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Mathematical Intuition - Phenomenology and Mathematical Knowledge (Hardcover, 1989 ed.)
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Mathematical Intuition - Phenomenology and Mathematical Knowledge (Hardcover, 1989 ed.)
Series: Synthese Library, 203
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"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
portrayed as if it were the Third Eye, something only mathematical
"mystics," like Ramanujan, possess. In mathematics the notion has
also been used in a host of other senses: by "intuitive" one might
mean informal, or non-rigourous, or visual, or holistic, or
incomplete, or perhaps even convincing in spite of lack of proof.
My aim in this book is to sweep all of this aside, to argue that
there is a perfectly coherent, philosophically respectable notion
of mathematical intuition according to which intuition is a
condition necessary for mathemati cal knowledge. I shall argue that
mathematical intuition is not any special or mysterious kind of
faculty, and that it is possible to make progress in the
philosophical analysis of this notion. This kind of undertaking has
a precedent in the philosophy of Kant. While I shall be mostly
developing ideas about intuition due to Edmund Husser there will be
a kind of Kantian argument underlying the entire book."
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