[logic-ml] 論理哲学ワークショップ 2月27日(金) / Workshop on Philosophy of Logic, Feb 27th (Fri)

[Yuta Takahashi]

みなさま、

こんにちは、慶応大学の高橋優太と申します。この場をお借りして、次のワークショップのご案内を
させていただきます。重複して受け取られた場合はご容赦ください。

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論理哲学ワークショップ 2月27日(金) / Workshop on Philosophy of Logic, Feb 27th (Fri)

次のような「論理哲学ワークショップ」を予定しております。
今回は特に、現代 論理の歴史的背景についても議論します。参加自由です。

The following Workshop on Philosophy of Logic is scheduled.
The historical background of some modern logic will be discussed among
others.

日時/Date&Time: 2015年2月27日(金) 14:00-17:00, Feb 27 (Fri), 2015
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
Place: Distance Learning Room (B4F), South Building, Mita campus of Keio
University.

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1.  Speaker: Juan Luis Gastaldi (IRePH, Université Paris Ouest Nanterre La
Défense)
Title: The relation between logical content and arithmetic in the semiotic
constitution of Boolean logic

2. Speaker: Yuta Takahashi (Keio University)
Title: The Intuitionistic Background of Gentzen's 1935/36 Consistency Proofs

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問合せ先:
Mita Logic Seminar
思考と行動判断の研究拠点事務局
logic at abelard.flet.keio.ac.jp

ABSTRACTS ENCLOSED BELOW:

1. Speaker: Juan Luis Gastaldi (IRePH, Université Paris Ouest Nanterre La
Défense)
Title: The relation between logical content and arithmetic in the semiotic
constitution of Boolean logic

Abstract: After the publication of his Begriffsschrift, Frege distanced
himself from the Booleans by insistently opposing the content that his
logic was able to express to the abstraction of Boolean logic. Frege’s
commitment to the notion of content would last until the end of his work,
becoming in particular the source of his famous distinction between sense
and denotation. But what did Frege exactly mean by this opposition between
“contentual” (inhaltlich) and abstract, as a properties of logical systems?
A semiotic perspective on the constitution of Boolean logic shows that this
distinction can be associated with the one between Arithmetic and Algebra,
considered as different mathematical practices on signs respectively
underpinning the constitution of these two logical systems. Moreover, a
particular attention paid to Boole's own voluntary deviations from what
would soon become the standard Boolean system permits to identify different
figures of what can be seen as a content dimension arising as a logical
effect of the semiotic properties of Arithmetic.

2. Speaker: Yuta Takahashi (Keio University)
Title: The Intuitionistic Background of Gentzen's 1935/36 Consistency Proofs

Abstract: Gerhald Gentzen gave three consistency proofs for number theory.
These consistency proofs have a common aim that originates from Hilbert's
Program. Hilbert, in his program, aimed to justify the use of ideal
propositions in mathematics, by showing that no contradiction can be
derived in a formal system of the ideal parts of mathematics. Gentzen aimed
to justify the use of ideal propositions in number theory, and this aim is
prominent especially in Gentzen's 1938 consistency proof. In Gentzen's
1935/36 consistency proofs, there is another aim that is not found in
Hilbert's Program. The aim is to formulate a ``finitary'' interpretation
that gives a meaning to every ideal proposition of number theory and makes
the theory sound.
In this talk, first we argue that what motivated Gentzen to give such an
interpretation is an intuitionists' objection against the significance of
consistency proofs. Second, we show that his way of the interpretation
appealed to a notion being very close to the notion of spreads, which was
introduced in intuitionistic mathematics. As a consequence, we claim that
intuitionism was deeply related to both Gentzen's motivation and method for
the interpretation.

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