  22. 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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  23. Chris Pincock , Mathematics and Scientific Representation . Reviewed By. [REVIEW]Sam Baron - 2013 - Philosophy in Review 33 (1):63-66.
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  24. Review of I. Ekeland, The Broken Dice, and Other Mathematical Tales of Chance[REVIEW]Jeffrey A. Barrett - 1995 - Philosophia Mathematica 3 (3):310-313.
  25. Mathematical Explanation.John D. Barrow - 2004 - In John Cornwell (ed.), Explanations: Styles of Explanation in Science. Oxford University Press. pp. 81--109.
  26. On the Explanatory Role of Mathematics in Empirical Science.Robert Batterman - 2010 - British Journal for the Philosophy of Science 61 (1):1-25.
    This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.
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  27. 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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  28. Surprising User-Friendliness.Sandy Berkovski - 2002 - Logique Et Analyse 45 (179-180):283-297.
    Some theorists are bewildered by the effectiveness of mathematical concepts. For example, Steiner attempts to show that there can be no rational explanation of mathematical applicability in physics. Others (notably Penrose) are concerned primarily with the unexpected effectiveness within mathematics. Both views consist of two parts: a puzzle and a positive solution. I defend their paradoxical parts against the sceptics who do not believe that the very problem of effectiveness is a genuine one. Utilising Horwich’s theory of surprise, I argue (...)
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  29. Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'.H. Billinge - 2000 - British Journal for the Philosophy of Science 51 (2):299-318.
    claims that constructive mathematics is inadequate for spacetime physics and hence that constructive mathematics cannot be considered as an alternative to classical mathematics. He also argues that the contructivist must be guilty of a form of a priorism unless she adopts a strong form of anti-realism for science. Here I want to dispute both claims. First, even if there are non-constructive results in physics this does not show that adequate constructive alternatives could not be formulated. Secondly, the constructivist adopts a (...)
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  30. What is Applied Mathematics?James Robert Brown - 1997 - Foundations of Science 2 (1):21-37.
    A number of issues connected with the nature of applied mathematics are discussed. Among the claims are these: mathematics "hooks onto" the world by providing models or representations, not by describing the world; classic platonism is to be preferred to structuralism; and several issues in the philosophy of science are intimately connected to the nature of applied mathematics.
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  31. Justifying and Exploring Realistic Monism.Paul Budnik - manuscript
    The foundations of mathematics and physics no longer start with fundamental entities and their properties like spatial extension, points, lines or the billiard ball like particles of Newtonian physics. Mathematics has abolished these from its foundations in set theory by making all assumptions explicit and structural. Particle physics has become completely mathematical, connecting to physical reality only through experimental technique. Applying the principles guiding the foundations of mathematics and physics to philosophical analysis underscores that only conscious experience has an intrinsic (...)
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  32. An Easy Road to Nominalism.O. Bueno - 2012 - Mind 121 (484):967-982.
    In this paper, I provide an easy road to nominalism which does not rely on a Field-type nominalization strategy for mathematics. According to this proposal, applications of mathematics to science, and alleged mathematical explanations of physical phenomena, only emerge when suitable physical interpretations of the mathematical formalism are advanced. And since these interpretations are rarely distinguished from the mathematical formalism, the impression arises that mathematical explanations derive from the mathematical formalism alone. I correct this misimpression by pointing out, in the (...)
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  33. An Inferential Conception of the Application of Mathematics.Otávio Bueno & Mark Colyvan - 2011 - Noûs 45 (2):345-374.
    A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. (...)
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  34. Can Mathematics Explain Physical Phenomena?Otávio Bueno & Steven French - 2012 - British Journal for the Philosophy of Science 63 (1):85-113.
    Batterman raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan. Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within the (...)
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  35. How Foundational Work in Mathematics Can Be Relevant to Philosophy of Science.John P. Burgess - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:433 - 441.
    Foundational work in mathematics by some of the other participants in the symposium helps towards answering the question whether a heterodox mathematics could in principle be used as successfully as is orthodox mathematics in scientific applications. This question is turn, it will be argued, is relevant to the question how far current science is the way it is because the world is the way it is, and how far because we are the way we are, which is a central question, (...)
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  36. The Metaphysical Foundations of Modern Physical Science.Edwin A. Burtt - 1932 - Garden City, N.Y., Doubleday.
    CHAPTER I INTRODUCTION (A) Historical Problem Suggested by the Nature of Modern Thought How curious, after all, is the way in which we moderns think about ...
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  37. Mathematics and Logic: Response to Mark Wilson.O. Chateaubriand - 2008 - Manuscrito 31 (1):355-359.
    Mark Wilson argues that in order to make physical first-order properties suitable for inclusion in the bottom levels of a logical hierarchy of properties, their proper treatment must take into account the methods of applied mathematics. I agree that the methods of applied mathematics are essential for studying physical properties, and in my response focus on the nature of the logical hierarchy and on the requirements of classical logic.Mark Wilson argumenta que um tratamento adequado para tornar as propriedades físicas de (...)
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  38. Figuring Space Philosophy, Mathematics, and Physics.Gilles Châtelet - 2000
  39. Some Foundational Problems in Mathematics Suggested by Physics.Maria Luisa Dalla Chiara - 1985 - Synthese 62 (2):303 - 315.
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  40. Mathematical Understanding and the Physical Sciences.Harry Collins - 2007 - Studies in History and Philosophy of Science Part A 38 (4):667-685.
    The author claims to have developed interactional expertise in gravitational wave physics without engaging with the mathematical or quantitative aspects of the subject. Is this possible? In other words, is it possible to understand the physical world at a high enough level to argue and make judgments about it without the corresponding mathematics? This question is empirically approached in three ways: anecdotes about non-mathematical physicists are presented; the author undertakes a reflective reading of a passage of physics, first without going (...)
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  41. Review of M Steiner, 'The Application of Mathematics as a Philosophical Problem'. [REVIEW]M. Colyvan - 2000 - Mind 109 (No 434):390-394.
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  42. Applying Inconsistent Mathematics.Mark Colyvan - unknown
    At various times, mathematicians have been forced to work with inconsistent mathematical theories. Sometimes the inconsistency of the theory in question was apparent (e.g. the early calculus), while at other times it was not (e.g. pre-paradox na¨ıve set theory). The way mathematicians confronted such difficulties is the subject of a great deal of interesting work in the history of mathematics but, apart from the crisis in set theory, there has been very little philosophical work on the topic of inconsistent mathematics. (...)
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  43. The Miracle of Applied Mathematics.Mark Colyvan - 2001 - Synthese 127 (3):265-277.
    Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...)
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  44. Triangle of Thoughts.Alain Connes, André Lichnerowicz & Marcel P. Schützenberger - 2001
  45. Complementarity and Convergence in the Philosophies of Mathematics and Physics.David Corfield - 2006 - Metascience 15 (2):363-366.
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  46. Reflections on Michael Friedman's Dynamics of Reason.David Corfield - unknown
    Friedman's rich account of the way the mathematical sciences ideally are transformed affords mathematics a more influential role than is common in the philosophy of science. In this paper I assess Friedman's position and argue that we can improve on it by pursuing further the parallels between mathematics and science. We find a richness to the organisation of mathematics similar to that Friedman finds in physics.
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  47. The Spirit of Applied Mathematics.C. A. Coulson - 1953 - Oxford, Clarendon Press.
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  48. Applied Mathematics in the Sciences.Jacquette Dale - 2006 - Croatian Journal of Philosophy 17 (2):237-267.
    A complete philosophy of mathematics must address Paul Benacerraf’s dilemma. The requirements of a general semantics for the truth of mathematical theorems that coheres also with the meaning and truth conditions for non-mathematical sentences, according to Benacerraf, should ideally be coupled with an adequate epistemology for the discovery of mathematical knowledge. Standard approaches to the philosophy of mathematics are criticized against their own merits and against the background of Benacerraf’s dilemma, particularly with respect to the problem of understanding the distinction (...)
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  49. Bridging the Gap: Philosophy, Mathematics, and Physics.M. L. Dalla Chiara, G. Toraldo di Francia, G. Corsi & G. C. Ghirardi - 1993 - Boston Studies in the Philosophy of Science 140:261-283.
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  50. Mathematical Explanation and Indispensability Arguments.Chris Daly & Simon Langford - 2009 - Philosophical Quarterly 59 (237):641-658.
    We defend Joseph Melia's thesis that the role of mathematics in scientific theory is to 'index' quantities, and that even if mathematics is indispensable to scientific explanations of concrete phenomena, it does not explain any of those phenomena. This thesis is defended against objections by Mark Colyvan and Alan Baker.
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