THREE QUESTIONS TO FABIEN SCHANG


1) When and how did you first hear about paraconsistent logic and start your work?
Let us start by defining paraconsistency inferentially, as a non-explosive system. Then how deep a system may be 'inconsistent', and to what extent such a technical issue has really to do with more 'philosophical' ones is what we are going to discuss in the following. I heard about paraconsistency for the first time by reading Graham Priest's “To be and not to be - that is the answer. On Aristotle on the Law of Non-Contradiction”, Logical Analysis and History of Philosophy 1 (1998). Then my attention was called to the possibility of thinking about contradictions for real, despite the alleged impossibility claimed by Aristotle. So the question was launched: how would it make sense to assert contradictions without doing "mere noise" as the Heracliteans, to paraphrase the Stagirite master? This also means that my first contact with paraconsistency was a strong and challenging one, namely: through the glasses of Priest's dialetheism. I started to write about paraconsistency on its own with the paper “Inconsistent Logics! Incoherent Logics?” (see my bibliography in the end of this document). In this short paper, I wanted to clarify the conceptual situation around paraconsistency just as the regretted Hartley Slater intended to do in his famous “Paraconsistent logics?”. I approached the problem from a rejectivist perspective, echoing with my early inquiry on the nature of logical values: if you think of the latter in terms of answers to corresponding questions in an arbitrary dialogue, then a distinction is to be made between two kinds of inconsistency: a mild one, where saying 'yes' to whether a given sentence is true does not prevent from saying 'yes' to whether it is false as well, due to a tolerant or weak view of truth as having evidence for; a strong one, in which saying 'yes' to whether the sentence is false does entail that it is not true as well. Inconsistency may rightly occur in the mild sense of weak or epistemic paraconsistency, whereas incoherence wrongly occurs by producing a forbidden case of assertion. Pandora's Box was opened by this way, however.

2) How did you further develop your work on paraconsistent logic?
My first short publication was (as described here above) about the sense of epistemic, weak paraconsistency as fallible belief. Then I directed my works related to paraconsistency into formal semantics, both in formal epistemology and in the area of Indian logic. In the first case, I wanted to constructed many-valued doxastic logics based on a variety of criteria of justification and breaking with the Platonic, realist-minded theory of knowledge. In the second case, I attempted to pursue a reflection in the area of Indian logic, especially the Jain theory of non-one-sidedness or saptabhangi. After writing a first abstract paper on 8- and 16-valued interpretations of it, I published a second related paper by commenting Jonardon Ganeri's reading of what the saptabhangi is according to Priest. Then a third paper proposed a review of two 'dual' Indian logics: saptabhangi and the catuskoti, a.k.a. Tetralemma, abandoning the many-valued approach and promoting an awkward one-valued 'logic' (which is not a proper logic any more in the Tarskian sense, by not separating a minimal set of accepted and non-accepted sentences). Fourth and a fifth related paper strove to precise my point about Indian logics and what a 'truth-value' is according to this non-Fregean way of thinking about logic. In sixth work -still a draft, I propose an alternative view of Hegel's 'logic' where his negation (or Aufhebung) is not a sentential operator at all but a sort of successor-forming operator in a domain of logical values. Thus, my ambition for paraconsistency should be to think about how formal semantics and formal ontologies deeply differ through a constructive theory of logical values as structured objects.

A final prayer before taking the plunge in the Ganga!
5th World Congress on Paraconsistency, Kolkata, India, 2014

3) How do you see the evolution of paraconsistent logic? What are the future challenges?
I take the community of paraconsistentists to center their reflection on epistemology. In this sense, the main problem is how to handle with inconsistent information within theories. I doubt that paraconsistency gets closer with more philosophical issues like dialectics or Priest's plea for 'true contradictions' -this point has been dealt with by Slater and pursued by Béziau, with the help of the theory of opposition; but this has been made in a conceptual way and has been closed more or less within the debate around Suszko's point: can there be more than two logical values properly speaking? This issue, as amazing as it could be for my own purposes, does not seem to be the main path of paraconsistency logic in the future, however. I take it to keep more track of applied logics, as a helpful tool to streamline issues in philosophy of science or formal epistemology again. Functionality goes on a par with the future of logic, as far as I can see. We need new Gilles Gaston-Granger or Jean-Louis Gardiès to think about this very trend, I would say.

The trickiest, most exciting challenge for paraconsistency might relate to the area of formal ontology: how to build a world by means of structured informations, and what paraconsistency may say relevantly in this respect? Personally, my own concern would tend to focus on ontology: how to make sense of contradiction as a constitutive rule of world-making patterns (especially as a logic for dialectics), and what is the connection between what paraconsistent logics have to say about the obscure issue of dialectics: with respect to both the Chinese Yi-King (a set of 64 hexagrams combining a sort of Boolean bits) and the theory of predication (Hegel's Aufhebung or what Yvon Gauthier coined 'sursomption', as opposed to Kant's subsumption). Going beyond paraconsistency as a inference-based premise, accounting for paraconsistency as a proper feature of the world.

My papers referring to paraconsistency (in decreasing chronological order):
(1) “Epistemic Pluralism”, Logique et Analyse, Vol. 60(239), 2017: 337-35
(2) “Is ‘no’ a force-indicator? Yes, sooner or later!” (with J. Trafford), Logica Universalis, Vol. 11(2), 2017: 225-251
(3) “The Logical Burdens of Proof. Assertion and Hypothesis” (with D. Chiffi), Logic and Logical Philosophy, Vol. 26(2), 2017: 1-22
(4) “An Arithmetization of Logical Oppositions”, in The Square of Opposition: A Cornerstone of Thought, J.-Y. Béziau & G. Basti (ed.), Birkhäuser: Basel, 2016: 215-237
(5) “Une sémantique générale des croyances justifiées” (with A. Costa-Leite), CLE e-prints, Vol. 16(3), 2016: 1-24
(6) “Eastern Proto-logics”, in New Directions in Paraconsistent Logics, Béziau J.-Y. & Chakraborty, M. & Dutta, S (eds.), Springer Proceedings in Mathematics and Statistics, 2016: 529-552
(7) “A One-valued Logic for Non-One-Sidedness”, International Journal of Jaina Studies(Online), Vol. 9(1), 2013: 1-25
(8) “Believing the Self-Contradictory”, in The Right to Believe: Perspectives in Religious Epistemology, D. Lukasiewicz & R. Pouivet (eds.), Ontos Verlag, 2011: 127-140
(9) “Two Indian Dialectical Logics: saptabha?gi and catuskoti”, in Studies in Logic: Logic and Philosophy Today, 29, Gupta, A. & van Benthem, J. (eds.), 2011: 45-74
(10) “Relative Charity”, Revista Brasileira de Filosofia, Vol. 233, 2009: 159-172
(11) “A Plea for Epistemic Truth: Jaina logic from a Many-Valued Perspective”, in: A. Schumann (ed.), Logic in Religious Discourse, Ontos Verlag, 2009: 54-83
(12) “Negation and Dichotomy”, in D. Lukasiewicz & R. Pouivet (eds.), Scientific Knowledge and Common Knowledge, Epigram Publishing House/Kazimierz Wielki University Press, Bydgoszcz, 2009: 225-265
(13) “Inconsistent Logics! Incoherent Logics?”, The Reasoner, Vol. 3(7), 2009: 8-9
(14) “Depicting Negation in Diagrammatic Logic: Legacy and Prospects” (with A. Moktefi), in G. Stapleton, J. Howse, J. Lee (eds.), Diagrammatic Representation and Inference: Proceedings of the 5th international conference Diagrams 2008, Herrsching, coll. Lecture Notes in Artificial Intelligence, Vol. 5223, Springer, 2008: 236-241.