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Essays on the Foundations of Mathematics by Moritz Pasch (Hardcover, 2010 ed.)
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Essays on the Foundations of Mathematics by Moritz Pasch (Hardcover, 2010 ed.)
Series: The Western Ontario Series in Philosophy of Science, 83
Expected to ship within 10 - 15 working days
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Moritz Pasch (1843-1930) is justly celebrated as a key figure in
the history of axiomatic geometry. Less well known are his
contributions to other areas of foundational research. This volume
features English translations of 14 papers Pasch published in the
decade 1917-1926. In them, Pasch argues that geometry and, more
surprisingly, number theory are branches of empirical science; he
provides axioms for the combinatorial reasoning essential to
Hilbert's program of consistency proofs; he explores "implicit
definition" (a generalization of definition by abstraction) and
indicates how this technique yields an "empiricist" reconstruction
of set theory; he argues that we cannot fully understand the
logical structure of mathematics without clearly distinguishing
between decidable and undecidable properties; he offers a rare
glimpse into the mind of a master of axiomatics, surveying in
detail the thought experiments he employed as he struggled to
identify fundamental mathematical principles; and much more. This
volume will: Give English speakers access to an important body of
work from a turbulent and pivotal period in the history of
mathematics, help us look beyond the familiar triad of formalism,
intuitionism, and logicism, show how deeply we can see with the
help of a guide determined to present fundamental mathematical
ideas in ways that match our human capacities, will be of interest
to graduate students and researchers in logic and the foundations
of mathematics.
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