I have been greatly influenced by Jaakko Hintikka’s method of separating step by step reasoning based on rules from strategic reasoning. The relationship between these two can be illustrated through games: someone can master the rules of chess perfectly but still be a lousy player. There is another side to the matter that is of particular interest to philosophers: rules (or norms) are broken and sometimes people act “unreasonably” even within those rules. What should you do then?

I collaborated with Hintikka for years. We worked together closely both during his trips to Finland and at his home in Marlborough near Boston, which had a home library larger than Philosophica, our departmental library. I followed in his footsteps in trying to find strategic concepts in logic and language and analysing them with the help of game theory. In this manner we isolated the “logical skeleton” of our language (quantifiers, pronouns, connectives) in our book On the Methodology of Linguistics (1991).

Game theory can also be applied to semantic concepts, such as “truth”: the truth value of a sentence can be analysed by finding the winning strategy in a verification game. Likewise the logical consistency of sentences can be seen as a guideline that reveals how the verification strategy for one sentence is changed into the verification strategy for another logically consistent sentence. I presented and developed this idea in the book Independence-Friendly Logic. A Game-Theoretic Approach (2011).

Both of the applications of game theory start with the assumption that the non-logical words in a language have pre-set “meanings.” But how to describe the social conventions that lead to the determination of these meanings? David Lewis has presented a game-theoretical analysis of these conventions. In the book Logic, Language and Games (2015), I look more closely at the relationship between different games.

Hintikka also convinced me of the benefits and necessity of taking a “transversal” approach to research. A researcher must study theoretical concepts in the fields in which they are used. At this level the boundaries between disciplines cease to exist. If one is interpreting phenomena of natural language, then it is necessary to look into what linguists are saying. If the object of interest is proofs, you have to find out how they are applied in mathematics.

More on transversal research and the importance of formal methods