Results for 'mathematics'

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  1.  89
    Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
    Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable (...)
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  2.  83
    The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Bob Hale (ed.) - 2001 - Oxford University Press.
    Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as (...)
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  3. Morality and Mathematics: The Evolutionary Challenge.Justin Clarke-Doane - 2012 - Ethics 122 (2):313-340.
    It is commonly suggested that evolutionary considerations generate an epistemological challenge for moral realism. At first approximation, the challenge for the moral realist is to explain our having many true moral beliefs, given that those beliefs are the products of evolutionary forces that would be indifferent to the moral truth. An important question surrounding this challenge is the extent to which it generalizes. In particular, it is of interest whether the Evolutionary Challenge for moral realism is equally a challenge for (...)
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  4. Mathematics as a Science of Patterns.D. Resnik Michael - 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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  5. From Kant to Hilbert: A Source Book in the Foundations of Mathematics.William Bragg Ewald (ed.) - 1996 - Oxford University Press.
    This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here (...)
     
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  6. Naturalism in Mathematics.Penelope Maddy - 1997 - 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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  7. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.John P. Burgess & Gideon A. Rosen - 1997 - Oxford University Press.
    Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured (...)
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  8. Mathematics Intelligent Tutoring System.Nour N. AbuEloun & Samy S. Abu Naser - 2017 - International Journal of Advanced Scientific Research 2 (1):11-16.
    In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...)
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  9. Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version (...)
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  10. The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1931 - Paterson, N.J., Littlefield, Adams.
    THE FOUNDATIONS OF MATHEMATICS () PREFACE The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with..
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  11.  10
    Mathematics and Philosophy. Translated by Simon B. Duffy.Alain Badiou - 2006 - In Simon B. Duffy (ed.), Virtual Mathematics: the logic of difference. Clinamen.
    In order to address to the relation between philosophy and mathematics it is first necessary to distinguish the grand style and the little style. The little style painstakingly constructs mathematics as the object for philosophical scrutiny. It is called the little style for a precise reason, because it assigns mathematics to the subservient role of that which supports the definition and perpetuation of a philosophical specialisation. This specialisation is called the ‘philosophy of mathematics’, where the ‘of’ (...)
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  12.  13
    Crunchy Methods in Practical Mathematics.Michael Wood - 2001 - Philosophy of Mathematics Education Journal 14.
    This paper focuses on the distinction between methods which are mathematically "clever", and those which are simply crude, typically repetitive and computer intensive, approaches for "crunching" out answers to problems. Examples of the latter include simulated probability distributions and resampling methods in statistics, and iterative methods for solving equations or optimisation problems. Most of these methods require software support, but this is easily provided by a PC. The paper argues that the crunchier methods often have substantial advantages from the perspectives (...)
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  13.  20
    The Mathematics of Deleuze’s Differential Logic and Metaphysics.Simon B. Duffy - 2006 - In Virtual Mathematics: the logic of difference. Clinamen.
    In Difference and Repetition, Deleuze explores the manner by means of which concepts are implicated in the problematic Idea by using a mathematics problem as an example, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is a historical account of the mathematical problematic that Deleuze deploys in his philosophy, and an introduction to the role played by this problematic in the development of his philosophy of difference. (...)
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  14.  16
    Albert Lautman and the Creative Dialectic of Modern Mathematics. Translated by Simon B. Duffy.Fernando Zalamea - 2011 - In Mathematics, Ideas and the physical real, by Albert Lautman. Continuum.
    It is possible today to observe in hindsight the epistemological landscape of the twentieth century, and the work of Albert Lautman in mathematical philosophy appears as a profound turning point, opening to a true under- standing of creativity in mathematics and its relation with the real. Little understood in its time or even today, Lautman’s work explores the difficult but exciting intersection where modern mathematics, advanced mathe- matical invention, the structural or unitary relations of mathematical knowledge and, finally, (...)
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  15.  7
    Deleuze and Mathematics.Simon B. Duffy - 2006 - In Virtual Mathematics: the logic of difference. Clinamen.
    The collection Virtual Mathematics: the logic of difference brings together a range of new philosophical engagements with mathematics, using the work of French philosopher Gilles Deleuze as its focus. Deleuze’s engagements with mathematics rely upon the construction of alternative lineages in the history of mathematics in order to reconfigure particular philosophical problems and to develop new concepts. These alternative conceptual histories also challenge some of the self-imposed limits of the discipline of mathematics, and suggest the (...)
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  16. The Reality of Numbers: A Physicalist's Philosophy of Mathematics.John Bigelow - 1988 - Oxford University Press.
    Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.
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  17. Mathematics and Reality.Mary Leng - 2010 - Oxford University Press.
    Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction. On this view, the claims of our ordinary mathematical theories are more closely analogous to utterances made in the context of storytelling than to utterances whose aim is to assert literal truths.
     
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  18. Realism, Mathematics & Modality.Hartry Field - 1989 - Blackwell.
  19.  79
    Aristotelian Realist Philosophy of Mathematics.James Franklin - 2014 - Palgrave MacMillan.
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts (...)
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  20. Thinking About Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2000 - Oxford University Press.
    This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that (...) is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)
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  21. Philosophical Papers, Volume 1: Mathematics, Matter, and Method.Hilary Putnam (ed.) - 1979 - Cambridge University Press.
    Professor Hilary Putnam has been one of the most influential and sharply original of recent American philosophers in a whole range of fields. His most important published work is collected here, together with several new and substantial studies, in two volumes. The first deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry; the second deals with the philosophy of language and mind. Volume one is now issued in a new edition, including (...)
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  22.  29
    The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - Cambridge University Press.
    This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. (...)
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  23.  75
    From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s.Paolo Mancosu (ed.) - 1998 - Oxford University Press.
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors (...)
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  24.  95
    Visual Thinking in Mathematics: An Epistemological Study.M. Giaquinto - 2007 - Oxford University Press.
    Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual (...)
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  25. Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble - forthcoming - Journal Progress in Biophysics and Molecular Biology 119 (2).
  26.  62
    Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu - 1996 - Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting (...)
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  27.  47
    The Applicability of Mathematics as a Philosophical Problem.Mark Steiner - 1998 - Harvard University Press.
    This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics ...
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  28. Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.
    I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My (...)
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  29.  57
    Does Participation Matter? An Inconsistency in Parfit's Moral Mathematics: Ben Eggleston.Ben Eggleston - 2003 - Utilitas 15 (1):92-105.
    Consequentialists typically think that the moral quality of one's conduct depends on the difference one makes. But consequentialists may also think that even if one is not making a difference, the moral quality of one's conduct can still be affected by whether one is participating in an endeavour that does make a difference. Derek Parfit discusses this issue – the moral significance of what I call ‘participation’ – in the chapter of Reasons and Persons that he devotes to what he (...)
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  30. Editorial. Special Issue on Integral Biomathics: Can Biology Create a Profoundly New Mathematics and Computation?Plamen L. Simeonov, Koichiro Matsuno & Robert S. Root-Bernstein - 2013 - J. Progress in Biophysics and Molecular Biology 113 (1):1-4.
    The idea behind this special theme journal issue was to continue the work we have started with the INBIOSA initiative (www.inbiosa.eu) and our small inter-disciplinary scientific community. The result of this EU funded project was a white paper (Simeonov et al., 2012a) defining a new direction for future research in theoretical biology we called Integral Biomathics and a volume (Simeonov et al., 2012b) with contributions from two workshops and our first international conference in this field in 2011. The initial impulse (...)
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  31.  30
    From Mathematics to Philosophy.H. Wang - 1974 - 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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  32.  35
    The Ethnomethodological Foundations of Mathematics.Eric Livingston - 1986 - Routledge and Kegan Paul.
    A Non-Technical Introduction to Ethnomethodological Investigations of the Foundations of Mathematics through the Use of a Theorem of Euclidean Geometry* I ...
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  33.  33
    Varieties of Constructive Mathematics.D. S. Bridges - 1987 - Cambridge University Press.
    This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.
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  34. Indispensability Arguments in the Philosophy of Mathematics.Mark Colyvan - 2008 - Stanford Encyclopedia of Philosophy.
    One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these (...)
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  35. Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice.Lisa Shabel - 2002 - Routledge.
    Mathematics in Kant's Critical Philosophy provides a much needed reading (and re-reading) of Kant's theory of the construction of mathematical concepts through a fully contextualized analysis. In this work Lisa Shabel convincingly argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, can the material and context necessary for a successful interpretation of Kant's philosophy be provided. This is borne out through sustained readings of Euclid and Woolf in (...)
     
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  36.  58
    Metaphysics, Mathematics, and Meaning.Nathan U. Salmon - 2005 - 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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  37. Five Theories of Reasoning: Interconnections and Applications to Mathematics.Alison Pease & Andrew Aberdein - 2011 - Logic and Logical Philosophy 20 (1-2):7-57.
    The last century has seen many disciplines place a greater priority on understanding how people reason in a particular domain, and several illuminating theories of informal logic and argumentation have been developed. Perhaps owing to their diverse backgrounds, there are several connections and overlapping ideas between the theories, which appear to have been overlooked. We focus on Peirce’s development of abductive reasoning [39], Toulmin’s argumentation layout [52], Lakatos’s theory of reasoning in mathematics [23], Pollock’s notions of counterexample [44], and (...)
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  38.  45
    What is Mathematics, Really?Reuben Hersh - 1997 - Oxford University Press.
    Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue (...)
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  39.  63
    Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Blackwell.
  40. Agent-Based Modeling: The Right Mathematics for the Social Sciences?Paul L. Borrill & Leigh Tesfatsion - 2011 - In J. B. Davis & D. W. Hands (eds.), Elgar Companion to Recent Economic Methodology. Edward Elgar Publishers. pp. 228.
    This study provides a basic introduction to agent-based modeling (ABM) as a powerful blend of classical and constructive mathematics, with a primary focus on its applicability for social science research. The typical goals of ABM social science researchers are discussed along with the culture-dish nature of their computer experiments. The applicability of ABM for science more generally is also considered, with special attention to physics. Finally, two distinct types of ABM applications are summarized in order to illustrate concretely the (...)
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  41. Aristotle's Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225 - 235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...)
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  42. Formalizing Darwinism, Naturalizing Mathematics.Fabio Sterpetti - 2015 - Paradigmi. Rivista di Critica Filosofica 33 (2):133-160.
    In the last decades two different and apparently unrelated lines of research have increasingly connected mathematics and evolutionism. Indeed, on the one hand different attempts to formalize darwinism have been made, while, on the other hand, different attempts to naturalize logic and mathematics have been put forward. Those researches may appear either to be completely distinct or at least in some way convergent. They may in fact both be seen as supporting a naturalistic stance. Evolutionism is indeed crucial (...)
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  43.  87
    Knowledge of Mathematics Without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.
    Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show (...)
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  44.  96
    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 (...)
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  45.  76
    The Oxford Handbook of Philosophy of Mathematics and Logic.Stewart Shapiro (ed.) - 2005 - Oxford University Press.
    Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on (...)
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  46.  21
    Logic and Philosophy of Mathematics in the Early Husserl.Stefania Centrone - 2010 - Springer.
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  47.  55
    Pasch's Philosophy of Mathematics.Dirk Schlimm - 2010 - Review of Symbolic Logic 3 (1):93-118.
    Moritz Pasch (1843ber neuere Geometrie (1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics, which he continued to elaborate on throughout the rest of his life. This philosophy is quite unique in combining a deductivist methodology with a radically empiricist epistemology for mathematics. By taking into consideration publications from the entire span (...)
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  48.  18
    Philosophy of Mathematics.Paul Benacerraf - 1964 - Englewood Cliffs, N.J., Prentice-Hall.
    The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.
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  49. Philosophy of Mathematics: Selected Readings.Paul Benacerraf & Hilary Putnam (eds.) - 1964 - Cambridge University Press.
    The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, (...)
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  50. Epistemology of Mathematics: What Are the Questions? What Count as Answers?Stewart Shapiro - 2011 - Philosophical Quarterly 61 (242):130-150.
    A paper in this journal by Fraser MacBride, ‘Can Ante Rem Structuralism Solve the Access Problem?’, raises important issues concerning the epistemological goals and burdens of contemporary philosophy of mathematics, and perhaps philosophy of science and other disciplines as well. I use a response to MacBride's paper as a framework for developing a broadly holistic framework for these issues, and I attempt to steer a middle course between reductive foundationalism and extreme naturalistic quietism. For this purpose the notion of (...)
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