Abstract
In this paper, we critically discuss the idea of a ‘philosophical interpretation’ of paraconsistent logics. We do so by considering the epistemic approach to paraconsistency, by Carnielli and Rodrigues (2019a), according to which paraconsistent logics should be interpreted exclusively in terms of non-conclusive evidence, and also, by considering counter-arguments by Barrio (2018) and Barrio and Da Re (2018), according to whom paraconsistent logics are not specially tied to any specific interpretation. We begin by presenting the positions involved, and by arguing that the debate may be profitably understood in terms of the distinction between pure and applied logics. We argue that dialetheism is not an interpretation of paraconsistent logics, but rather a view on truth and negation which requires use of paraconsistent logics. Something similar may be said about the epistemic approach itself. The result is that there is nothing distinctive to be called a philosophical interpretation of paraconsistent logics, but rather what we have are distinct applications of paraconsistent logics. Arguments by Barrio (2018) and Barrio and Da Re (2018) may be then re-framed more effectively.
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Notes
Also, it is clear that ‘interpretation’, in this context, is not what is typically called an interpretation in logical textbooks, that is, a formal semantics developed inside some set theory employed in the metalanguage (see, in particular, the discussion in Carnielli and Rodrigues 2019b). In the present paper, ‘interpretation’ always refers to the idea of informal interpretation as advanced by Carnielli and Rodrigues; whenever we have to refer to the usual notion of interpretation as provided in logic textbooks, we use the word ‘formal semantics’.
Curiously, Rahman and Carnielli seem to suggest that lack of information requires a paraconsistent treatment. Latter on, in Carnielli and Rodrigues (see Carnielli and Rodrigues 2015), the distinction between ‘lack of evidence’ (requiring paracompleteness) and ‘conflicting evidence’ (requiring paraconsistency) is made clearer and properly distinguished. See also Arenhart and Krause (2019) for further discussion of the limits of applying paraconsistency to discuss lack of information.
The claim that true contradictions are ‘ontological’, and that the truth theory adopted by dialetheists is a correspondence theory, is common in Carnielli and Rodrigues’ papers. This is certainly more than most dialetheists would claim. See in particular Priest (2019a) for a reply on these issues.
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This paper was produced while the author benefited from a research fellowship at the Vienna Circle Institute, at the University of Vienna, Austria. The author is partially supported by CNPq (Brazilian National Research Council).
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Arenhart, J.R.B. Interpreting philosophical interpretations of paraconsistency. Synthese 200, 449 (2022). https://doi.org/10.1007/s11229-022-03941-2
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DOI: https://doi.org/10.1007/s11229-022-03941-2