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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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Mathematics as Sign - Writing, Imagining, Counting (Hardcover)
Loot Price: R2,487
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Mathematics as Sign - Writing, Imagining, Counting (Hardcover)
Series: Writing Science
Expected to ship within 12 - 17 working days
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Two features of mathematics stand out: its menagerie of seemingly
eternal objects (numbers, spaces, patterns, functions, categories,
morphisms, graphs, and so on), and the hieroglyphics of special
notations, signs, symbols, and diagrams associated with them. The
author challenges the widespread belief in the extra-human origins
of these objects and the understanding of mathematics as either a
purely mental activity about them or a formal game of manipulating
symbols. Instead, he argues that mathematics is a vast and unique
man-made imagination machine controlled by writing.
"Mathematics as Sign" addresses both aspects--mental and
linguistic--of this machine. The opening essay, "Toward a Semiotics
of Mathematics" (long acknowledged as a seminal contribution to its
field), sets out the author's underlying model. According to this
model, "doing" mathematics constitutes a kind of waking dream or
thought experiment in which a proxy of the self is propelled around
imagined worlds that are conjured into intersubjective being
through signs.
Other essays explore the status of these signs and the nature of
mathematical objects, how mathematical ideograms and diagrams
differ from each other and from written words, the probable fate of
the real number continuum and calculus in the digital era, the
manner in which Platonic and Aristotelean metaphysics are enshrined
in the contemporary mathematical infinitude of endless counting,
and the possibility of creating a new conception of the sequence of
whole numbers based on what the author calls non-Euclidean
counting.
Reprising and going beyond the critique of number in "Ad
Infinitum," the essays in this volume offer an accessible insight
into Rotman's project, one that has been called "one of the most
original and important recent contributions to the philosophy of
mathematics."
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