Volker Halbach

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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 thought it may be useful to have a separate list of the axioms for my theory of expressions. It is here.

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.