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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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Realizing Reason - A Narrative of Truth and Knowing (Hardcover)
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Realizing Reason - A Narrative of Truth and Knowing (Hardcover)
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Realizing Reason pursues three interrelated themes. First, it
traces the essential moments in the historical unfolding-from the
ancient Greeks, through Descartes, Kant, and developments in the
nineteenth century, to the present-that culminates in the
realization of pure reason as a power of knowing. Second, it
provides a cogent account of mathematical practice as a mode of
inquiry into objective truth. And finally, it develops and defends
a new conception of our being in the world, one that builds on and
transforms the now standard conception according to which our
experience of reality arises out of brain activity due, in part, to
merely causal impacts on our sense organs. Danielle Macbeth shows
that to achieve an adequate understanding of the striving for truth
in the exact sciences we must overcome this standard conception and
that the way to do that is through a more adequate understanding of
the nature of mathematical practice and the profound
transformations it has undergone over the course of its history,
the history through which reason is first realized as a power of
knowing. Because we can understand mathematical practice only if we
attend to the systems of written signs within which to do
mathematics, Macbeth provides an account of the nature and role of
written notations, specifically, of the principal systems that have
been developed within which to reason in mathematics: Euclidean
diagrams, the symbolic language of arithmetic and algebra, and
Frege's concept-script, Begriffsschrift.
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