[logic-ml] Lectures by Prof. Jeremy Gray

[久木田水生]

皆さま、

重複して受け取られた方はご容赦願います。名古屋大学情報学研究科の久木田水生です。

数学者であり数学史研究家の Jeremy Gray
教授の講演が3月28日に慶應大学、4月2日に京都大学、4月7日に名古屋大学にて開催されます。いずれも参加費無料、事前登録は不要です。どうぞ奮ってご参加ください。

時間・場所、タイトル、要旨、プロフィールなどはこちらのウェブページ
http://www.is.nagoya-u.ac.jp/dep-ss/phil/kukita/seminars/jeremy-gray.html
または本メールの末尾をご覧ください。

なお4月7日の講演は応用哲学会年次大会の中のシンポジウムとして開催され、大会には参加費がかかりますが、シンポジウムのみの聴講は無料です。このシンポジウムでは
Gray 教授に加え、林晋教授（京都大学文学研究科）も登壇されます。

どうぞよろしくお願いいたします。

久木田水生


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Lectures by Prof. Jeremy Gray


March 28th, 2018, Keio University

Time: 15:00-18:00
Place: Meeting room, 4F of East Research Building, Keio University
Mita Campus. (Building No. 3 of this map:
https://www.keio.ac.jp/en/maps/mita.html)

Lecture 1 (15:00-16:00): ``Poincaré on proof and understanding''

Poincaré has an exaggerated reputation not being rigorous in his work.
In this talk I shall show that he cared about rigour in
mathematics,but had justified criticisms of it. However, the more
important task was to understand mathematics and physics, and this
meant to be enabled to discover new ideas. Certainty in abstract
mathematics was provided by the principle of recurrence, which imposed
limits on any theory of sets. Thereafter, a pragmatic sense of
certainty was provided in applied mathematics and physics by the use
of conventions. Conventions, he believed, govern our choice of a
geometry for space and the choice of the laws of mechanics and other
branches of physics. Objectivity, he said, depended on discourse, and
I shall argue that Poincaré’s fundamental position is that the use of
mathematics in science is close to Wittgenstein’s idea of a language
game.

Lecture 2 (16:00-17:00): ``The philosophy of Hermann Weyl''

By 1910, the year he turned 25, Weyl was developing a finitist
philosophy of mathematics, based on a logical theory of relations. He
also believed that the human mind can understand ideas only
sequentially. He developed this approach on his book The Continuum
(1918), and for a time came close to agreeing with Brouwer’s
intuitionism, but he abandoned them in the mid-1920s when he became
involved in exploring the theory of Lie groups. He then had to turn
back towards Hilbert’s ideas about mathematics and physics, and
developed his own theory of what he called the symbolic universe in
which mathematics and physics supported each other in complementary
ways. Weyl sought a unified philosophy that would govern not only his
scientific practice but be rooted in a theory of knowledge and an
understanding of how it is acquired.



April 2nd, 2018, Kyoto University

Time: 16:30-18:00
Place: Large conference room in the basement, Faculty of Letters Main
Building, Yoshida Campus, Kyoto University. (No. 8 of this map:
http://www.kyoto-u.ac.jp/en/access/yoshida/main.html)

``The philosophy of Hermann Weyl''

By 1910, the year he turned 25, Weyl was developing a finitist
philosophy of mathematics, based on a logical theory of relations. He
also believed that the human mind can understand ideas only
sequentially. He developed this approach on his book The Continuum
(1918), and for a time came close to agreeing with Brouwer’s
intuitionism, but he abandoned them in the mid-1920s when he became
involved in exploring the theory of Lie groups. He then had to turn
back towards Hilbert’s ideas about mathematics and physics, and
developed his own theory of what he called the symbolic universe in
which mathematics and physics supported each other in complementary
ways. Weyl sought a unified philosophy that would govern not only his
scientific practice but be rooted in a theory of knowledge and an
understanding of how it is acquired.



April 7th, Nagoya University: Symposium on Modernism and Modernisation
of Mathematics

Time: 16:15-18:35
Place: Room A31, Liberal Arts and Sciences Building A, Higashiyama
Campus, Nagoya University. (No. A4(1) of this map:
http://en.nagoya-u.ac.jp/map/index.html)

Lecture 1: Jeremy Gray, ``Poincaré and Weyl: two dissenters from
mathematical modernism''

Around 1900 a characteristic form of modern mathematics took over the
subject, which we associate with Georg Cantor, Richard Dedekind, and
David Hilbert among others. It sees mathematics as an autonomous
system of ideas, emphasises the formal or axiomatic aspects, and
brings about a complicated relationship with the sciences. Henri
Poincaré (1854?1912) and Hermann Weyl (1885?1955) preferred a much
more intimate connection between mathematics and physics and argued in
different ways for a symbiotic approach, which they also linked to a
broader philosophical vision.

Lecture 2: Susumu Hayashi, ``How was Mathematics modernized?''

I have been developing a historical view on the modernization, in the
sense of Max Weber sociology, of mathematics for the last 19 years. I
will outline it in this presentation. The starting point of my
research was an enigmatic (to me) claim by Kurt Godel in his
unpublished philosophical essay. His claim may be interpreted as
“World-views have been disenchanted (modernized) through the history
since the Renaissance. Particularly in physics, this development
reached a peak in the 20 th century. However, mathematics alone went
in the opposite direction as set theory was introduced into it.” My
historical view was slightly changed from Godel’s to make it fit into
Weber’s modernization theory. I will discuss how important Hilbert’s
program and Godel’s incompleteness theorems were for the modernization
of mathematics, and how they made the process of modernization of
mathematics somewhat different from the process of modernization of
physics.



Jeremy Gray short bio

Jeremy Gray is an Emeritus Professor of The Open University and an
Honorary Professor in the Mathematics Department at the University of
Warwick. His research interests are in the history of mathematics,
specifically the history of algebra, analysis, and geometry, and
mathematical modernism in the 19th and early 20th Centuries. The work
on mathematical modernism links the history of mathematics with the
history of science and issues in mathematical logic and the philosophy
of mathematics.

He was awarded the Otto Neugebauer Prize of the European Mathematical
Society in 2016 for his work in the history of mathematics, and the
Albert Leon Whiteman Memorial Prize of the American Mathematical
Society in 2009 for his contributions to the study of the history of
modern mathematics internationally. In 2012 he was elected an
Inaugural Fellow of the American Mathematical Society. In 2010 he was
one of the nine founder members of the Association for the Philosophy
of Mathematical Practice (APMP).

He is the author of eleven books, of which among the most recent are
Plato’s Ghost: The Modernist Transformation of Mathematics (Princeton
U.P. 2008), Henri Poincaré: a scientific biography (Princeton 2012),
and The Real and the Complex (Springer 2015). Two more books are to be
published in 2018: Under the Banner of Number: A History of Abstract
Algebra, by Springer, and Simply Riemann in the Simply Charly series
of e-books.

Contact Information
Minao Kukita (久木田水生), minao.kukita at i.nagoya-u.ac.jp