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.

1.2. What are the challenges facing contemporary philosophical logic? In Kant’s words, what should logicians do nowadays?

I think the main challenge has to do with our having “too much of a good thing,” as the saying goes. Putting it quickly, once there was only the syllogism, then it was extended to classical logic, then we added intuitionistic logic, and now one new logic every couple of minutes or so around the world. How do we sort out those that are worth pursuing from those that are not? Of course, there can be many reasons that might go into such a decision: philosophical motivations, practical motivations, elegance, mathematical interest, etc.

1.3. What's the essence and the purpose of philosophical logic? Who could be needing it and for what?

For me, the essence of philosophical logic is creating formal structures that capture philosophical intuitions and notions.

1.4. Do you think that it is possible for contemporary philosophical logic to reach the God’s Eye point of view and become a universal, unified and general system, a single theory that is containing all of the different types of logic and therefore become a sole logic as classical logic was the sole in its time?

I do not think this is possible. It is no more possible than creating a universal tool. Different tools are needed for different purposes.

1.5. What should the "post-non-classical logic" look like?

As I just said, I don’t think there will be a single post-non-classical logic. But maybe there could be something like a Swiss Army Knife of at least a number of logics, where one could choose which features to use for which purpose. Substructural logics perhaps form a paradigm here, where one can have various logics depending on what structural rules one allows, permutation, thinning, contraction, etc. And one might combine these with various modalities. And I dream of mixing probabilities into the mix somehow too.

2.1. What are the relationships between logic and metaphysics? What is a logical discovery most important for metaphysics?

Metaphysics by its nature attempts to derive the first principles of things, and hence it ideally should provide an account of the foundations of logic. Traditionally logic was understood as based on truth and its preservation under consequence, and of course, metaphysics is concerned with the nature of truth. But things get more interesting with modal logic, where Kripke used the idea of a “possible world” to analyze the necessity operator. And of course, this opens new doors to metaphysical analysis. Various non-classical logics open even more doors, e.g. temporal logic (the nature of time), intuitionistic logic (the nature of constructive proof), relevance logic, and other substructural logics (the nature of information), etc. Perhaps the logical discovery most important to metaphysics was Gődel’s Incompleteness Theorem, where in he showed (assuming a formal system for arithmetic that is sufficiently strong but consistent, e.g. Peano arithmetic) that there will always be truths of arithmetic that are not provable in the system. This can be viewed as separating reality from our knowledge of it.

2.2. Can we use philosophical logic as an instrument of formalization of phenomenological data reports and descriptions? For example, is it helpful to formalize such arguments as the Cartesian cogito or Chalmers’ zombie?

I don’t know about the general
issue. Certainly, Jaakko Hintikka has
argued forcefully that Descarte’s *Cogito ergo
sum* is not effective as a mere logical argument, but needs to have a
performative interpretation. And
certainly, Chalmers used basic ideas from modal logic in his attack on
physicalism and his defense of consciousness. (Transparency requires me to reveal that I was co-director of his Ph.D.
dissertation along with Douglas Hofstadter.)

2.3. What do you think about Plantinga’s modal ontological argument?

My first job was as an assistant professor at Wayne State University in Detroit, and Alvin Plantinga, although he had left to be a professor at Calvin College, still taught graduate seminars in philosophy of logic at Wayne State. Invariably the students would come to me, because I was a logician, asking for my opinion about Al’s latest version of the ontological argument. Plantinga’s argument begins by in effect defining “God” as a being of maximal greatness. (Incidentally what Plantinga calls “maximal perfection “is required by maximal greatness, but I won’t go into that here). Plantinga argues that maximal greatness requires this being to exist with maximal greatness in all possible worlds. The next step is to argue that such a being is possible, so it must exist in some possible world. But then it would exist in all possible worlds, including this world.

Plantinga’s argument is ingenious and subtle, and I cannot fully explore it here. But I do not believe it is correct. If we follow Carnap and Kripke and regard a concept as the set of possible worlds where it is instantiated, then the concept of God will be the set of possible worlds where a being of maximal greatness exists. Then for each world in this set, a being of maximal greatness must exist in all worlds possible relative to it. But I see no reason why this set should be the set of all possible worlds. I am of course using the concept of relative necessity introduced by Kripke, which depends on an accessibility relation, but there are other issues that arise if one uses the original Carnapian notion of absolute possibility, where there is no accessibility relation, and possibility means simply truth in some possible world. Then it is not clear to me that such a concept is even possibly realizable – certainly not in every model, maybe not the one with our world in it.

3.1. If you were asked about four or five great revolutions in philosophical logic (and their authors) then what would you say? In other words, can you name the top five greatest logicians of all time?

Aristotle for creating the idea of formal logic with his theory of the syllogism, Boole creating an algebraic way of viewing propositional calculus, Frege for adding quantifiers and sets (even though Russell showed this system is inconsistent), Tarski for in effect creating model theory, and Gődel for his incompleteness theorem. I would also like to add some non-classical logicians, perhaps C. I. Lewis or Łukasiewicz.

3.2. What do you think about Quine’s project of naturalizing logic, and epistemology in general? What is Quine’s place in the history of philosophical logic?

As to Quine’s place in the history of philosophical logic, I am probably prejudiced because I “grew up” in the hostile environment of Quine and his followers attacking modal and other non-classical logics. But I can think of no lasting contribution that he has made. Even his very interesting set theories NF and ML have no real following but are objects of curiosity I think.

3.3. How would you comment on the criticism of formal logic presented by Fichte, Hegel, and Marx (so-called dialectic logic)? and how would you comment on later works of Wittgenstein, which presented another type of such criticism?

I never appreciated any of these criticisms, I hope not just because I never paid them much attention. ☺ I guess I understood the so-called “later Wittgenstein” best, and I, like many other logicians, thought that he misunderstood things like the Gődel Incompleteness Theorem. Fiche, Hegel, and Marx were writing before modern formal logic had really been invented/discovered, and were likely reacting to something like Aristotle’s syllogistic logic. (It would make for an interesting play to imagine Marx interacting with, say, the logician Charles Dodgson (pen name: Lewis Carroll) after Marx moved to England).

3.4. What did you think about philosophical logic in Russia? For example, have you read Nikolay Vasiliev’s articles?

Russia has a strong history in logic generally, including such seminal figures as Kolmogorov, Maltsev, Schoenfinkel, and Zinovyev. Russia has had very strong logicians during the more recent time that I have been working on logic. Some of these are institutionally philosophers, others mathematicians, but even the mathematicians have made contributions to philosophical logic as I think of it. To give just one example of this I mention Larisa Maksimova at the Russian Academy of Sciences in Novosibirsk. She has made major and pioneering contributions to non-classical logic, including modal logic, intuitionistic logic, and relevance logic. But my understanding is that the leading force in creating philosophical logic in Russia was Vladimir Smirnov, and of course the Department of Logic at Lomonosov Moscow State University. I met Smirnov several times at international conferences when I was a young logician, and he was very supportive of my career.

Regarding my reading of Vasiliev, I have read some of his articles, but I must admit only after my last visit to Russia. His “Imaginary Logic” is clearly underappreciated, I think maybe even in Russia.

4. What have you never thought about?

Do you mean until now? ☺

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