When and how did you hear about paraconsistent logic and start your work?
I am a philosopher and have arrived at paraconsistency via metaphilosophical and metametaphysical questions related to the history of philosophy. During my studies at the University of Turin (Italy) and then at the University of Cologne (Germany) I have always been interested in traditional philosophy, especially in Kant and Hegel and in the question: what has become of the Aristotelian idea of first philosophy in Kant and Hegel? This kind of metaphilosophical and metametaphysical issues brought me to focus, first of all, on transcendental logic (the Kantian answer to the first philosophy question) and dialectical/speculative logic (the Hegelian answer). In Hegel it becomes evident that transcendental, dialectical and speculative logic is the logic of philosophy, and that this logic involves a notion of truth that does not exclude, but rather requires the programmatic use of contradiction and the acceptance of (some) contradictions as true. This is the basic idea that drew me to paraconsistency.
Born January 20 1974, Turin, Italy.
2. How did you further develop your work on paraconsistent logic ?
I developed my work along three lines:
– by working on the binomial dialectics/dialetheism
– by examining the roots of paraconsistency and dialetheism in discussions about dialectics and its formalization at the time of the birth of the first non-classical logics
– by working on contradictions at the intersection between different disciplines (especially logic, metaphysics and politics).
The exploration of the binomial dialectics/dialetheism meant using dialetheism’s technical tools for asking about the form of Hegel’s dialectical logic, and using the metaphysical and metaphilosophical awareness that is typical of the traditional account for philosophically grounding dialetheism. In the course of this analysis, new logical features and new research fields have emerged: by examining dialectical double negation in the perspective of the dialetheic semantics of negation (Ficara 2014a) traits have become visible that are not considered in extant semantics of negation – for example, from the iteration of negation, in dialectics, it follows contradiction. By examining the behaviour of the connective that joins the opposites in a dialectical contradiction, a new conjunction of contradictories has come into view (Beall and Ficara 2014 (now published as Beall and Ficara 2023), d’Agostini and Ficara 2021) in which the conjuncts are untrue and simplification fails, and which is related to a new exciting approach to paraconsistency (Ripley 2015, Barrio and Da Ré 2018, d’Agostini 2021). By examining the form of dialectical inferences in the light of paradoxical deductions a new behaviour of true liarlike biconditionals can be highlighted, for which consequentia mirabilis fails (Ficara 2015, see also Francez 2023).
Evidently, establishing a connection between Hegel’s dialectics and paraconsistency is not an arbitrary operation, but it is rooted in the very history of paraconsistency (see Marconi 1979). In 2021 I reconstruct the interplays between the first attempts to formalize Hegel’s dialectics and the birth of paraconsistent logics. In Ficara and Priest 2023 we reopen the “old” debate about the formalization of Hegel’s dialectics.
The topic of contradictions is located at the intersection of different fields, traditions and schools, and it is particularly apt to overcome the divides between philosophical approaches, constituting a common ground of philosophical research. The aim of 2014b is trying to stimulate a dialogue between different approaches (history of philosophy, logic and metaphysics, political philosophy), so that the understanding of the problem of contradictions becomes as complete as possible. My current project (together with d’Agostini and Schang) of a Special Issue of History and Philosophy of Logic on Logic and Politics, as well as various ongoing projects revolving around Beall’s contradictory Christology (see Beall 2021) belong to this line of research.
3. How do you see the evolution and further challenges for paraconsistent logic ?
Answering this question is not easy – I can only say that working on paraconsistency with an awareness about philosophy, its problems and its history seems to be logically extremely fertile. It seems to be essential for increasing the awareness about the leading and fruitful lines of research and for decreasing the proliferation of disconnected semantics.
Barrio, E. A., & Da Re, B. (2018). Paraconsistency and its Philosophical Interpretations. Australasian Journal of Logic, 15 (2), 151–170.
Beall, J. C. (2021), The Contradictory Christ, Oxford Studies in Analytic Theology. Oxford: Oxford University Press.
Beall, J. C. & Ficara, E. (2023) Hegelian Conjunction, Hegelian Contradiction, History and Philosophy of Logic, 44/2, 119-131.
d’Agostini, F. (2021), Conjunctive paraconsistency. Synthese 199, 6845–6874.
d’Agostini, F., Ficara, E. (2021), Hegel’s Interpretation of the Liar Paradox, History and Philosophy of Logic, 43/2, 105-128.
Ficara, E. (2013), Dialectic and Dialetheism, History and Philosophy of Logic, 34/1, 35-52.
Ficara, E. (2014a), Hegel’s Glutty Negation, History and Philosophy of Logic, 36/1, 29-38.
Ficara, E. (2014b) (ed.), Contradictions. Logic, History, Actuality, Berlin New York: De Gruyter.
Ficara, E. (2015), Hegel and the Consequentia Mirabilis, History and Philosophy of Logic 39, 357-368.
Ficara, E. (2021), The Birth of Dialetheism, History and Philosophy of Logic, 42/3, 281-296.
Ficara, E. & Priest, G. (2023) (eds.), The Formalization of Dialectics, History and Philosophy of Logic, 44/2, 115-118.
Francez, N. (2023), A Dialectic Contra-Classical Logic, Logica Universalis 17, 221–229.
Marconi, D. (1979) (ed.), La formalizzazione della dialettica, Torino: Rosenberg & Sellier.
Norman, J., Priest, G. and Routley, R. 1989. Paraconsistency. Essays on the Inconsistent, München: Philosophia Verlag.
Priest, G. (1989), Dialectic and Dialetheic, in Science and Society 53/4, 388–415.
Ripley, D. (2015). Paraconsistent logic. Journal of Philosophical Logic, 44(6), 771–780.
Special Issue Formalization of Dialectics, edited by Elena Ficara and Graham Priest