THREE QUESTIONS TO FRANCESCO PAOLI

1) When and how did you first hear about paraconsistent logic and start your work?
My first encounter with logic took place when I was an undergraduate student in Philosophy at the University of Florence. The intro to logic course was given by Ettore Casari, who was later to become my thesis advisor. Although that awesome course made me immediately fall in love with the discipline, it included no mention of paraconsistent logic, focussed as it was on the standard metatheory of classical first-order logic. Paraconsistent logic was briefly mentioned, though, in the history of logic course, delivered by Massimo Mugnai. Around that time, I happened to browse the catalogue of a relatively minor publisher, Philosophia Verlag. A title in there caught my attention – Paraconsistent Logic: Essays on the Inconsistent, edited by Priest, Routley, and Norman. The résumé of the book made it clear that, unlike other more established approaches to logic I had encountered before, paraconsistent logic reached out to pretty much every area in the philosophical curriculum: metaphysics, epistemology, the philosophy of law… And it provided formal tools to deal with these issues! As much as all of this intrigued me, I didn’t pursue this direction any further until I got the chance to spend a year at the University of Konstanz as an exchange student. There, André Fuhrmann (who had just returned home from down under) introduced me to relevant logics, inviting me to seriously study a paraconsistent logic for the first time. It was then that I learnt, to my surprise, that my mentor Casari was into paraconsistency himself, having come up with Abelian logic independently of Meyer and Slaney a few years before... So I eagerly embraced the paraconsistent side of Casari’s research interest and went on to write my PhD thesis on his comparative logic. In the following years, I was lucky enough to meet in person some of the greats of paraconsistent logic, including Meyer, Priest, Carnielli, Béziau, Beall and many others – each one of these people made a deep impact on my views that I am glad to acknowledge.

2) How did you further develop your work on paraconsistent logic?
Throughout my career I investigated a number of logics that are technically paraconsistent, from comparative logic to Abelian logic, from linear logic and its variants to Paraconsistent Weak Kleene Logic (PWK). I argued that at least some paraconsistent logics (linear logic being a prime example) can be considered as genuine rivals of classical logic, and that at least some paraconsistent negations are real negations. Along these lines, I have been trying to simultaneously defuse Quine’s meaning variance argument against deviant logics and Slater’s attack to paraconsistent negations and logics. On other occasions, what has been driving me to approach paraconsistent logics like Abelian logic or PWK was the beauty of their algebraic semantics, or their providing interesting case studies for some unusual logical phenomena. I admit that these motivations are different from the typical reasons why other logicians move towards paraconsistent logics. But I do hope that my being a heterodox member of a heterodox logical community brings me nowhere near orthodoxy!

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3) How do you see the evolution of paraconsistent logic? What are the future challenges? Being kind of a left-fielder, I probably lack the global perspective and the centrality that would make me fully qualified to answer such a difficult question. So, let me just say this. I may be wrong, but I have the impression that much of the research on paraconsistent logic, lately, has centred either on its philosophical foundations or on its applications. These are excellent pursuits, sure, but perhaps not the ideal ground to persuade outsiders to become involved into paraconsistent logics. I suppose that what should be more emphasised is the fact that paraconsistent logics are an outstanding repertoire of intriguing unsolved logical problems, waiting for smart people who want to try their hand. What I mean is, paraconsistent logicians should try to do what Bob Meyer did with Harvey Friedman when he managed to get him involved in his relevant arithmetic project! This is the lesson we are taught from the history of science, and of logic in particular: the more revolving doors you have between different disciplines, the more beneficial this exchange becomes for all of them. From this point of view, events like the Universal Logic conferences are a wonderful opportunity. Paraconsistent logicians should go there in disguise, so to speak, talk about their open problems, and disclose only at the end the area of logic they belong to. Then you’d hear people saying: “Oh, was that paraconsistent logic? Man, who would have thought it was such a challenge? Let’s give it a try!”