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Summary: Visual Thinking in Mathematics: An Epistemological Study
by Marcus Giaquinto
ISBN: 978-0-19-928594-5, vii+287
reviewed by Jeremy Avigad1
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 in-
formed, to set in their place new ones which are, if possible,
more adequately secured. [7, p. 5]2
But the ensuing strategy for grounding mathematical knowledge sounds
strange to the modern ear. For Husserl cast his work as a sequence of
"psychological and logical investigations," providing a psychological analy-
sis
. . . of the concepts multiplicity, unity, and number, insofar as they
are given to use authentically and not through indirect symbol-
izations. (ibid., pp. 67)
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