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。
--- 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''.
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