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  1.  12
    Marcus Giaquinto, Mathematical Proofs: The Beautiful and The Explanatory.
    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 (...)
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  2.  10
    Marcus Giaquinto (2011). Visual Thinking in Mathematics. OUP Oxford.
    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.
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  3.  49
    Marcus Giaquinto (2001). Knowing Numbers. Journal of Philosophy 98 (1):5-18.
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  4.  93
    Marcus Giaquinto (1983). Hilbert's Philosophy of Mathematics. British Journal for the Philosophy of Science 34 (2):119-132.
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  5.  40
    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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  6.  34
    Marcus Giaquinto (1993). Diagrams: Socrates and Meno's Slave. International Journal of Philosophical Studies 1 (1):81 – 97.
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  7. Marcus Giaquinto (2004). The Search for Certainty: A Philosophical Account of Foundations of Mathematics. 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 (...)
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  8. Marcus Giaquinto (2008). Visualization. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. OUP Oxford
     
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  9.  25
    Marcus Giaquinto (2001). What Cognitive Systems Underlie Arithmetical Abilities? Mind and Language 16 (1):56–68.
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  10.  27
    Marcus Giaquinto (1992). Visualizing as a Means of Geometrical Discovery. Mind and Language 7 (4):382-401.
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  11.  36
    Marcus Giaquinto (1998). Epistemology of the Obvious: A Geometrical Case. Philosophical Studies 92 (1/2):181 - 204.
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  12.  32
    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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  13.  10
    Marcus Giaquinto (1992). Infant Arithmetic: Wynn's Hypothesis Should Not Be Dismissed. Mind and Language 7 (4):364-366.
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  14.  6
    Marcus Giaquinto (1983). Science and Ideology. Proceedings of the Aristotelian Society 84:167 - 192.
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