Interview with J. Michael Dunn, Professor Emeritus of Philosophy, Computing and Computer Science at Indiana University, one of the greatest living logicians, specialist in algebraic methods in logic, relevant and quantum logics, editor of the Journal of Symbolic Logic (1982–1988). Together with N. Belnap, Dunn had designed the so-called "American plan" for constructing semantics for systems of relevant logic and developed the famous four-valued semantics for the first-degree entailment logic.
The Russian version interview was first published in Dunn, M.J. Too much of a good thing // Date Palm Compote, 2016. no. 10. pp. 59-62. DOI 10.24411/2587-9308-2016-00015 (cyberleninka.ru/article/n/u-nas-vse-slishkom-horosho-poluchaetsya)
The questions were prepared by Alexander Belikov, Andrew Mertsalov, Evgeny Loginov, and Artem Iunusov. Illustration by Anna Davydova
1.1. What's the difference between philosophical logic and mathematical logic?
I don’t think there is a real distinction. I should confess for the sake of transparency that I wrote the book Algebraic Methods in Philosophical Logic with Gary Hardegree. Perhaps I am being too cynical, but I see the difference as largely a cultural/political/marketing distinction. When I was Dean of Indiana’s School of Informatics, I made up the saying “I see tribes everywhere.” I think it is part of our nature and nurture. Once upon a time, there was logic, and it was part of philosophy. Then mathematicians began to study it too. Universities and their /departments/disciplines arose, and mathematicians needed a name that would legitimatize their studies to their colleagues, hence “mathematical logic.” This came to dominate the field of logic, with model theory, recursion theory, etc. Philosophers need a name that would legitimatize their studies, hence “philosophical logic,” or something like that. Now logic is of key importance in computer science, but somehow “computer logic” refers to the logic of computer circuits, not to the more general relations of logic to computer science, and vice versa, which includes as well computability theory, complexity theory, artificial reasoning/intelligence, and program and machine verification using modal logic. This whole mass/mess falls under the general heading of (computer) theory. Maybe Gary and I should put out a new edition of our book: Algebraic Methods in Philosophical Logic for Computer Scientists.
But trying to put aside these tribal distinctions, I think that logic involves all these aspects, and it is impossible nowadays to do serious logic without having some knowledge of all these fields, and depending on what one is working on one might also need some knowledge of linguistics and even psychology. I wonder what Frege, who correctly defended the foundations of logic from what he termed “psychologism,” would think of cognitive science today, and the emerging role that logic, correctly, plays in it.