Aim

The aim of this workshop is to discuss and exchange new ideas and recent developments related to themes from Russell and Leśniewski. 

Date & Venue

• Date: March 13, 2024.

• Venue: Room 203 of Building 31, Toyama Campus, Waseda University. 

Speakers

• Andrzej Indrzejczak (University of Łódź)

• Ryo Ito (Waseda University)

• Nils Kürbis (Ruhr University Bochum & University of Łódź)

Program

14:00--15:15 Nils Kürbis "Definite Descriptions formalised by Binary Quantifiers" 

15:15--15:30 Break

15:30--16:45 Ryo Ito "Russell's Notion of Genuine Names"

16:45--17:00 Break

17:00--18:15 Andrzej Indrzejczak "When Epsilon meets Lambda; Extended Lesniewski’s Ontology"

Abstracts

Nils Kürbis: In this talk I’ll present a method for formalising definite descriptions that is Russellian in spirit but lends itself  also to the formalisation of unRussellian approaches to definite descriptions. According to Russell, we should not look for the meaning of a definite description ’the F’ in isolation, but only in the context of complete sentences ’The F is G’ (compare with Frege’s context principle). In fact, according to Russell ’the F’ has no meaning by itself. But Russell’s analysis provides every sentence in which it occurs with meaning. According to Russell, ’The F is G’ means that there is exactly one F and it is G. In my approach sentences of this kind are formalised by a binary quantifier as Ix(F, G). Thus a definite description is formalised perspicuously together with its scope. That’s the Russellian part of the talk. The unRussellian part concerns the addition of the binary quantifier to positive free logic and then to quantified modal logic. In positive free logic, ’The F is G’ can be true even no unique F exists. It is widely accepted that the best underlying logic for quantified modal logic is a positive free logic. This requires care to formulate the rules for I correctly. Time permitting, I’ll also consider how to transpose the important notion of rigidity from singular terms to definite descriptions formalised by the binary quantifier.

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Ryo Ito: tba.

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Andrzej Indrzejczak: Lesniewski’s ontology LO is the expressive calculus of names. It provides a basis for mereology but allows also for the direct formalisation of reasoning in natural languages. Recently its elementary part was characterised by means of the cut-free sequent calculus GO. In this paper we investigate its extended version ELO which introduces lambda terms to represent complex descriptive names. The hierarchy of three systems is formalised in terms of sequent calculi which satisfy cut elimination and the subformula property for two of them.

Organizers

The workshop is organized by Ryo Ito and Hitoshi Omori. For any inquiries, please write to Hitoshi at: hitoshiomori [at] gmail [dot] com.