Results for 'mathematical intuition'

993 found
Order:
See also
  1.  20
    Mathematical Intuition: Phenomenology and Mathematical Knowledge.Richard L. Tieszen - 1989 - Dordrecht/Boston/London: Kluwer Academic Publishers.
    "Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes (...)
    Direct download  
     
    Export citation  
     
    Bookmark   23 citations  
  2. Mathematical Intuition: Phenomenology and Mathematical Knowledge.Richard L. TIESZEN - 1993 - Studia Logica 52 (3):484-486.
    The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a (...)
     
    Export citation  
     
    Bookmark   15 citations  
  3. X*—Mathematical Intuition.Charles Parsons - 1980 - Proceedings of the Aristotelian Society 80 (1):145-168.
    Charles Parsons; X*—Mathematical Intuition, Proceedings of the Aristotelian Society, Volume 80, Issue 1, 1 June 1980, Pages 145–168, https://doi.org/10.1093/ari.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   56 citations  
  4. Mathematical intuition and the cognitive roots of mathematical concepts.Giuseppe Longo & Arnaud Viarouge - 2010 - 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 analysis (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5. Kitcher, Mathematical Intuition, and Experience.Mark McEvoy - 2007 - Philosophia Mathematica 15 (2):227-237.
    Mathematical apriorists sometimes hold that our non-derived mathematical beliefs are warranted by mathematical intuition. Against this, Philip Kitcher has argued that if we had the experience of encountering mathematical experts who insisted that an intuition-produced belief was mistaken, this would undermine that belief. Since this would be a case of experience undermining the warrant provided by intuition, such warrant cannot be a priori.I argue that this leaves untouched a conception of intuition as (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  6.  38
    Mathematical intuition.John-E. Nolt - 1983 - Philosophy and Phenomenological Research 44:189-212.
    MATHEMATICAL INTUITION IS OFTEN REGARDED AS A SPECIAL FORM\nOF PERCEPTION WHOSE OBJECTS ARE ABSTRACT ENTITIES. THE\nTHESIS OF THIS PAPER IS THAT MATHEMATICAL INTUITION IS JUST\nORDINARY PERCEPTION AND IMAGINATION OF FAMILIAR OBJECTS. IT\nIS DISTINGUISHED, HOWEVER, BY ITS MODE OF\nCONCEPTUALIZATION, WHICH UTILIZES RELATIVELY FEW PREDICATES\nAND HENCE TREATS MANY DISTINCT OBJECTS AS\nINDISTINGUISHABLE.
    Direct download  
     
    Export citation  
     
    Bookmark  
  7. Mathematical intuition vs. mathematical monsters.Solomon Feferman - 2000 - Synthese 125 (3):317-332.
    Geometrical and physical intuition, both untutored andcultivated, is ubiquitous in the research, teaching,and development of mathematics. A number ofmathematical ``monsters'', or pathological objects, havebeen produced which – according to somemathematicians – seriously challenge the reliability ofintuition. We examine several famous geometrical,topological and set-theoretical examples of suchmonsters in order to see to what extent, if at all,intuition is undermined in its everyday roles.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   22 citations  
  8. Mathematical Intuition and Wittgenstein.David Henley - 1992 - In Christopher Ormell (ed.), New Thinking About the Nature of Mathematics. pp. 39-43.
    This paper covers some large subjects: as well as intuition and Wittgenstein, it also discusses modern computing. However it only traces one thread through these topics. Basically it proposes that a computational analysis of Wittgenstein's Tractatus can shed light upon processes of discovery in mathematics.
     
    Export citation  
     
    Bookmark   1 citation  
  9. Arithmetic, Mathematical Intuition, and Evidence.Richard Tieszen - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):28-56.
    This paper provides examples in arithmetic of the account of rational intuition and evidence developed in my book After Gödel: Platonism and Rationalism in Mathematics and Logic . The paper supplements the book but can be read independently of it. It starts with some simple examples of problem-solving in arithmetic practice and proceeds to general phenomenological conditions that make such problem-solving possible. In proceeding from elementary ‘authentic’ parts of arithmetic to axiomatic formal arithmetic, the paper exhibits some elements of (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  10.  42
    Parsons’ Mathematical Intuition: a Brief Introduction.Iris Merkač - 2013 - Croatian Journal of Philosophy 13 (1):99-107.
    The paper offers one of Parsons’ main themes in his book Mathematical Thought and Its Objects of 2008 : the role of intuition in our understanding of arithmetic. Our discussion does not cover all of the issues that have relevance for Parsons’ account of mathematical intuition, but we focus on the question: whether our knowledge that there is a model for arithmetic can reasonably be called intuitive. We focus on this question because we have some concerns (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. Mathematical Intuition and Natural Numbers: A Critical Discussion.Felix Mühlhölzer - 2010 - Erkenntnis 73 (2):265-292.
    Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  12. Mathematical intuition and Husserl's phenomenology.Richard Tieszen - 1984 - Noûs 18 (3):395-421.
  13. Mathematical intuition and physical intuition in Wittgenstein's later philosophy.Mark Steiner - 2000 - Synthese 125 (3):333-340.
  14. Mathematical intuition and objectivity.Daniel Isaacson - 1994 - In Alexander George (ed.), Mathematics and Mind. Oxford University Press. pp. 118--140.
    Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  15.  84
    Mathematical intuition.John E. Nolt - 1983 - Philosophy and Phenomenological Research 44 (2):189-211.
  16. Mathematical Discourse vs. Mathematical Intuition.Carlo Cellucci - 2005 - In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics. College Publications. pp. 137-165..
    The aim of this article is to show that intuition plays no role in mathematics. That intuition plays a role in mathematics is mainly associated to the view that the method of mathematics is the axiomatic method. It is assumed that axioms are directly (Gödel) or indirectly (Hilbert) justified by intuition. This article argues that all attempts to justify axioms in terms of intuition fail. As an alternative, the article supports the view that the method of (...)
     
    Export citation  
     
    Bookmark   9 citations  
  17. Platonism and mathematical intuition in Kurt gödel's thought.Charles Parsons - 1995 - Bulletin of Symbolic Logic 1 (1):44-74.
    The best known and most widely discussed aspect of Kurt Gödel's philosophy of mathematics is undoubtedly his robust realism or platonism about mathematical objects and mathematical knowledge. This has scandalized many philosophers but probably has done so less in recent years than earlier. Bertrand Russell's report in his autobiography of one or more encounters with Gödel is well known:Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal “not” was laid up in heaven, where (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   46 citations  
  18. Perception and mathematical intuition.Penelope Maddy - 1980 - Philosophical Review 89 (2):163-196.
  19. Mathematical Intuition.Philip Kitcher - 1983 - In The nature of mathematical knowledge. Oxford: Oxford University Press.
    If we are to obtain a priori mathematical knowledge by following proofs, then we have to be able to have a priori knowledge of the axioms. This chapter examines the major accounts of how such knowledge might be gained. It is argued that all these accounts fail.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  20. Nominalism and Mathematical Intuition.Otávio Bueno - 2008 - ProtoSociology 25:89-107.
    As part of the development of an epistemology for mathematics, some Platonists have defended the view that we have (i) intuition that certain mathematical principles hold, and (ii) intuition of the properties of some mathematical objects. In this paper, I discuss some difficulties that this view faces to accommodate some salient features of mathematical practice. I then offer an alternative, agnostic nominalist proposal in which, despite the role played by mathematical intuition, these difficulties (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  21. Gödelian platonism and mathematical intuition.Wesley Wrigley - 2021 - European Journal of Philosophy 30 (2):578-600.
    European Journal of Philosophy, Volume 30, Issue 2, Page 578-600, June 2022.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  22.  12
    Mathematical Intuition: Phenomenology and Mathematical Knowledge. [REVIEW]Michael D. Resnik - 1990 - Review of Metaphysics 44 (2):442-443.
    Both phenomenologists and analytical philosophers of mathematics should profit from this excellent exposition and defense of Husserl's account of mathematical knowledge. Tieszen places Philosophie der Arithmetik in the context of Husserl's later phenomenological thinking and demonstrates thereby that Husserl's contributions to the philosophy of mathematics are much more important than most of us, influenced by Frege's denigrating critique of Husserl's early psychologism, had thought. He also makes a convincing case for the phenomenological approach to constructive mathematics.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  23.  55
    Poincare on Mathematics, Intuition and the Foundations of Science.Janet Folina - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:217 - 226.
    In his first philosophy book, Science and Hypothesis, Poincare provides a picture in which the different sciences are arranged in a hierarchy. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; and so on. Poincare's basic view was that experiment in science depends on fixing other concepts first. More generally, certain concepts must be fixed before others: hence the (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  24.  33
    Mathematical Intuition[REVIEW]Michael D. Resnik - 1990 - Review of Metaphysics 44 (2):442-444.
  25.  29
    Poincaré on mathematical intuition. A phenomenological approach to Poincaré's philosophy of arithmetic.Jairo José Da Silva - 1996 - Philosophia Scientiae 1 (2):87-99.
  26.  19
    Mathematical Intuition and Natural Numbers: A Critical Discussion. [REVIEW]Felix Mühlhölzer - 2010 - Erkenntnis 73 (2):265-292.
    Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  27. Parsons on mathematical intuition.James Page - 1993 - Mind 102 (406):223-232.
    Charles Parsons has argued that we have the ability to apprehend, or "intuit", certain kinds of abstract objects; that among the objects we can intuit are some which form a model for arithmetic; and that our knowledge that the axioms of arithmetic are true in this model involves our intuition of these objects. I find a problem with Parson's claim that we know this model is infinite through intuition. Unless this problem can be resolved. I question whether our (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  28. Parsons on mathematical intuition and obviousness.Michael D. Resnik - 2000 - In Gila Sher & Richard Tieszen (eds.), Between logic and intuition: essays in honor of Charles Parsons. New York: Cambridge University Press. pp. 219--231.
     
    Export citation  
     
    Bookmark   2 citations  
  29.  73
    Gödel, Realism and Mathematical 'Intuition'.Michael Hallett - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 113--131.
    Direct download  
     
    Export citation  
     
    Bookmark  
  30. Nominalism and Mathematical Intuition.Otávio Bueno - 2008 - In Gerhard Preyer (ed.), Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism. Frankfort, Germany: Ontos. pp. 93-111.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  31. A Few Remarks about Mathematical Intuition.Jerzy Pogonowski - 2012 - Filozofia Nauki 20 (2).
  32. Kitcher on Kant and Mathematical Intuition.A. T. Winterbourne - 1989 - Kant Studien 80 (2):180.
     
    Export citation  
     
    Bookmark  
  33. Platonism and mathematical intuition in Kurt Gödel's thought.Charles Parsons - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: essays for his centennial. Association for Symbolic Logic.
     
    Export citation  
     
    Bookmark  
  34.  14
    Chapter Eight. Mathematical Intuition.Øystein Linnebo - 2017 - In Philosophy of Mathematics. Princeton, NJ: Princeton University Press. pp. 116-125.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  35.  2
    On the source of mathematical intuition.António Machiavelo - 2013 - Kairos 6:223-237.
    info:eu-repo/semantics/publishedVersion.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  36.  25
    Transcendental Arguments and Mathematical Intuition in Kant.B. E. Oguah - 1980 - Kant Studien 71 (1-4):35-46.
  37.  3
    Transcendental Arguments and Mathematical Intuition in Kant.B. E. Oguah - 1980 - Kant Studien 71 (1-4):35-46.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  38.  42
    The Three Formal Phenomenological Structures: A Means to Assess the Essence of Mathematical Intuition.A. Van-Quynh - 2019 - Journal of Consciousness Studies 26 (5-6):219-241.
    In a recent article I detailed at length the methodology employed to explore the reflective and pre-reflective contents of singular intuitive experiences in contemporary mathematics in order to propose an essential structure of intuition arousal in mathematics. In this paper I present the phenomenological assessment of the essential structure according to the three formal structures as proposed by Sokolowski's scheme and show their relevance in the description of the intuitive experience in mathematics. I also show that this essential structure (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  39.  1
    Book Review. Richard Tieszen, Mathematical Intuition: Phenomenology and Mathematical Knowledge. [REVIEW]D. van Dalen - 1993 - Husserl Studies 10 (3):249-252.
  40.  32
    Richard L. Tieszen. Mathematical intuition. Phenomenology and mathematical knowledge. Synthese library, vol. 203. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1989, xv + 209 pp. [REVIEW]Guillermo E. Rosado Haddock - 1991 - Journal of Symbolic Logic 56 (1):356-360.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  41.  16
    Ethics and Mathematics. Intuitive Thinking in Cantor, Gödel and Steiner. [REVIEW]Reiner Wimmer - 1987 - Philosophy and History 20 (1):36-36.
  42. Richard L. Tieszen. 'Mathematical Intuition: Phenomenology and Mathematical Knowledge'. [REVIEW]D. van Dalen - 1993 - Husserl Studies 10 (3):249-252.
  43. Poincaré, Kant, and the Scope of Mathematical Intuition.Terry F. Godlove - 2009 - Review of Metaphysics 62 (4):779-801.
    Today it is no news to point out that Kant’s doctrine of space as a form of intuition is motivated by epistemological considerations independent of his commitment to Euclidean geometry. These considerations surface—apparently without his own recognition—in Poincaré’s, Science and Hypothesis, the very work that helped turn analytically-minded philosophers away from the Critique. I argue that we should view Poincaré as refining Kant’s doctrine of space as the form of intuition, even as we see both views as arbitrarily (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  44. Intuition in Mathematics.Elijah Chudnoff - 2014 - In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press.
    The literature on mathematics suggests that intuition plays a role in it as a ground of belief. This article explores the nature of intuition as it occurs in mathematical thinking. Section 1 suggests that intuitions should be understood by analogy with perceptions. Section 2 explains what fleshing out such an analogy requires. Section 3 discusses Kantian ways of fleshing it out. Section 4 discusses Platonist ways of fleshing it out. Section 5 sketches a proposal for resolving the (...)
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  45. Intuition and visualization in mathematical problem solving.Valeria Giardino - 2010 - Topoi 29 (1):29-39.
    In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  46. Reliabilism, Intuition, and Mathematical Knowledge.Jennifer Wilson Mulnix - 2008 - Filozofia 62 (8):715-723.
    It is alleged that the causal inertness of abstract objects and the causal conditions of certain naturalized epistemologies precludes the possibility of mathematical know- ledge. This paper rejects this alleged incompatibility, while also maintaining that the objects of mathematical beliefs are abstract objects, by incorporating a naturalistically acceptable account of ‘rational intuition.’ On this view, rational intuition consists in a non-inferential belief-forming process where the entertaining of propositions or certain contemplations results in true beliefs. This view (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  47. Poincaré: Mathematics & logic & intuition.Colin Mclarty - 1997 - Philosophia Mathematica 5 (2):97-115.
    often insisted existence in mathematics means logical consistency, and formal logic is the sole guarantor of rigor. The paper joins this to his view of intuition and his own mathematics. It looks at predicativity and the infinite, Poincaré's early endorsement of the axiom of choice, and Cantor's set theory versus Zermelo's axioms. Poincaré discussed constructivism sympathetically only once, a few months before his death, and conspicuously avoided committing himself. We end with Poincaré on Couturat, Russell, and Hilbert.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  48.  50
    Intuition and Infinity: A Kantian Theme with Echoes in the Foundations of Mathematics.Carl Posy - 2008 - Royal Institute of Philosophy Supplement 63:165-193.
    Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’. And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can have (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  49.  37
    Intuition in Mathematics: a Perceptive Experience.Alexandra Van-Quynh - 2017 - Journal of Phenomenological Psychology 48 (1):1-38.
    This study applied a method of assisted introspection to investigate the phenomenology of mathematical intuition arousal. The aim was to propose an essential structure for the intuitive experience of mathematics. To achieve an intersubjective comparison of different experiences, several contemporary mathematicians were interviewed in accordance with the elicitation interview method in order to collect pinpoint experiential descriptions. Data collection and analysis was then performed using steps similar to those outlined in the descriptive phenomenological method that led to a (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  50. Mathematics, Metaphysics and Intuition in Kant.Emily Carson - 1996 - Dissertation, Harvard University
    This thesis attempts to argue against an influential interpretation of Kant's philosophy of mathematics according to which the role of pure intuition is primarily logical. Kant's appeal to pure intuition, and consequently his belief in the synthetic character of mathematics, is, on this view, a result of the limitations of the logical resources available in his time. In contrast to this, a reading is presented of the development of Kant's philosophy of mathematics which emphasises a much richer philosophical (...)
     
    Export citation  
     
    Bookmark   1 citation  
1 — 50 / 993