Abstract

In this paper I analyze some of the negation operators from the family of paraconsistent logics from the perspective of logical realism. I start by taking as cases two cases of study: the LP negation operator along with its metaphysical interpretation stated as dialetheism and the FDE negation with the metaphysical interpretation proposed by Beall (2016). I use this operators to draw a comparison with the different level of metaphysical commitments in some other paraconsistent negations. I discuss how LP negation a robust metaphysical commitment such as dialetheism relies on a leading role of logical negation while in Beall’s interpretation the search for a metaphysically balanced picture entails the disappearance of logical negation as a substantive notion. I the argue that it is possible to obtain an intermediate alternative, with a four-valued paraconsistent logic SF, which is compatible with a metaphysically balanced picture as Beall’s but it recovers a substantive notion of logical negation as a fundamental connective.

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