<div dir="ltr"><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">早稲田大学高等研究所の秋吉と申します。</span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif"><br></span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">以下の要領で</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">ワークショップ「</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Computations, Proofs, and
Intuitions: A Workshop on Philosophy of Mathematics</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">」</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">(</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">WIAS Top Runners’ Lecture
Collection of Science)</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">開催のご案内をさせて頂きます。</span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif"><br></span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">ご都合よろしければぜひご参加ください。</span></p><p class="MsoNormal" align="left"><br></p><p class="MsoNormal" align="left">------------------------------------------------------------------------------------------------------------------------</p><p class="MsoNormal" align="left"><br></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">***Please
accept our apologies if you receive multiple copies of this email. ***</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">ワークショップご案内：</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">“</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Computations, Proofs, and
Intuitions: A Workshop on Philosophy of Mathematics</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">”</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">We
are pleased to invite you to a workshop titled “</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Computations, Proofs, and Intuitions: A
Workshop on Philosophy of Mathematics</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">” (WIAS Top Runners’ Lecture
Collection).</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">ワークショップ「</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Computations, Proofs, and
Intuitions: A Workshop on Philosophy of Mathematics</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">」</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">(</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">WIAS Top Runners’ Lecture
Collection of Science)</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">開催のご案内をさせて頂きます。参加自由です。お気軽にご参加ください。</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">----</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Title: Computations, Proofs,
and Intuitions: A Workshop on Philosophy of Mathematics</span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">「計算，証明，直観」：数学の哲学ワークショップ</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Date:
September 18 (Fri.), 2015</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Time:
10:00 – 18:00</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Place:
International Conference Center (Meeting Room 2, 3rd floor), Waseda University.</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">日時</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">: 2015</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">年</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">9</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">月</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">18</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">日</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">(</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">金</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">) 10:00 –
18:00</span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">会場</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">: </span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">早稲田大学早稲田キャンパス</span><span style="font-family:Helvetica,sans-serif"> </span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">国際会議場</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"> 3</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">階第</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">2</span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">会議室</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><u><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif;color:rgb(56,110,255)">（</span></u><span lang="EN-US"><a href="https://www.waseda.jp/top/access/waseda-campus#anc_8"><span style="font-family:Helvetica,sans-serif">https://www.waseda.jp/top/access/waseda-campus#anc_8</span></a></span><u><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif;color:rgb(56,110,255)">）</span></u><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US"><a href="http://www.waseda.jp/top/assets/uploads/2015/08/waseda-campus-map.pdf"><span style="font-family:Helvetica,sans-serif">http://www.waseda.jp/top/assets/uploads/2015/08/waseda-campus-map.pdf</span></a></span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">*
Bldg. 18 on the map.</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">PROGRAM</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">*************</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">10:00-10:10
Opening Remarks<a name="_GoBack"></a></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">10:10-11:10
“</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Game Theory and
"Symbolic" Logic”</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Speaker:
Mamoru Kaneko (Waseda University)</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">11:10-12:10
“</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Proof theory of the
lambda-calculus</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">”</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Speaker:
Masahiko Sato (Kyoto University)</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">12:10-14:00
Lunch Break</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">14:00-15:20
“</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">The <i>concept</i> of computation - an axiomatic characterization”</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Speaker:
Wilfried Sieg (Carnegie Mellon University)</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">15:20-15:40
Break</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">15:40-16:40
“</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Kant on mathematical
intuition: from an educational point of view”</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"> Speaker: Yasuo
Deguchi (Kyoto University)</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">16:40-17:00
Break</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">17:00-18:00
“Aspects of the notion of computability</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">”</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Speaker:
Makoto Kikuchi (Kobe University)</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">---------------------------------------------------------------------</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">世話人</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">: </span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">秋吉亮太（早稲田高等研究所助教）</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">主催</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">: </span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">早稲田高等研究所</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">問合せ先</span><span lang="EN-US" style="font-family:Helvetica,sans-serif">: </span><span style="font-family:'\00ff2d\00ff33 \00660e\00671d',serif">秋吉亮太</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal"><span lang="EN-US"><a href="mailto:georg.logic@gmail.com"><span style="font-family:Helvetica,sans-serif">georg.logic@gmail.com</span></a></span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">---------------------------------------------------------------------</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">ABSTRACTS</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">*************</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Speaker] Mamoru Kaneko
(Waseda University)</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial">[Title]
Game Theory and "Symbolic" Logic</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial">[Abstract]</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">In game theory, a
player chooses/adjusts his behavior based on his understanding of the game
situation and his decision/prediction criterion. In logic, a (ideal)
mathematician calculates/proves a target theorem from his assumptions. An
engine for such adjustments and calculations is logical inference. Such
behavior is of a highly symbolic nature. However, it has been customary in the
fields of mathematics as well as game theory that real targets are actual
models but not symbolic expressions (axiomatizations). This attitude should be
reversed when we take game theory as a serious study of human
behavior/decision-making in social contexts including considerations of
experiential sources for individual beliefs. This is very compatible with the
basic idea of “symbolic” logic. In this presentation, we discuss various
problems related to this interpretation.</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial"> </span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Speaker] Masahiko Sato
(Kyoto University)</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial">[Title]
Proof theory of the lambda-calculus</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Abstract]</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial">We present a new representation of
lambda-terms as a subalgebra</span><span lang="EN-US" style="font-family:Helvetica,sans-serif"><br>
<span style="background-image:initial;background-repeat:initial">of a free algebra. As elements of the free
algebra, lambda-terms are</span><br>
<span style="background-image:initial;background-repeat:initial">constructed without employing the abstraction
operation, and this</span><br>
<span style="background-image:initial;background-repeat:initial">construction of lambda-terms enables us to study
lambda-terms as</span><br>
<span style="background-image:initial;background-repeat:initial">natural finitary objects.</span><br>
<span style="background-image:initial;background-repeat:initial">In this setting, we will develop the
lambda-calculus by defining</span><br>
<span style="background-image:initial;background-repeat:initial">reductions as derivations and study the proof
theory of the</span><br>
<span style="background-image:initial;background-repeat:initial">lambda-calculus. We will develop the
theory in the Minlog proof</span><br>
<span style="background-image:initial;background-repeat:initial">assistant developed by Helmut Schwichtenberg.</span></span><span lang="EN-US" style="font-family:Helvetica,sans-serif"></span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Speaker] Wilfried Sieg (<span style="background-image:initial;background-repeat:initial">Carnegie
Mellon University</span>)</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Title] The <i>concept </i>of computation - an
axiomatic characterization</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Abstract]</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Computations are pervasive in contemporary science and
life; they are visible everywhere. However, the <i>concept </i>of computation
emerged in an almost invisible corner of our intellectual life. I will describe
the context for the emergence of computability as a crucial notion in
mathematics and logic with a normative philosophical component.</span></p><p class="MsoNormal" style="text-indent:12pt"><span lang="EN-US" style="font-family:Helvetica,sans-serif">My
analysis of the emergence of this concept provides a novel perspective on <i>the
central methodological issue </i>that surrounds computations, the
“Church-Turing Thesis”. We focus on <i>calculable functions </i>on natural
numbers and <i>mechanical operations </i>on syntactic configurations.</span></p><p class="MsoNormal" style="text-indent:12pt"><span lang="EN-US" style="font-family:Helvetica,sans-serif">The
latter analysis leads to boundedness and locality conditions that motivate
axioms for <i>computable dynamical systems</i>. Models of these axioms are all
reducible to Turing machines. Cellular automata and a variety of artificial
neural nets can be shown to satisfy them.</span></p><p class="MsoNormal" style="text-indent:12pt"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Finally,
I draw connections and point out directions for fascinating work. As to
connections, I will emphasize that my novel perspective is rooted in the
radical transformation of mathematics of the 19<sup>th</sup> century;
especially, in the new form of structural axiomatics introduced by Dedekind and
Hilbert.</span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Speaker]
Yasuo Deguchi (Kyoto University)</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Title]
Kant on mathematical intuition: from an educational point of view</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Abstract]</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">Kantian
notion of mathematical intuition has been criticized, notably by Frege, as too
psychological or private to be the proper base of mathematics. This talk will
challenge such an allegation by paying attentions to its historical
backgrounds, especially that of German mathematical education. First, it
focuses on Kantian notion of arithmetical intuition, and identifies one of its
main resources; ’Segner’s arithmetic'. Since Vaihinger published his
influential commentary of the first critique, Kantians of many variants have
almost unanimously believed that it was one of his books; i.e., ‘Principle’.
But this talk claims that it is his another book; i.e., ‘Lectures’. Segner’s
‘Lecture’ rather than ‘principle’ occupies a significant position in German
history of mathematical education: it is a complement to the pedagogical
tradition, so called, 'formal cultivation’ that was initiated by Ch.
Wolff. In ‘Lectures', Segner employed such intuitive representations of numbers
as points and asterisks, to make the rigid formality of mathematical thinking
more approachable to the younger audiences. Since Segner’s intuitive examples
of numbers and arithmetic operations were intended to be used in the context of
classroom education, they should be publicly available for both teachers and
students, and therefore visible and even manipulatable. Based on those
observations, this talk claims that Kantian notion of mathematical intuition
inherited this visibility, manipulability and public nature of Segner’s
exemplars, and is not to be interpreted as being psychological or private.</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif"> </span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">[Speaker] Makoto
Kikuchi (Kobe University)</span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial">[Title] </span><span lang="EN-US" style="font-family:Helvetica,sans-serif">Aspects of the notion of
computability</span><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial"> </span></p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial">[Abstract] </span></p><p class="MsoNormal" align="left">
</p><p class="MsoNormal"><span lang="EN-US" style="font-family:Helvetica,sans-serif">There
are two important subclasses of the set of partial recursive functions. One is
the set of primitive recursive functions and the other is the set of general or
total recursive functions. The notion of computability had been scrutinized and
expanded in 1930's and nowadays it is widely believed that we have succeeded in
formulating the notion of computability accurately and adequately by reaching
the concept of partial recursive functions. In this talk, we observe the two gaps
of the three classes of computable functions and argue that the former
expansion from primitive recursive functions to general recursive functions is
somewhat mathematical while the latter enlargement from general recursive
functions to partial recursive functions is rather philosophical. We discuss
also consequences of observations of the discontinuity in the latter transition
in the notion of computability.</span><span lang="EN-US" style="font-family:Helvetica,sans-serif;background-image:initial;background-repeat:initial"></span></p><div><br></div>
</div>