Series: Penn State Logic Seminar
Date: Tuesday, April 18, 2000
Speaker: Ryan Kohl, Penn State, Mathematics and Philosophy
Title: Lesniewski's Protothetic
Time: 2:30 - 3:20 PM
Place: 219 Thomas Building
Abstract:
Stanislaw Lesniewski was a prominent logician working at the
Lwow-Warsaw School of Logic between 1910 and 1939. In that time he
formulated a new logical system with which he hoped to provide a
foundation for mathematics. The fundamental structure used in his
foundational system is called the Protothetic. This formal structure
is most similar to the Propositional Calculus, but possesses a greater
generality. This generality is gained through the use of creative
definitions. A definition is said to be creative in a deductive
theory for a thesis X if and only if X does not contain the defined
term (nor any defined via it) and is provable using the definition,
but not without it. I will present a brief outline of the
Lesniewski’s logical system and proceed to focus on the use of
creative definitions in his Protothetic. I will draw conclusions that
have a direct impact on foundations of mathematics and natural
language modeling.