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

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  1. Hans-Christoph Nuerk Korbinian Moeller, Laura Martignon, Silvia Wessolowski, Joachim Engel (2011). Effects of Finger Counting on Numerical Development – The Opposing Views of Neurocognition and Mathematics Education. Frontiers in Psychology 2.score: 72.0
    Usually children learn the basic principles of number and arithmetic by the help of finger-based representations. However, whether the reliance on finger-based representations is only beneficial or whether it may even become detrimental is the subject of an ongoing debate between neuro-cognitive and mathematics education researchers. From the neuro-cognitive perspective finger counting provides multi-sensory input conveying both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that (...)
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  2. Tobias U. Hauser, Stephanie Rotzer, Roland H. Grabner, Susan Mérillat & Lutz Jäncke (2013). Enhancing Performance in Numerical Magnitude Processing and Mental Arithmetic Using Transcranial Direct Current Stimulation (tDCS). Frontiers in Human Neuroscience 7.score: 45.0
    The ability to accurately process numerical magnitudes and solve mental arithmetic is of highest importance for schooling and professional career. Although impairments in these domains in disorders such as developmental dyscalculia (DD) are highly detrimental, remediation is still sparse. In recent years, transcranial brain stimulation methods such as transcranial Direct Current Stimulation (tDCS) have been suggested as a treatment for various neurologic and neuropsychiatric disorders. The posterior parietal cortex (PPC) is known to be crucially involved in numerical magnitude (...)
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  3. Han Geurdes, The Construction of Transfinite Equivalence Algorithms.score: 43.0
    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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  4. Giuseppe Longo & Arnaud Viarouge (2010). Mathematical Intuition and the Cognitive Roots of Mathematical Concepts. Topoi 29 (1):15-27.score: 39.0
    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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  5. 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.score: 36.0
    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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  6. 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).score: 36.0
    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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  7. 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.score: 36.0
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  8. Vitor G. Haase Annelise Júlio-Costa, Andressa M. Antunes, Júlia B. Lopes-Silva, Bárbara C. Moreira, Gabrielle S. Vianna, Guilherme Wood, Maria R. S. Carvalho (2013). Count on Dopamine: Influences of COMT Polymorphisms on Numerical Cognition. Frontiers in Psychology 4.score: 36.0
    Catechol-O-methyltransferase (COMT) is an enzyme that is particularly important for the metabolism of dopamine. Functional polymorphisms of COMT have been implicated in working memory and numerical cognition. This is an exploratory study that aims at investigating associations between COMT polymorphisms, working memory and numerical cognition. Elementary school children from 2th to 6th grades were divided into two groups according to their COMT val158met polymorphism (homozygous for valine allele [n= 61] versus heterozygous plus methionine homozygous children or met+ group (...)
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  9. Korbinian Moeller, Laura Martignon, Silvia Wessolowski, Joachim Engel & Hans-Christoph Nuerk (2011). Effects of Finger Counting on Numerical Development–the Opposing Views of Neurocognition and Mathematics Education. Frontiers in Psychology 2.score: 36.0
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  10. 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.score: 36.0
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  11. Daniel Ansari Filip Van Opstal, Seppe Santens (2012). The Numerate Brain: Recent Findings and Theoretical Reviews on the Neurocognitive Foundations of Number Processing. Frontiers in Human Neuroscience 6.score: 28.0
    The Numerate Brain: Recent Findings and Theoretical Reviews on the Neurocognitive Foundations of Number Processing.
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  12. Filip Van Opstal, Seppe Santens & Daniel Ansari (2012). The Numerate Brain: Recent Findings and Theoretical Reviews on the Neurocognitive Foundations of Number Processing. Frontiers in Human Neuroscience 6.score: 28.0
    The Numerate Brain: Recent Findings and Theoretical Reviews on the Neurocognitive Foundations of Number Processing.
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  13. M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.score: 27.0
    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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  14. Nathan U. Salmon (2005). Metaphysics, Mathematics, and Meaning. Oxford University Press.score: 27.0
    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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  15. Beckett Sterner (forthcoming). Well-Structured Biology: Numerical Taxonomy's Epistemic Vision for Systematics. In Andrew Hamilton (ed.), Patterns in Nature. University of California Press.score: 27.0
    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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  16. 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.score: 27.0
    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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  17. Amélie Lubin, Sandrine Rossi, Gregory Simon, Céline Lanoë, Gaëlle Leroux, Nicolas Poirel, Arlette Pineau & Olivier Houdé (2013). Numerical Transcoding Proficiency in 10-Year-Old Schoolchildren is Associated with Gray Matter Inter-Individual Differences: A Voxel-Based Morphometry Study. Frontiers in Psychology 4.score: 27.0
    Are individual differences in numerical performance sustained by variations in grey matter volume in schoolchildren? To our knowledge, this challenging question for neuroeducation has not yet been investigated in typical development. We used the Voxel-Based Morphometry method to search for possible structural brain differences between two groups of 10-year-old schoolchildren (N=22) whose performance differed only in numerical transcoding between analog and symbolic systems. The results indicated that children with low numerical proficiency have less grey matter volume in (...)
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  18. Sarah Wu, Hitha Amin, Maria Barth, Vanessa Malcarne & Vinod Menon (2012). Math Anxiety in Second and Third Graders and Its Relation to Mathematics Achievement. Frontiers in Psychology 3.score: 27.0
    Although the detrimental effects of math anxiety in adults are well understood, few studies have examined how it affects younger children who are beginning to learn math in a formal academic setting. Here, we examine the relationship between math anxiety and math achievement in 2nd and 3rd graders. In response to the need for a grade-appropriate measure of assessing math anxiety in this group we first describe the development of Scale for Early Mathematics Anxiety (SEMA), a new measure for (...)
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  19. Christian Agrillo (2013). One Vs. Two Non-Symbolic Numerical Systems? Looking to the ATOM Theory for Clues to the Mystery. Frontiers in Human Neuroscience 7.score: 24.0
    One vs. two non-symbolic numerical systems? Looking to the ATOM theory for clues to the mystery.
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  20. Andrea Bender & Sieghard Beller (2013). Of Adding Oranges and Apples: How Non-Abstract Representations May Foster Abstract Numerical Cognition. Frontiers in Human Neuroscience 7:903.score: 24.0
    Of adding oranges and apples: how non-abstract representations may foster abstract numerical cognition.
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  21. Elizabeth S. Spelke, Sex Differences in Intrinsic Aptitude for Mathematics and Science?score: 21.0
    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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  22. Felice L. Bedford (2001). Generality, Mathematical Elegance, and Evolution of Numerical/Object Identity. Behavioral and Brain Sciences 24 (4):654-655.score: 21.0
    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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  23. Marcus Giaquinto (2011). Visual Thinking in Mathematics. OUP Oxford.score: 21.0
    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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  24. Ursula Anderson & Sara Cordes (2013). 1 < 2 and 2 < 3: Non-Linguistic Appreciations of Numerical Order. Frontiers in Psychology 4.score: 21.0
    Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding to number at a highly abstract, conceptual level. In this paper, we review the findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in nonhuman animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate (...)
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  25. William Bragg Ewald (ed.) (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford University Press.score: 21.0
    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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  26. Davide Rizza (2006). Measurement-Theoretic Observations on Field's Instrumentalism and the Applicability of Mathematics. Abstracta 2 (2):148-171.score: 21.0
    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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  27. Simon B. Duffy (ed.) (2006). Virtual Mathematics: The Logic of Difference. Clinamen.score: 19.0
    Of all twentieth century philosophers, it is Gilles Deleuze whose work agitates most forcefully for a worldview privileging becoming over being, difference over sameness; the world as a complex, open set of multiplicities. Nevertheless, Deleuze remains singular in enlisting mathematical resources to underpin and inform such a position, refusing the hackneyed opposition between ‘static’ mathematical logic versus ‘dynamic’ physical world. This is an international collection of work commissioned from foremost philosophers, mathematicians and philosophers of science, to address the wide range (...)
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  28. Jeffry L. Hirst (1999). Reverse Mathematics of Prime Factorization of Ordinals. Archive for Mathematical Logic 38 (3):195-201.score: 19.0
    One of the earliest applications of Cantor's Normal Form Theorem is Jacobstahl's proof of the existence of prime factorizations of ordinals. Applying the techniques of reverse mathematics, we show that the full strength of the Normal Form Theorem is used in this proof.
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  29. Jeffry L. Hirst (2006). Reverse Mathematics of Separably Closed Sets. Archive for Mathematical Logic 45 (1):1-2.score: 19.0
    This paper contains a corrected proof that the statement “every non-empty closed subset of a compact complete separable metric space is separably closed” implies the arithmetical comprehension axiom of reverse mathematics.
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  30. Sam Sanders & Keita Yokoyama (2012). The Dirac Delta Function in Two Settings of Reverse Mathematics. Archive for Mathematical Logic 51 (1-2):99-121.score: 19.0
    The program of Reverse Mathematics (Simpson 2009) has provided us with the insight that most theorems of ordinary mathematics are either equivalent to one of a select few logical principles, or provable in a weak base theory. In this paper, we study the properties of the Dirac delta function (Dirac 1927; Schwartz 1951) in two settings of Reverse Mathematics. In particular, we consider the Dirac Delta Theorem, which formalizes the well-known property ${\int_\mathbb{R}f(x)\delta(x)\,dx=f(0)}$ of the Dirac delta function. (...)
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  31. Justin Clarke-Doane (2012). Morality and Mathematics: The Evolutionary Challenge. Ethics 122 (2):313-340.score: 18.0
    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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  32. Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.score: 18.0
    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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  33. Stewart Shapiro (2011). Epistemology of Mathematics: What Are the Questions? What Count as Answers? Philosophical Quarterly 61 (242):130-150.score: 18.0
    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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  34. Ian Hacking (2011). Why is There Philosophy of Mathematics AT ALL? South African Journal of Philosophy 30 (1):1-15.score: 18.0
    Mathematics plays an inordinate role in the work of many of famous Western philosophers, from the time of Plato, through Husserl and Wittgenstein, and even to the present. Why? This paper points to the experience of learning or making mathematics, with an emphasis on proof. It distinguishes two sources of the perennial impact of mathematics on philosophy. They are classified as Ancient and Enlightenment. Plato is emblematic of the former, and Kant of the latter. The Ancient fascination (...)
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  35. Antony Eagle (2008). Mathematics and Conceptual Analysis. Synthese 161 (1):67–88.score: 18.0
    Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number (...)
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  36. John P. Burgess & Gideon A. Rosen (1997). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford University Press.score: 18.0
    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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  37. John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.score: 18.0
    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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  38. Eric Mandelbaum (2013). Numerical Architecture. Topics in Cognitive Science 5 (1):367-386.score: 18.0
    The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, (...)
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  39. Paola Cantù, Bolzano Versus Kant: Mathematics as a Scientia Universalis. Philosophical Papers Dedicated to Kevin Mulligan.score: 18.0
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome (...)
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  40. Mikhail G. Katz & Thomas Mormann, Infinitesimals and Other Idealizing Completions in Neo-Kantian Philosophy of Mathematics.score: 18.0
    We seek to elucidate the philosophical context in which the so-called revolution of rigor in inifinitesimal calculus and mathematical analysis took place. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at that time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our main thesis is that Marburg Neo-Kantian philosophy formulated a sophisticated (...)
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  41. Richard L. Tieszen (2005). Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge University Press.score: 18.0
    Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this book is divided into three parts. Part I, Reason, Science, and Mathematics contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay oN phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some (...)
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  42. Mark Colyvan, Indispensability Arguments in the Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.score: 18.0
    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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  43. Paul Benacerraf & Hilary Putnam (eds.) (1983). Philosophy of Mathematics: Selected Readings. Cambridge University Press.score: 18.0
    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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  44. Carlo Cellucci (1996). Mathematical Logic: What has It Done for the Philosophy of Mathematics? In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel, pp. 365-388. A K Peters.score: 18.0
    onl y to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community and so seem worth discussing anyhow. Such claims will be used as reference to make some remarks about the present state of relations between mathematical logic and the philosophy of mathematics.
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  45. Nicholas Maxwell (2010). Wisdom Mathematics. Friends of Wisdom Newsletter (6):1-6.score: 18.0
    For over thirty years I have argued that all branches of science and scholarship would have both their intellectual and humanitarian value enhanced if pursued in accordance with the edicts of wisdom-inquiry rather than knowledge-inquiry. I argue that this is true of mathematics. Viewed from the perspective of knowledge-inquiry, mathematics confronts us with two fundamental problems. (1) How can mathematics be held to be a branch of knowledge, in view of the difficulties that view engenders? What could (...)
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  46. Paola Cantù (2010). Aristotle's Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities. Synthese 174 (2):225 - 235.score: 18.0
    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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  47. James Robert Brown (1999). Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. Routledge.score: 18.0
    Philosophy of Mathematics is clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.
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  48. Michael D. Resnik (1997). Mathematics as a Science of Patterns. New York ;Oxford University Press.score: 18.0
    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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  49. Penelope Maddy (1997). Naturalism in Mathematics. Oxford University Press.score: 18.0
    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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  50. Hilary Putnam (1979). Mathematics, Matter, and Method. Cambridge University Press.score: 18.0
    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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