37 found
Order:
Disambiguations
Marcus Giaquinto [26]M. Giaquinto [12]
  1.  59
    Visual Thinking in Mathematics: An Epistemological Study.Marcus Giaquinto - 2007 - Oxford, England: Oxford University Press.
    Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof.
  2. Visual Thinking in Mathematics: An Epistemological Study.Marcus Giaquinto - 2007 - Oxford, England: 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 thinking in (...)
  3.  12
    Visual Thinking in Mathematics. [REVIEW]Marcus Giaquinto - 2009 - Analysis 69 (2):401-403.
    Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians had for (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   60 citations  
  4. The Search for Certainty: A Philosophical Account of Foundations of Mathematics.Marcus Giaquinto - 2002 - Oxford, England: Oxford University Press.
    Marcus Giaquinto tells the compelling story of one of the great intellectual adventures of the modern era: the attempt to find firm foundations for mathematics. From the late nineteenth century to the present day, this project has stimulated some of the most original and influential work in logic and philosophy.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  5. Visualizing in Mathematics.Marcus Giaquinto - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 22-42.
    Visual thinking in mathematics is widespread; it also has diverse kinds and uses. Which of these uses is legitimate? What epistemic roles, if any, can visualization play in mathematics? These are the central philosophical questions in this area. In this introduction I aim to show that visual thinking does have epistemically significant uses. The discussion focuses mainly on visual thinking in proof and discovery and touches lightly on its role in understanding.
     
    Export citation  
     
    Bookmark   16 citations  
  6.  2
    The Search for Certainty: A Philosophical Account of Foundations of Mathematics.Marcus Giaquinto - 2002 - Oxford, England: Oxford University Press UK.
    Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty focuses (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  7. Crossing Curves: A Limit to the Use of Diagrams in Proofs†: Articles.Marcus Giaquinto - 2011 - Philosophia Mathematica 19 (3):281-307.
    This paper investigates the following question: when can one reliably infer the existence of an intersection point from a diagram presenting crossing curves or lines? Two cases are considered, one from Euclid's geometry and the other from basic real analysis. I argue for the acceptability of such an inference in the geometric case but against in the analytic case. Though this question is somewhat specific, the investigation is intended to contribute to the more general question of the extent and limits (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  8.  21
    Thought Experiments in Mathematics.Irina Starikova & Marcus Giaquinto - unknown
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  9. Non-Analytic Conceptual Knowledge.M. Giaquinto - 1996 - Mind 105 (418):249-268.
  10. The Search for Certainty. A Philosophical Account of Foundations of Mathematics.Marcus Giaquinto - 2004 - Revue Philosophique de la France Et de l'Etranger 194 (2):239-239.
     
    Export citation  
     
    Bookmark   11 citations  
  11. Hilbert's Philosophy of Mathematics.Marcus Giaquinto - 1983 - British Journal for the Philosophy of Science 34 (2):119-132.
  12.  8
    The Rationality of Induction.M. Giaquinto - 1987 - Philosophy of Science 54 (4):612-615.
  13.  15
    Knowing Numbers.Marcus Giaquinto - 2001 - Journal of Philosophy 98 (1):5.
  14.  72
    Knowing Numbers.Marcus Giaquinto - 2001 - Journal of Philosophy 98 (1):5-18.
  15.  15
    Cognitive Access to Numbers: The Philosophical Significance of Empirical Findings About Basic Number Abilities.Marcus Giaquinto - unknown
    How can we acquire a grasp of cardinal numbers, even the first very small positive cardinal numbers, given that they are abstract mathematical entities? That problem of cognitive access is the main focus of this paper. All the major rival views about the nature and existence of cardinal numbers face difficulties; and the view most consonant with our normal thought and talk about numbers, the view that cardinal numbers are sizes of sets, runs into the cognitive access problem. The source (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  16.  83
    Russell on Knowledge of Universals by Acquaintance.M. Giaquinto - 2012 - Philosophy 87 (4):497-508.
    Russell's book The Problems of Philosophy was first published a hundred years ago.¹ A remarkable feature of this enduring text is the glint of Platonism it presents on a dark empiricist sea: while our knowledge of physical objects is entirely mediated by direct awareness of sense data, we can also have direct awareness of certain universals, Russell claims.² This is questionable, even if one has no empiricist inclination. Universals are abstract, hence causally inert. How, then, can we have any knowledge (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  17.  30
    The Linguistic View of a Priori Knowledge.M. Giaquinto - 2008 - Philosophy 83 (1):89-111.
    This paper presents considerations against the linguistic view of a priori knowledge. The paper has two parts. In the first part I argue that problems about the individuation of lexical meanings provide evidence for a moderate indeterminacy, as distinct from the radical indeterminacy of meaning claimed by Quine, and that this undermines the idea of a priori knowledge based on knowledge of synonymies. In the second part of the paper I argue against the idea that a priori knowledge not based (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  18.  59
    Epistemology of Visual Thinking in Elementary Real Analysis.Marcus Giaquinto - 1994 - British Journal for the Philosophy of Science 45 (3):789-813.
    Can visual thinking be a means of discovery in elementary analysis, as well as a means of illustration and a stimulus to discovery? The answer to the corresponding question for geometry and arithmetic seems to be ‘yes’ (Giaquinto [1992], [1993]), and so a positive answer might be expected for elementary analysis too. But I argue here that only in a severely restricted range of cases can visual thinking be a means of discovery in analysis. Examination of persuasive visual routes to (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  19. Visualization.Marcus Giaquinto - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press.
     
    Export citation  
     
    Bookmark   4 citations  
  20.  39
    Visualizing as a Means of Geometrical Discovery.Marcus Giaquinto - 1992 - Mind and Language 7 (4):382-401.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  21.  47
    Mathematical Proofs: The Beautiful and The Explanatory.Marcus Giaquinto - unknown
    Mathematicians sometimes judge a mathematical proof to be beautiful and in doing so seem to be making a judgement of the same kind as aesthetic judgements of works of visual art, music or literature. Mathematical proofs are also appraised for explanatoriness: some proofs merely establish their conclusions as true, while others also show why their conclusions are true. This paper will focus on the prima facie plausible assumption that, for mathematical proofs, beauty and explanatoriness tend to go together. To make (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  22. Mathematical Activity.M. Giaquinto - 2005 - In Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. Dordrecht: Springer. pp. 75-87.
     
    Export citation  
     
    Bookmark   3 citations  
  23.  49
    Diagrams: Socrates and Meno's Slave.Marcus Giaquinto - 1993 - International Journal of Philosophical Studies 1 (1):81 – 97.
  24.  44
    Epistemology of the Obvious: A Geometrical Case.Marcus Giaquinto - 1998 - Philosophical Studies 92 (1/2):181 - 204.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  25. Visualizing in Arithmetic.M. Giaquinto - 1993 - Philosophy and Phenomenological Research 53 (2):385-396.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  26. Review of Mathematics as a Science of Patterns. [REVIEW]M. Giaquinto - forthcoming - Mind.
     
    Export citation  
     
    Bookmark   1 citation  
  27. Wang, H., "Reflections on Kurt Gödel". [REVIEW]M. Giaquinto - 1988 - Mind 97:634.
  28. On Mathematical Realism.M. Giaquinto - 1980
     
    Export citation  
     
    Bookmark  
  29.  57
    By Marcus Giaquinto.Marcus Giaquinto & Jeremy Avigad - unknown
    Published in 1891, Edmund Husserl’s first book, Philosophie der Arithmetik, aimed to “prepare the scientific foundations for a future construction of that discipline.” His goals should seem reasonable to contemporary philosophers of mathematics: . . . through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. [7, p. 5]2 But the (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  30.  32
    Infant Arithmetic: Wynn's Hypothesis Should Not Be Dismissed.Marcus Giaquinto - 1992 - Mind and Language 7 (4):364-366.
  31. Review of M. Resnik, Mathematics as a Science of Patterns[REVIEW]M. Giaquinto - 1999 - Mind 108 (432):761-788.
  32.  30
    The Rationality of Induction. D. C. Stove. [REVIEW]M. Giaquinto - 1987 - Philosophy of Science 54 (4):612-615.
  33.  2
    What Cognitive Systems Underlie Arithmetical Abilities?Marcus Giaquinto - 2001 - Mind and Language 16 (1):56-68.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  34.  11
    Science and Ideology.Marcus Giaquinto - 1984 - Proceedings of the Aristotelian Society 84:167 - 192.
    Direct download  
     
    Export citation  
     
    Bookmark  
  35.  1
    Visualizing in Arithmetic.M. Giaquinto - 1993 - Philosophy and Phenomenological Research 53 (2):385-396.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  36.  4
    X—Science and Ideology.Marcus Giaquinto - 1984 - Proceedings of the Aristotelian Society 84 (1):167-192.
  37.  32
    What Cognitive Systems Underlie Arithmetical Abilities?Marcus Giaquinto - 2001 - Mind and Language 16 (1):56–68.