[Alta-Logic] Save the Date: The Calgary Mathematics & Philosophy Lecture March 16: Emily Grosholz

[Richard Zach]

  Theory Reduction, Algebraic Number Theory, and the Complex
  Plane<https://ucalgary.ca/mathphil/files/mathphil/grosholz-poster.pdf>


    Emily Grosholz
    Pennsylvania State University


    Thursday, March 16, 2017, 3:30 pm
    ICT 121 (Lecture Theatre Five)

How does mathematical knowledge grow? According to an influential 
formulation due to philosopher Ernest Nagel, when a scientific theory 
"reduces" another, the reduced theory is deductively subsumed under the 
reducing theory: thus for example chemistry is deduced from quantum 
mechanics, and molecular biology from chemistry. Recent critics, using 
examples from science, argue that Nagel's criteria for theory reduction 
are both too strict, and too weak. Prof. Grosholz reviews Nagel's model 
and its difficulties, and argues that theory reduction faces similar 
problems in mathematics. Certain proofs of Fermat's conjectures about 
whole number solutions of quadratic and cubic polynomials, by means of 
the alliance of number theory with complex analysis, lead not 
deductively but abductively (adding content) to the study of algebraic 
number fields, and class field theory. This extension of number theory 
is at once too strong and too weak to look like Nagelian theory 
reduction, which is precisely why it turns out to be so fruitful.

*Emily Grosholz* <http://emilygrosholz.com/> is Edwin Erle Sparks 
Professor of Philosophy at the Pennsylvania State University. She is the 
author of monographs on Descartes, Leibniz and the role of "productive 
ambiguity" in mathematics and the sciences. She edited a collection of 
essays on Leibniz, time and history, as a special issue of /Studia 
Leibnitiana/ (44 / 1 2012), as well as collection of essays on modern 
cosmology and time as a special issue of /Studies in the History and 
Philosophy of Modern Physics/ (52 / Part A 2015). Her new philosophy 
book /Starry Reckoning: Reference and Analysis in Mathematics and 
Cosmology/ is just out from Springer in the SAPERE series edited by 
Lorenzo Magnani. Next year, Springer will publish her book on poetry and 
mathematics, /Great Circles: The Transits of Mathematics and Poetry/ in 
a new series, Mathematics, Culture and the Arts, edited by Margerie 
Senechal, Jeremy Gray and Jed Buchwald. /

This talk is the third annual Calgary Mathematics & Philosophy Lecture 
<https://www.ucalgary.ca/mathphil/>, co-sponsored by PIMS 
<http://www.pims.math.ca/>, the Pacific Institute for the Mathematical 
Sciences, the Department of Philosophy, <http://phil.ucalgary.ca/> and 
the /Department of Mathematics <http://math.ucalgary.ca/>/. The 
Mathematics & Philosophy Lectures aim to introduce topics at the 
intersection of mathematics and philosophy to a general academic 
audience. The event is free & open to the public; a reception follows/
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