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Abstract
In discussions concerning modal logic, two theses--that identicals are necessarily identical, and that identicals coincide in their necessary properties--have constituted a focus of necessitarian/anti-necessitarian debate.
(1) for allxfor ally[(x = y) if-then necessarily(x = y)]
(Identicals are necessarily identical.)

(2) for allxfor ally[(x = y) if-then (necessarilyFx if-then necessarilyFy)]
(Identicals coincide in their necessary properties.)

To persistent anti-necessitarian concerns about the universal applicability of (1, 2), a constant necessitarian refrain has been that (1, 2) hold in all normal models.  The necessitarian thus dismisses judgments of contingent identity and modal discernibility that the anti-necessitarian deploys against (1, 2)1 as the products of intellectual confusion. For, contends the necessitarian, validity in all normal models is a touchstone of logical truth. I enter this fray on the anti-necessitarian side, with countermodels of (1, 2) which delineate the ontological dimensions of contingent identity and modal discernibility, and so put in question phenomenological restrictions on the interpretation of individual variables2 which grease the necessitarian's slide from validity in all "normal" models to logical truth.

In Part One, I suggest that despite necessitarian attempts to ward off the "dark doctrine of a relation of 'contingent identity'" (Saul Kripke, Naming and Necessity, p. 4), this doctrine is no more logically exceptionable than the contending doctrine of a relation of necessary identity. How then to react to the failure of necessitarian discourse to make sense of (1, 2) AND their contradictory negations? Applaud, with Kripke ("the model theory made it clear...", p. 3) a world-cruncher's night in which all cows are black? Or seek a standpoint which encompasses both necessary and contingent identity.

I undertake the latter in Part Two, by assigning to individual variables structured individuals which, unlike the (logically) unstructured individuals of FOL, give rise to an ontologically complex identity relation. From the moments of this relation, I then constitute a logico-ontological framework which permits sense to be made of contingent identity and modal discernibility, as well as of necessary identity and modal indiscernibility.

 

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Copyright© 1999, William J. Greenberg, all rights reserved.