Formal Theories of Truth
Abstract. The origins of the area known as Formal/Axiomatic Theories of Truth can be found in Tarski's groundbreaking investigations in the first half of the twentieth century, and particularly his explication of the notion of "truth in a structure'', and his famous theorem about undefinability of truth. The area has been actively investigated both by mathematical and philosophical logicians, using advanced methods, especially those from model theory and proof theory. The aim of the course is to introduce the audience to the general concepts, questions, results, techniques, and literature of the subject, as expounded in the recent excellent expositions in the books Axiomatic Theories of Truth by Volker Halbach (2015), and The Epistemic Lightness of Truth (2017), by Cezary Cieśliński.
Recommended Readings Before the Course:
- Axiomatic Theories of Truth, Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/truth-axiomatic/
- Tarski's Truth Definitions, Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/tarski-truth/
*School of Mathematics, Institute for Research in Fundamental Sciences (IPM)
**Institut für Diskrete Mathematik und Geometrie, TU Wien
Abstract. Our aim in this mini-course is to present a gentle introduction to the method of forcing, of which our presentation will be accompanied by many examples, explanations and justifications of used terms. We will be teaching the materials very smoothly and in a fashion that the participants are then able to perceive the crux of the forcing method. In particular the first session will be devoted to experiencing some easy concepts related to partially ordered sets. We intend then to focus on a detailed proof of the independence of Continuum Hypothesis from ZFC.
Institute for Logic, Language and Computation (ILLC)
University of Amsterdam
Abstract. In this tutorial I will discuss Stone, Priestley and Esakia dualities for Boolean algebras, distributive lattices and Heyting algebras, respectively. I will also give a few examples of applications of these dualities. In particular, I will show how to obtain a characterization of profinite Heyting algebras using these dualities.
School of Electronic Engineering and Computer Science
Queen Mary, University of London (QMUL)
Abstract. Functional interpretations provide us with a systematic way of translating logical dependencies into functional dependencies. The most well-known such interpretations include Kleene’s realizability, Kreisel’s modified realizability and Gödel’s Dialectica interpretation. In this series of lectures we will cover the basic concepts behind such functional interpretations, looking at each interpretation individually and then identifying the common features between them. We will also discuss the foundational motivations for the development of such interpretation as well as its more recent applications to program extraction from proofs and proof mining.