AUC Logic Lectures: Reasoning about Quantity
Logicians have studied reasoning with quantifier expressions like "all", "some" ever since Antiquity, as these underlie both ordinary language and the mathematical language of science. We look at the history of logical systems for quantifiers, flagging intriguing issues still alive today, such as the interplay of formal and natural languages (with philosophical repercussions), expressive power of language for discrete and continuous quantities, and fast natural quantifier inference versus slow deductive proof. If time permits, we will add a coda about epistemic expressions in natural language, connecting the topic of quantification with the second main theme of your course.
Prof. Dr. Johan van Benthem is a University Professor emeritus of pure and applied logic, University of Amsterdam; Henry Waldgrave Stuart Professor of philosophy, Stanford University (philosophy and CSLI); Changjiang Professor, Chinese Ministry of Education, Tsinghua University, Beijing; Co-director, UvA-Tsinghua joint research center in logic. He was awarded the Spinozapremie in 1996 and elected a Foreign Fellow of the American Academy of Arts & Sciences in 2015. Van Benthem is known for his research in the area of modal logic. He has also been active in the fields of philosophy of science, logical structures in natural language (generalised quantifiers, categorial grammar, substructural proof theory), dynamic logic and update logic, and applications of logic to game theory as well as applications of game theory to logic (game semantics).