Workshop on Philosophy of Logic
- 2015年2月27日(金) 14:00-17:00
- Fri 27, 2015 (Fri) 14:00-17:00
- 應義塾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) (キャンパスマップ)
- Distance Learning Room (B4F), South Building, Mita campus of Keio University. (Campus Map)
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.
- Juan Luis Gastaldi
- The relation between logical content and arithmetic in the semiotic constitution of Boolean logic
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.
- Yuta Takahashi
- The Intuitionistic Background of Gentzen's 1935/36 Consistency Proofs
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.
Organizer: Mitsuhiro Okada (Keio University)
公開日時: February 22, 2015 06:41