[logic-ml] 論理と論証の哲学日仏集会 １月１５－１６日 (Philosophy of Logic and Proofs (JAN 15-16), TOKYO

[Mitsuhiro Okada]

基礎論学会様、

貴学会の会員に興味をもたれる方が多くいらっしゃると思いますので、貴学会の 
メーリングリストで流していただけるとありがたいです。
慶應義塾大学文学部　岡田光弘

ーーーーーーーーーーーーーーーーーーーーーーー
論理と論証の哲学　(パリ第１大学哲学科、パリ科学史科学哲学研究所との共同 
企画集会）
French-Japanese Workshop on ｏｇｉｃ　and Philosophy of  Proofs

パリ大学第1校哲学科（及びパリ科学史・科学哲学研究所）からの５名の訪問団 
を迎え、論理および論証について議論する会を開催しま す。　参加自由です。 
(プログラムの最新版については，以下のURLをご覧ください) 
http://abelard.flet.keio.ac.jp/seminar/frjp16jan.html
また、１５日午前中に同じ会場で非公式研究会を行います。

証明の表現、幾何学証明、証明の対象、証明の同一性、証明と論理的規範性など 
について議論します。、．
ご興味がございましたら是非お立ち寄りください、
到着分のabstractsは下ににあります。最新情報については上記ＵＲＬをご覧く 
ださい。

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Date: January 15th–16th, 2016 　１月１５日ー１６日

Place: Distance Learning Room (B4F), South Building, Mita campus of Keio 
University. TOKYO
場所: 慶應大学三田キャンパス 南館地下4階 ディスタンスラーニングルーム 
(最寄駅:JR 田町、地下鉄三田又は赤羽橋)
(http://www.keio.ac.jp/en/maps/mita.html 13番の建物です。/ Building #13 
on this map.)

Speakers: and Discussants
フランス側:
Pierre Wagner (Professor, Université Paris 1, IHPST)
Marco Panza (Professor, Université Paris 1, IHPST)
Andrew Arana (Professor, Université Paris 1, IHPST)
Alberto Naibo (Associate Professor, Université Paris 1, IHPST)
Florencia Di Rocco (Ph.D candidate, Université Paris 1)
and others Discussants

日本側:
Kengo Okamoto (Tokyo Metropolitan University)
Koji Mineshima (Ochanomizu University)
Mitsuhiro Okada ( Keio University)
Yutaro Sugimoto (Keio University)
Yuta Takahashi (Keio University)
Yuki Nishimuta (Keio University)


Program (tentative):


Friday, January 15th
(Morning Closed discussion meeting)

14:00 Session I
  Yuta Takahashi“Philosophy of Gentzen's proof theory''
  Koji Mineshima“Combining a type-logical semantics and a wide-coverage 
statistical parser”
  Florencia Di Rocco “Logic and Mathematics of Japanese Counters''
Discussion
17:00 Close


Saturday, January 16th

10:30 Session II
  Kengo Okamoto “TBA”
  Pierre Wagner & Mitsuhiro Okada “TBA”
Discussion
12:30 Lunch Break
14:00 Session III
  Marco Panza “The twofold role of diagrams in Euclid's geometry”
  Alberto Naibo “Representing inferences and proofs: the case of harmony 
and conservativity”
  Andrew Arana “Complexity of proof and purity of methods”
Discussion
17:00
Close

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Abstracts:

Koji Mineshima “Combining a type-logical semantics and a wide-coverage 
statistical parser”
We present a type-logical semantics for wide-coverage statistical 
parsers based on Combinatorial Categorical Grammar (CCG) developed for 
English and Japanese. The system we have been developing enables to map 
open-domain texts into formulas in higher-order logic that capture a 
variety of semantic information such as quantification and 
intensionality. We also discuss how a robust model of lexical knowledge 
can be integrated into our type-theoretical framework. (Joint work with 
Pascual Martinez-Gomez, Yusuke Miyao and Daisuke Bekki)

Andrew Arana “Complexity of proof and purity of methods”
Roughly, a proof of a theorem, is “pure” if it draws only on what is 
“close” or “intrinsic” to that theorem. Mathematicians employ a variety 
of terms to identify pure proofs, saying that a pure proof is one that 
avoids what is “extrinsic”, “extraneous”, “distant”, “remote”, “alien”, 
or “foreign” to the problem or theorem under investigation. In the 
background of these attributions is the view that there is a distance 
measure (or a variety of such measures) between mathematical statements 
and proofs. Mathematicians have paid little attention to specifying such 
distance measures precisely because in practice certain methods of proof 
have seemed self-evidently impure by design: think for instance of 
analytic geometry and analytic number theory. By contrast mathematicians 
have paid considerable attention to whether such impurities are a good 
thing or to be avoided, and some have claimed that they are valuable 
because generally impure proofs are simpler than pure proofs. This talk 
is an investigation of this claim, formulated more precisely by 
proof-theoretic means. Our thesis is that evidence from proof theory 
does not support this claim.

Marco Panza “The twofold role of diagrams in Euclid's geometry”
Proposition I.1 of the Elements is, by far, the most popular example 
used to justify the thesis that many of Euclid's geometric arguments are 
diagram-based. Many scholars have articulated this thesis in different 
ways and argued for it. I suggest to reformulate it in a quite general 
way, by describing what I take to be the twofold role that diagrams play 
in Euclid's plane geometry (EPG). Euclid's arguments are object 
dependent. They are about geometric objects. Hence, they cannot be 
diagram-based unless diagrams are supposed to have an appropriate 
relation with these objects. I take this relation to be a quite peculiar 
sort of representation. Its peculiarity depends on the two following 
claims that I shall argue for: (i) The identity conditions of EPG 
objects are provided by the identity conditions of the diagrams that 
represent them; (ii) EPG objects inherit some properties and relations 
from these diagrams.

Alberto Naibo “Representing inferences and proofs: the case of harmony 
and conservativity”
Traditionally, proof-theoretic semantics focuses on the study of logical 
theories from a general point of view, rather than on specific 
mathematical theories. Yet, when mathematical theories are analyzed, 
they seem to behave quite differently from purely logical theories. A 
well-known example has been given by Prawitz (1994): adding of a set of 
inferentially harmonious rules to arithmetic does not always guarantee 
to obtain a theory which is a conservative extension of arithmetic 
itself. This means that outside logic the nice correspondence between 
harmony and conservativity (advocated for example by Dummett (1991)) 
seems to be broken. However, as it has been pointed out by Sundholm 
(1998), this is not necessarily a consequence due to the passage from a 
logical setting to a mathematical one. It could depend also on the way 
in which proofs are represented. In particular, if proofs are seen as 
composed by rules which act on judgments involving proof-objects, rather 
than on rules which a
ct on propositions, then the aforementioned correspondence can be in 
fact be reestablished. An analysis of this phenomenon is proposed. In 
particular, two different ways of representing proof-objects are taken 
into consideration: the Church-style presentation and the Curry-style 
presentation. It is then shown that a crucial difference can be obtained 
by choosing the first rather than the second.
Bibliographical references: Dummett, M. (1991). The Logical Basis of 
Metaphysics. London: Duckworth.
Prawitz, D. (1994). Review of 'The Logical Basis of Metaphysics' by 
Michael Dummett. Mind, NS, 103 (411): 373–376. Sundholm, G. (1998). 
Proofs as acts and proofs as objects: Some questions for Dag Prawitz. 
Theoria, 64 (2-3): 187–216.

Florencia Di Rocco “Logic and Mathematics of Japanese Counters''
Either a feature of a “conceptual scheme'' -Quine- or a triviality of 
“syntax'' -Peyraube, Thekla-, the function of counters is traditionally 
think as that of getting “individuals'' out from the noun they apply to. 
I will challenge this classical approach by a contextualist position in 
philosophy of language. Extending linguistics -Hashimoto, Chao- from 
Chinese to Japanese, I will present counters as operators enlightening 
contextual relevant features. Through every-day examples in Japanese, we 
will show how counters work as Austin's “adjuster words'', their 
“logic'' being ascribed to the dynamics of “language games'' 
-Wittgenstein- or “rules of adjustment of salience'' in a “well-run 
conversation'' -David Lewis-. This position will progressively lead to 
the idea that counting operations do not necessarily deal with 
“individuals''. We will thus raise up a certain number of problems 
related to philosophy of mathematics, logic and pragmatics concerned in 
the use of Jap
anese counters -such as the link between unities and individuals, 
counting and measuring, and between numbers, counters and ordinary 
concepts- and sketch a wittgensteinian type of answer. By showing their 
contextual plasticity, I will challenge the mere idea of the existence 
of rigid “counter words''.

お問い合わせ先: 慶應義塾大学文学部岡田研究室内 三田ロジックセミナー 講演 
会事務局
E-mail：logic [AT] abelard.flet.keio.ac.jp

主催：慶應義塾大学 論理と感性のグローバルリサーチセンター
共催：慶應義塾大学次世代研究プロジェクト 論理思考の次世代型研究と論理的 
思考力発達支援への応用研究

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