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Marcus Giaquinto [13]M. Giaquinto [12]
  1. Marcus Giaquinto & Jeremy Avigad, By Marcus Giaquinto.
    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 (...)
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  2. M. Giaquinto (forthcoming). Review of Mathematics as a Science of Patterns. [REVIEW] Mind.
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  3. M. Giaquinto (2012). Russell on Knowledge of Universals by Acquaintance. Philosophy 87 (04):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 (...)
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  4. M. Giaquinto (2011). Crossing Curves: A Limit to the Use of Diagrams in Proofs. 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 (...)
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  5. Marcus Giaquinto (2011). Visual Thinking in Mathematics. OUP Oxford.
    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 (...)
     
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  6. M. Giaquinto (2008). The Linguistic View of a Priori Knowledge. 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 (...)
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  7. Marcus Giaquinto (2008). Visualization. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oup Oxford.
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  8. M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.
    Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in (...)
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  9. M. Giaquinto, Mathematical Activity.
    Book description: This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams, etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. (...)
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  10. M. Giaquinto (2002). The Search for Certainty: A Philosophical Account of Foundations of Mathematics. 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.
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  11. Marcus Giaquinto (2001). Knowing Numbers. Journal of Philosophy 98 (1):5-18.
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  12. Marcus Giaquinto (2001). What Cognitive Systems Underlie Arithmetical Abilities? Mind and Language 16 (1):56–68.
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  13. M. Giaquinto (1999). Review of M. Resnik, Mathematics as a Science of Patterns. [REVIEW] Mind 108 (432):761-788.
  14. Marcus Giaquinto (1998). Epistemology of the Obvious: A Geometrical Case. Philosophical Studies 92 (1/2):181 - 204.
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  15. M. Giaquinto (1997). Reflections on Kurt Gödel. Mind 97:634-638.
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  16. M. Giaquinto (1996). Non-Analytic Conceptual Knowledge. Mind 105 (418):249-268.
  17. Marcus Giaquinto (1994). Epistemology of Visual Thinking in Elementary Real Analysis. 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 (...)
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  18. M. Giaquinto (1993). Visualizing in Arithmetic. Philosophy and Phenomenological Research 53 (2):385-396.
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  19. Marcus Giaquinto (1993). Diagrams: Socrates and Meno's Slave. International Journal of Philosophical Studies 1 (1):81 – 97.
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  20. Marcus Giaquinto (1992). Infant Arithmetic: Wynn's Hypothesis Should Not Be Dismissed. Mind and Language 7 (4):364-366.
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  21. Marcus Giaquinto (1992). Visualizing as a Means of Geometrical Discovery. Mind and Language 7 (4):382-401.
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  22. M. Giaquinto (1987). Book Review:The Rationality of Induction D. C. Stove. [REVIEW] Philosophy of Science 54 (4):612-.
  23. Marcus Giaquinto (1983). Hilbert's Philosophy of Mathematics. British Journal for the Philosophy of Science 34 (2):119-132.
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  24. Marcus Giaquinto (1983). Science and Ideology. Proceedings of the Aristotelian Society 84:167 - 192.
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