Search results for 'Numerical mathematics' (try it on Scholar)

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  1.  7
    Laurence Rousselle & Marie-Pascale Noël (2007). Basic Numerical Skills in Children with Mathematics Learning Disabilities: A Comparison of Symbolic Vs Non-Symbolic Number Magnitude Processing. Cognition 102 (3):361-395.
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  2.  4
    John Myhill (1972). Review: Errett Bishop, Foundations of Constructive Analysis; Errett Bishop, A. Kino, J. Myhill, R. E. Vesley, Mathematics as a Numerical Language. [REVIEW] Journal of Symbolic Logic 37 (4):744-747.
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  3. John Myhill (1972). Bishop Errett. Foundations of Constructive Analysis. McGraw-Hill Book Company, New York, San Francisco, St. Louis, Toronto, London, and Sydney, 1967, Xiii + 370 Pp.Bishop Errett. Mathematics as a Numerical Language. Intuitionism and Proof Theory, Proceedings of the Summer Conference at Buffalo N.Y. 1968, Edited by Kino A., Myhill J., and Vesley R. E., Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam and London 1970, Pp. 53–71. [REVIEW] Journal of Symbolic Logic 37 (4):744-747.
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  4. Belinda Pletzer, Martin Kronbichler, Hans-Christoph Nuerk & Hubert H. Kerschbaum (2015). Mathematics Anxiety Reduces Default Mode Network Deactivation in Response to Numerical Tasks. Frontiers in Human Neuroscience 9.
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  5. Han Geurdes, The Construction of Transfinite Equivalence Algorithms.
    Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics (...)
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  6.  21
    Fenna van Nes (2011). Mathematics Education and Neurosciences: Towards Interdisciplinary Insights Into the Development of Young Children's Mathematical Abilities. Educational Philosophy and Theory 43 (1):75-80.
    The Mathematics Education and Neurosciences project is an interdisciplinary research program that bridges mathematics education research with neuroscientific research. The bidirectional collaboration will provide greater insight into young children's (aged four to six years) mathematical abilities. Specifically, by combining qualitative ‘design research’ with quantitative ‘experimental research’, we aim to come to a more thorough understanding of prerequisites that are involved in the development of early spatial and number sense. The mathematics education researchers are concerned with kindergartner's spatial (...)
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  7. Giuseppe Longo & Arnaud Viarouge (2010). Mathematical Intuition and the Cognitive Roots of Mathematical Concepts. Topoi 29 (1):15-27.
    The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the foundational (...)
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  8.  9
    Mauro Engelmann (2010). As Filosofias da Matemática de Wittgenstein: Intensionalismo Sistêmico e a Aplicação de um Novo Método (Sobre o Desenvolvimento da Filosofia da Matemática de Wittgenstein). Doispontos 6 (2).
    This essay intends to identify intentionalism (infinity given by rules, not by extensions) and the idea of multiple complete mathematical systems (several “mathematics”) as the central characteristics of Wittgenstein’s philosophy of mathematics. We intend to roughly show how these ideas come up, interact to each other, how they develop and, in the end, how they are abandoned in the late period. According to the Tractatus Logico-Philosophicus, infinities can only be given by rules and there is a single (...) system (the number’s essence is the general idea of ordering). Intentionalism is up to at least 1933, but the idea of a single system is abandoned in 1929-30 (already in the Philosophische Bemerkungen). In its place one finds the idea of multiple, independent and complete numerical systems. This idea will engender some key moves in Wittgenstein’s philosophy of Mathematics. The notion of “seeing an aspect” from the Big Typescript, of instance, comes up so as to explain such systems. From 1934 onwards, Wittgenstein gradually abandons intentionalism and the idea of multiple, independent and complete systems. In his late philosophy, both ideas are used only as instruments to dissolve philosophical prose regarding mathematics. (shrink)
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  9.  78
    M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. 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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  10.  53
    Nathan U. Salmon (2005). Metaphysics, Mathematics, and Meaning. 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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  11.  72
    Beckett Sterner (2014). Well-Structured Biology: Numerical Taxonomy's Epistemic Vision for Systematics. In Andrew Hamilton (ed.), The Evolution of Phylogenetic Systematics. University of California Press 213-244.
    What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. (...)
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  12.  38
    D. F. M. Strauss (2010). The Significance of a Non-Reductionist Ontology for the Discipline of Mathematics: A Historical and Systematic Analysis. [REVIEW] Axiomathes 20 (1):19-52.
    A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism (...)
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  13. Elizabeth S. Spelke, Sex Differences in Intrinsic Aptitude for Mathematics and Science?
    This article considers 3 claims that cognitive sex differ- ences account for the differential representation of men and women in high-level careers in mathematics and sci- ence: (a) males are more focused on objects from the beginning of life and therefore are predisposed to better learning about mechanical systems; (b) males have a pro- file of spatial and numerical abilities producing greater aptitude for mathematics; and (c) males are more variable in their cognitive abilities and therefore predominate (...)
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  14. Nathan Salmon (2005). Metaphysics, Mathematics, and Meaning: Philosophical Papers, Volume 1. Oxford University Press Uk.
    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 Gödel'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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  15.  4
    Erik Stenius (1981). Kant and the Apriority of Mathematics. Dialectica 35 (1):147-166.
    SummaryThe key terms in Kant's argument for the synthetic apriority of mathematics are analyzed. The result is a somewhat “idealized” interpretation of these terms, which, however, is appropriate in respect of Kant's main argument. Taking this interpretation as a framework, a model for giving evidence for numerical statements is presented, which is in good agreement with Kant's argument, and according to which numerical statements are indeed synthetic and also, in a sense, a priori. Thus they formally render (...)
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  16.  2
    Davide Rizza (2006). Measurement-Theoretic Observations on Field's Instrumentalism and the Applicability of Mathematics. Abstracta 2 (2):148-171.
    In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools but (...)
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  17. Axel Arturo Barcelo Aspeitia (2000). Mathematics as Grammar: 'Grammar' in Wittgenstein's Philosophy of Mathematics During the Middle Period. Dissertation, Indiana University
    This dissertation looks to make sense of the role 'grammar' plays in Wittgenstein's philosophy of mathematics during the middle period of his career. It constructs a formal model of Wittgenstein's notion of grammar as expressed in his writings of the early thirties, addresses the appropriateness of that model and then employs it to test Wittgenstein's claim that mathematical propositions are ultimately grammatical. ;In order to test Wittgenstein's claim that mathematical propositions are grammatical, the dissertation provides a formalized theory of (...)
     
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  18. Gabriel Uzquiano (1999). Ontology and the Foundations of Mathematics. Dissertation, Massachusetts Institute of Technology
    "Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences place serious constraints on (...)
     
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  19.  35
    Lance J. Rips, Amber Bloomfield & Jennifer Asmuth (2008). From Numerical Concepts to Concepts of Number. Behavioral and Brain Sciences 31 (6):623-642.
    Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural (...)
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  20.  4
    S. Dehaene (1992). Varieties of Numerical Abilities. Cognition 44 (1-2):1-42.
  21. Manuela Piazza, Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene (2013). Education Enhances the Acuity of the Nonverbal Approximate Number System. Psychological Science 24 (4):p.
    All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to (...) education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)
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  22.  44
    Pierre Pica, Stanislas Dehaene, Elizabeth Spelke & Véronique Izard (2008). Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures. Science 320 (5880):1217-1220.
    The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers (...)
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  23. Karl Menger (1954). On Variables in Mathematics and in Natural Science. British Journal for the Philosophy of Science 5 (18):134-142.
    Attempting to answer the question "what is a variable?," menger discusses the following topics: (1) numerical variables and variables in the sense of the logicians, (2) variable quantities, (3) scientific variable quantities, (4) functions, And (5) variable quantities and functions in pure and applied analysis. (staff).
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  24.  4
    David Landy, Arthur Charlesworth & Erin Ottmar (2016). Categories of Large Numbers in Line Estimation. Cognitive Science 40 (4).
    How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and (...)
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  25.  17
    Catherine Rowett (2013). Philosophy's Numerical Turn: Why the Pythagoreans' Interest in Numbers is Truly Awesome. In Dirk Obbink & David Sider (eds.), Doctrine and Doxography: Studies on Heraclitus and Pythagoras. De Gruyter 3-32.
    Philosophers are generally somewhat wary of the hints of number mysticism in the reports about the beliefs and doctrines of the so-called Pythagoreans. It's not clear how much Pythagoras himself (as opposed to his later followers) indulged in speculation about numbers, or in more serious mathematics. But the Pythagoreans whom Aristotle discusses in the Metaphysics had some elaborate stories to tell about how the universe could be explained in terms of numbers—not just its physics but perhaps morality too. Was (...)
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  26.  9
    Jean W. Rioux (2012). Numerical Foundations. Review of Metaphysics 66 (1):3-29.
    Mathematics has had its share of historical shocks, beginning with the discovery by Hippasus the Pythagorean that the integers could not possibly be the elements of all things. Likewise with Kurt Gödel’s Incompleteness Theorems, which presented a serious obstacle to David Hilbert’s formalism, and Bertrand Russell’s own discovery of the paradox inherent in his intuitively simple set theory. More recently, Paul Benacerraf presented a problem for the foundations of arithmetic in “What Numbers Could Not Be” and “Mathematical Truth.” Drawing (...)
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  27.  15
    Charles Echelbarger (2013). Hume on the Objects of Mathematics. The European Legacy 18 (4):432-443.
    In this essay, I argue that Hume?s theory of Quantitative and Numerical Philosophical Relations can be interpreted in a way which allows mathematical knowledge to be about a body of objective and necessary truths, while preserving Hume?s nominalism and the basic principles of his theory of ideas. Attempts are made to clear up a number of obscure points about Hume?s claims concerning the abstract sciences of Arithmetic and Algebra by means of re-examining what he says and what he could (...)
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  28.  10
    Dfm Strauss (2011). Bernays, Dooyeweerd and Gödel – the Remarkable Convergence in Their Reflections on the Foundations of Mathematics. South African Journal of Philosophy 30 (1):70-94.
    In spite of differences the thought of Bernays, Dooyeweerd and Gödel evinces a remarkable convergence. This is particularly the case in respect of the acknowledgement of the difference between the discrete and the continuous, the foundational position of number and the fact that the idea of continuity is derived from space (geometry – Bernays). What is furthermore similar is the recognition of what is primitive (and indefinable) as well as the account of the coherence of what is unique, such as (...)
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  29. Stephen Wolfram, Mathematics by Computer.
    The most elementary way to think about Mathctrtati ca is as an enhance calculator — a calculator that does not only numerical computation but also algebraic computation and graphics. Matltcmatica can function much like a standard calt".1a- tor. you type in a question, you get back an answer. But Mat/tctttadca ga's turthcr I ue an ordinary calculator. You can type in questions that require answers that arc longer than a calculator can handle. For example, Matltcmatictt can giv; you thc (...)
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  30.  9
    Felice L. Bedford (2001). Generality, Mathematical Elegance, and Evolution of Numerical/Object Identity. Behavioral and Brain Sciences 24 (4):654-655.
    Object identity, the apprehension that two glimpses refer to the same object, is offered as an example of combining generality, mathematics, and evolution. We argue that it applies to glimpses in time (apparent motion), modality (ventriloquism), and space (Gestalt grouping); that it has a mathematically elegant solution of nested geometries (Euclidean, Similarity, Affine, Projective, Topology); and that it is evolutionarily sound despite our Euclidean world. [Shepard].
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  31.  5
    Susan C. Hale (1990). Elementarity and Anti-Matter in Contemporary Physics: Comments on Michael D. Resnik's "Between Mathematics and Physics". PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:379 - 383.
    I point out that conceptions of particles as mathematical, or quasi mathematical, entities have a longer history than Resnik notices. I argue that Resnik's attack on the distinction between mathematical and physical entities is not deep enough. The crucial problem for this distinction finds its locus in the numerical indeterminancy of elementary particles. This problem, traced by Heisenberg, emerges from the discovery of antimatter.
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  32. Luka Boršić (2007). Mjera – od matematike do etike: Measure – from Mathematics to Ethics. Filozofska Istrazivanja 27 (4):751-764.
    Ovaj rad pokazuje kako pojam mjere, koji je jedan od najmnogoznačnijih filozofijskih pojmova, počinje dobivati etički smisao tijekom povijesnog razvoja grčke filozofije. U prvom dijelu pokazuje se kako se u Homerovim epovima riječ ‘mjera’ i srodne riječi odnose isključivo na konkretno mjerljive količine. Drugi se dio bavi mijenom značenja, koja se zbiva u pitagorovskom mišljenju. Tu se najviše pažnje poklanja povijesnim okolnostima nastanka grčkog polisa, za što je vrlina umjerenosti bila neophodno potrebna. U tom kontekstu pobliže se razmatraju Filolajevi i (...)
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  33. Gerardo Santana Trujillo (2012). Las Matemáticas en el Pensamiento de Vilém Flusser. Flusser Studies 13.
    This paper aims to establish the importance of mathematical thinking in the work of Vilém Flusser. For this purpose highlights the concept of escalation of abstraction with which the Czech German philosopher finishes by reversing the top of the traditional pyramid of knowledge, we know from Plato and Aristotle. It also assumes the implicit cultural revolution in the refinement of the numerical element in a process of gradual abandonment of purely alphabetic code, highlights the new key code, together with (...)
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  34. William Bragg Ewald (ed.) (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. 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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  35.  67
    Stewart Shapiro (1997). Philosophy of Mathematics: Structure and Ontology. 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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  36. Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble (forthcoming). Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy. Journal Progress in Biophysics and Molecular Biology 119 (2).
    The is the Editorial of the 2015 JPBMB Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.
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  37.  5
    Michael Wood (2001). Crunchy Methods in Practical Mathematics. 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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  38. Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. 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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  39.  62
    Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. 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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  40. Michael D. Resnik (1997). Mathematics as a Science of Patterns. 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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  41.  83
    Penelope Maddy (1997). Naturalism in Mathematics. 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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  42. John P. Burgess & Gideon A. Rosen (1997). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. 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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  43.  86
    Marcus P. Adams (2016). Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics. 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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  44. Penelope Maddy (1990). Realism in Mathematics. 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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  45. Plamen L. Simeonov, Koichiro Matsuno & Robert S. Root-Bernstein (2013). Editorial. Special Issue on Integral Biomathics: Can Biology Create a Profoundly New Mathematics and Computation? 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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  46. Fabio Sterpetti (2015). Formalizing Darwinism, Naturalizing Mathematics. 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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  47. Mary Leng (2010). Mathematics and Reality. OUP Oxford.
    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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  48.  69
    James Franklin (2014). Aristotelian Realist Philosophy of Mathematics. 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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  49. Justin Clarke-Doane (2012). Morality and Mathematics: The Evolutionary Challenge. 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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  50. John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. 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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