Results for 'mathematics'

1000+ found
Order:
  1. 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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   114 citations  
  2. 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   43 citations  
  3. 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 (...)
     
    Export citation  
     
    My bibliography   26 citations  
  4.  98
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   70 citations  
  5. Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
    This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of (...)--the view that mathematics is about things that really exist. (shrink)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   85 citations  
  6.  51
    Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  7. 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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   78 citations  
  8. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.John P. Burgess & Gideon 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   75 citations  
  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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   96 citations  
  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’ (...)
    Translate
     
     
    Export citation  
     
    My bibliography   2 citations  
  11.  30
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  12.  25
    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. (...)
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  13.  21
    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, (...)
    Direct download  
    Translate
     
     
    Export citation  
     
    My bibliography  
  14.  11
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  15. 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..
    Direct download  
     
    Export citation  
     
    My bibliography   272 citations  
  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.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   77 citations  
  17. Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  18. 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.
     
    Export citation  
     
    My bibliography   18 citations  
  19.  91
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   7 citations  
  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)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   31 citations  
  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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   61 citations  
  22. Realism, Mathematics & Modality.Hartry Field - 1989 - Blackwell.
  23.  76
    The Necessity of Mathematics.Juhani Yli-Vakkuri & John Hawthorne - manuscript
    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.
    Direct download  
     
    Export citation  
     
    My bibliography  
  24.  36
    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. (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   32 citations  
  25. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  26.  83
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   28 citations  
  27. Visual Thinking in Mathematics: An Epistemological Study.Marcus 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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   15 citations  
  28.  17
    Computational Reverse Mathematics and Foundational Analysis.Benedict Eastaugh - manuscript
    Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  29.  77
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   28 citations  
  30.  51
    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 ...
    Direct download  
     
    Export citation  
     
    My bibliography   23 citations  
  31.  91
    Phenomenology, Logic, and the Philosophy of Mathematics.Richard Tieszen - 2005 - Cambridge University Press.
    Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I 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 work of Quine, Penelope (...)
    Direct download  
     
    Export citation  
     
    My bibliography   12 citations  
  32.  36
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   39 citations  
  33.  42
    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 ...
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   28 citations  
  34.  35
    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.
    Direct download  
     
    Export citation  
     
    My bibliography   27 citations  
  35. 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  36.  49
    Towards a Philosophy of Real Mathematics.David Corfield - 2005 - Cambridge University Press.
    In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   11 citations  
  37.  64
    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.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   11 citations  
  38. 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  39. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   12 citations  
  40. Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble - forthcoming - 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.
    Direct download  
     
    Export citation  
     
    My bibliography  
  41.  46
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   16 citations  
  42. Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice.Lisa Shabel - 2002 - Routledge.
    This book provides a reading of Kant's theory of the construction of mathematical concepts through a fully contextualised analysis. In this work the author argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, that the material and context necessary for a successful interpretation of Kant's philosophy can be provided.
     
    Export citation  
     
    My bibliography   12 citations  
  43.  85
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   9 citations  
  44. 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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  45.  44
    A Structural Account of Mathematics.Charles S. Chihara - 2003 - Oxford University Press UK.
    Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which (...)
    Direct download  
     
    Export citation  
     
    My bibliography   10 citations  
  46.  24
    Set Existence Principles and Closure Conditions: Unravelling the Standard View of Reverse Mathematics.Benedict Eastaugh - forthcoming - Philosophia Mathematica.
    It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  47. 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 (...)
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  48.  57
    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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   7 citations  
  49. 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  50.  21
    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.
    Direct download  
     
    Export citation  
     
    My bibliography   29 citations  
1 — 50 / 1000