Results for 'Mathematics'

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  1. A mathematical introduction to logic.Herbert Bruce Enderton - 1972 - New York,: Academic Press.
    A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with (...)
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  2.  1
    Classification Theory: Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985.J. T. Baldwin & U. Workshop on Model Theory in Mathematical Logic - 1987 - Springer.
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  3. Against Mathematical Explanation.Mark Zelcer - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):173-192.
    Lately, philosophers of mathematics have been exploring the notion of mathematical explanation within mathematics. This project is supposed to be analogous to the search for the correct analysis of scientific explanation. I argue here that given the way philosophers have been using “ explanation,” the term is not applicable to mathematics as it is in science.
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  4.  96
    Mathematical logic.Stephen Cole Kleene - 1967 - Mineola, N.Y.: Dover Publications.
    Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...)
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  5. A Lattice of Chapters of Mathematics.Jan Mycielski, Pavel Pudlák, Alan S. Stern & American Mathematical Society - 1990 - American Mathematical Society.
     
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  6.  60
    Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil.Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999 - American Mathematical Soc..
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...)
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  7. Mathematical logic.Willard Van Orman Quine - 1951 - Cambridge,: Harvard University Press.
    INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...
  8. Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
    This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of (...)--the view that mathematics is about things that really exist. (shrink)
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  9.  34
    Mathematics and Reality.Mary Leng - 2010 - Oxford: Oxford University Press.
    This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at (...)
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  10.  31
    Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
    On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.
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  11. Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.
    Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition (...)
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  12. Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both (...)
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  13.  55
    From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: Routledge.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more (...)
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  14.  3
    The mathematical philosophy of Bertrand Russell: origins and development.Francisco A. Rodríguez-Consuegra - 1991 - Boston: Birkhäuser Verlag.
    Traces the development of British philosopher Russell's (1872-1970) ideas on mathematics from the 1890s to the publication of his Principles of mathematics in 1903. Draws from Russell's unpublished manuscripts, correspondence, and published works to point out the influence of Hegel, Cantor, Whitehead, Peano, and others. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
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  15.  19
    Applying Mathematics: Immersion, Inference, Interpretation.Otávio Bueno & Steven French - 2018 - Oxford, England: Oxford University Press. Edited by Steven French.
    How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otavio Bueno and Steven French offer a middle way, which focuses on the moves that (...)
  16.  5
    Mathematical logic: a first course.Joel W. Robbin - 1969 - Mineola, N.Y.: Dover Publications.
    Suitable for advanced undergraduates and graduate students from diverse fields and varying backgrounds, this self-contained course in mathematical logic features numerous exercises that vary in difficulty. The author is a Professor of Mathematics at the University of Wisconsin.
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  17.  59
    Mathematical rigor and proof.Yacin Hamami - 2022 - Review of Symbolic Logic 15 (2):409-449.
    Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowl- edge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary (...)
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  18.  34
    Mathematics and plausible reasoning.George Pólya - 1954 - Princeton, N.J.,: Princeton University Press.
    2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques (...)
  19.  16
    Mathematics: The Loss of Certainty.Morris Kline - 1982 - New York, NY, USA: Galaxy Books.
    This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.
  20. Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I (...)
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  21.  74
    From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: London.
    First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more (...)
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  22. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2021 - Erkenntnis 86 (5):1119-1137.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content (...)
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  23. Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.
    Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the (...)
  24. Mathematical symbols as epistemic actions.Johan De Smedt & Helen De Cruz - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used (...)
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  25. Mathematical Pluralism and Indispensability.Silvia Jonas - 2023 - Erkenntnis 1:1-25.
    Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover (...)
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  26. Mathematics, Morality, and Self‐Effacement.Jack Woods - 2016 - Noûs.
    I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...)
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  27. The Mathematical Universe.Max Tegmark - 2007 - Foundations of Physics 38 (2):101-150.
    I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes (...)
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  28.  20
    Mathematics in Philosophy: Selected Essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell Univ Pr.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
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  29.  13
    The Mathematical Principles of Natural Philosophy.Isaac Newton - 2020 - Filozofski Vestnik 41 (3).
    The Mathematical Principles of Natural Philosophy.
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  30. Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
  31.  26
    The mathematical experience.Philip J. Davis - 1981 - Boston: Birkhäuser. Edited by Reuben Hersh & Elena Marchisotto.
    Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...
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  32. Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
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  33.  2
    Mathematics for human flourishing.Francis Su - 2020 - New Haven: Yale University Press. Edited by Christopher Jackson.
    An inclusive vision of mathematics-- its beauty, its humanity, and its power to build virtues that help us all flourish. For mathematician Francis Su, a society without mathematical affection is like a city without museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a diverse audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves personal reflections, puzzles, and (...)
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  34. Mathematical Intuition: Phenomenology and Mathematical Knowledge.Richard L. TIESZEN - 1993 - Studia Logica 52 (3):484-486.
    The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a (...)
     
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  35.  33
    Mathematical logic.Heinz-Dieter Ebbinghaus - 1996 - New York: Springer. Edited by Jörg Flum & Wolfgang Thomas.
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The (...)
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  36.  20
    Mathematics and the Natural Sciences: The Physical Singularity of Life.Francis Bailly - 2010 - Imperial College Press. Edited by Giuseppe Longo.
    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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  37. Magicicada, Mathematical Explanation and Mathematical Realism.Davide Rizza - 2011 - Erkenntnis 74 (1):101-114.
    Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and (...)
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  38.  90
    Metaphysics, mathematics, and meaning.Nathan U. Salmon - 2005 - New York: Oxford University Press.
    Metaphysics, Mathematics, and Meaning brings together Nathan Salmon's influential papers on topics in the metaphysics of existence, non-existence, and fiction; modality and its logic; strict identity, including personal identity; numbers and numerical quantifiers; the philosophical significance of Godel's Incompleteness theorems; and semantic content and designation. Including a previously unpublished essay and a helpful new introduction to orient the reader, the volume offers rich and varied sustenance for philosophers and logicians.
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  39.  20
    Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - Oxford, GB: Oxford University Press UK.
    Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to (...)
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  40.  98
    Mathematical Inference and Logical Inference.Yacin Hamami - 2018 - Review of Symbolic Logic 11 (4):665-704.
    The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as (...)
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  41. Mathematics in philosophy: selected essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell University Press.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
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  42.  38
    Mathematical logic.Joseph R. Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
    8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index.
  43.  29
    Mathematics and the image of reason.Mary Tiles - 1991 - New York: Routledge.
    A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.
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  44. How mathematical concepts get their bodies.Andrei Rodin - 2010 - Topoi 29 (1):53-60.
    When the traditional distinction between a mathematical concept and a mathematical intuition is tested against examples taken from the real history of mathematics one can observe the following interesting phenomena. First, there are multiple examples where concepts and intuitions do not well fit together; some of these examples can be described as “poorly conceptualised intuitions” while some others can be described as “poorly intuited concepts”. Second, the historical development of mathematics involves two kinds of corresponding processes: poorly conceptualised (...)
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  45.  94
    Realism, Mathematics & Modality.Hartry H. Field - 1989 - Blackwell.
  46.  84
    Mathematics, science, and epistemology.Imre Lakatos - 1978 - New York: Cambridge University Press. Edited by Gregory Currie & John Worrall.
    Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.
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  47.  13
    What Mathematics and Metaphysics of Corporeal Nature Offer to Each Other: Kant on the Foundations of Natural Science.Michael Bennett McNulty - 2023 - Kantian Review 28 (3):397-412.
    Kant famously distinguishes between the methods of mathematics and of metaphysics, holding that metaphysicians err when they avail themselves of the mathematical method. Nonetheless, in the Metaphysical Foundations of Natural Science, he insists that mathematics and metaphysics must jointly ground ‘proper natural science’. This article examines the distinctive contributions and unity of mathematics and metaphysics to the foundations of the science of body. I argue that the two are distinct insofar as they involve distinctive sorts of grounding (...)
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  48. Mathematical models: Questions of trustworthiness.Adam Morton - 1993 - British Journal for the Philosophy of Science 44 (4):659-674.
    I argue that the contrast between models and theories is important for public policy issues. I focus especially on the way a mathematical model explains just one aspect of the data.
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  49. Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematics.James Franklin - 2022 - Foundations of Science 27 (2):327-344.
    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 (...)
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  50. 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 (...)
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