Essays on the Foundations of Mathematics by Moritz Pasch (2010) (The Western Ontario Series in Philosophy of Science #83)

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Synopsis
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.
Copyright:
2010

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9789048194162
Related ISBNs:
9789048194155
Publisher:
Springer Netherlands
Date of Addition:
Copyrighted By:
Springer Netherlands, Dordrecht
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
History, Nonfiction, Science, Mathematics and Statistics, Philosophy
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.
Edited by:
Stephen Pollard

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