Lecture series on Logic and Philosophy (1)
Lecture Title:On the Question of Whether the Mind Can be Mechanized
Speaker: Prof. Peter Koellner (Havard University, USA)
Date and Time: 2021-04-21, 9:30am-11:30am Beijing Time
Platform: Zoom (ID: 652 9596 6662, Password: 900295)
School of Philosophy, Wuhan University
Dr. Zesheng Chen (University of California, Irvine, USA)
Dr. Zhaoqing Xu (Sichuan University, China)
Dr. Yunbao Shi (School of Wanxi at Anhui, China)
Host: Prof. Yong Cheng (Wuhan University, China)
In this talk I will discuss the question of whether Gödel's incompleteness theorems imply that "the mind cannot be mechanized". The story begins with Gödel. He argued for a weaker, disjunctive conclusion to the effect that the incompleteness theorems imply that either "the mind cannot be mechanized" or that “there are absolutely undecidable statements.” Since then others -- most notably Lucas and Penrose -- have argued for the stronger conclusion, namely, that the incompleteness theorems imply the first of these two disjuncts -- that "the mind cannot be mechanized".
In the first part of the talk I will sharpen the underlying notions. This will enable us to pull the discussion into a setting where definitive results can be proved. We shall see that (thus formalized) Gödel's disjunction is indeed provable. This then leads to the question: "Which disjunct holds?” I will discuss some recent independence results which show that when (thus formalized) one can show that although the disjunction is provable neither disjunct is provable or refutable. Moreover, the result is robust in that it persists when one strengthens the underlying principles of knowledge. I will conclude that the questions of whether "the mind can be mechanized" or whether "there are absolutely undecidable statements" are themselves good candidates for statements that are "absolutely undecidable.”
About the speaker:
Peter Koellner is Professor of Philosophy at Harvard University. He received his Ph.D from MIT in 2003. His main areas of research are mathematical logic, specifically set theory, and philosophy of mathematics, philosophy of physics, analytic philosophy, and philosophy of language. In 2008, Professor Koellner was awarded a Kurt Gödel Centenary Research Prize Fellowship. Currently, Koellner serves on the American Philosophical Association's Advisory Committee to the Eastern Division Program Committee in the area of Logic.
Lecture series on Logic and Philosophy (2)
Lecture Title: Self-reference, truth, and provability
Speaker: Prof. Volker Halbach (School of Philosophy, Oxford University, UK)
Date and Time: 2021-06-02, 19:00-21:00 Beijing Time（UTC 11:00-13:00）
Platform: Zoom (ID: 616 3088 3998, Password: 865948)
Organizer: School of Philosophy, Wuhan University, China
Dr. Balthasar Grabmayr (Humboldt University of Berlin, Germany)
Prof. Graham Leigh (The University of Gothenburg, Sweden)
Host: Prof. Albert Visser (University of Utrecht, Netherlands)
Philosophers have struggled for centuries with sentence that make claims about themselves such as the "liar sentence". The following is an example of a liar sentence: THE SENTENCE IN CAPITALS IS NOT TRUE.
The liar sentence is a threat to any theory of truth, and has been taken as evidence that the entire notion of truth and perhaps even realism have to be rejected. In the talk I will look at this and similar sentences. In particular, I will consider sentences that say about themselves that they are not provable (Gödel sentences) and sentences that say about themselves that they are true (truth teller sentences). I will look at consequences of the analysis of self-reference for the theory of truth and its paradoxes and for the Gödel incompleteness phenomena.
About the speaker:
Volker Halbach is a German logician and philosopher. He is Professor of Philosophy at the University of Oxford and a Fellow of New College Oxford. His main research interests are in logic, philosophy of mathematics, philosophy of language, and epistemology, with a focus on formal theories of truth. Halbach is author of several articles and books including The Logic Manual, a textbook on undergraduate logic, and Axiomatic Theories of Truth.
You can watch the lecture videos via the official bilibili channel of School of Philosophy at Wuhan University: