Third Nordic Logic Summer School 2017
Truth & Paradox
You can find here my teaching materials for my course Truth & Paradox at the summer school.
About the course
In the five sessions I will provide an introduction to the paradoxes and formal theories of truth and other modal notions. The material should be accessible to anyone with a knowledge of the basics of first-order logic; that is, participants should be familiar with a formal proof system such as Natural Deduction, a tableaux system, an axiomatic (Hilbert style) or sequent calculus. Knowledge of the semantics of first-order predicate logic (definition of satisfaction in a model) and propositional modal logic is useful, but not required. In particular, I do not presuppose any knowledge of arithmetization and the Gödel incompleteness theorems. My presentation does not rely on the arithmetization of syntax theory. Instead I will present an axiomatic theory of syntax that will be explained in detail. Thereby I completely avoid the need to go through the difficult parts of the proof of Gödel's diagonal lemma.
Topics to be covered include:
- formalization of the theory of syntax
- Gödel's diagonal lemma
- Tarski's theorem on the undefinability of truth
- the liar paradox
- Montague's, Yablo's, McGee's, Visser's and further paradoxes for truth, necessity, and other modal notions
- paradoxes arising for the interaction of modal notions such as truth and necessity
- self-reference and paradox
- some basics of axiomatic theories of truth
- operator vs predicate formalizations of model notions
- deflationism about truth
- possible worlds semantics for modal predicates
Here is a draft of my pdf slides (updated 5 August 2017).
I realize that it will be impossible to cover the entire material in my lectures. I am happy to adapt my lectures to the preferences of the audience.
Some of the material will appear in a book that I am coauthoring with Graham Leigh. The slides on axiomatic theories of truth are based on my monograph.