Leibnizian Identity and Paraconsistent Logic

History and Philosophy of Logic 41 (3):236-243 (2020)
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Abstract

The standard Leibnizian view of identity allows for substitutivity of identicals and validates transitivity of identity within classical semantics. However, in a series of works, Graham Priest argues that Leibnizian identity invalidates both principles when formalized in paraconsistent semantics. This paper aims to show the Leibnizian view of identity validates substitutivity of identicals and transitivity of identity whether the logic is classical or paraconsistent. After presenting Priest's semantics of identity, I show what a semantic expression of Leibnizian identity does amount to. Then, I argue that Priest's semantic definition of identity is not Leibnizian. Finally, I offer a semantics characterization of identity in paraconsistent logic that is truly Leibnizian. I demonstrate that the correct formalization of Leibnizian identity in paraconsistent logic also validates substitutivity of identicals and transitivity of identity.

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Ali Abasnezhad
Ludwig Maximilians Universität, München

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References found in this work

Can there be vague objects?Gareth Evans - 1978 - Analysis 38 (4):208.
Identity.Harold Noonan & Benjamin L. Curtis - 2022 - Stanford Encyclopedia of Philosophy.
A determinable-based account of metaphysical indeterminacy.Jessica M. Wilson - 2013 - Inquiry: An Interdisciplinary Journal of Philosophy 56 (4):359-385.
Can there be vague objects?Gareth Evans - 2004 - In Tim Crane & Katalin Farkas (eds.), Metaphysics: a guide and anthology. Oxford University Press UK.

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