The Logic of Instance Ontology

Author: Mertz, D.W.

Source: Journal of Philosophical Logic, Volume 28, Number 1, February 1999 , pp. 81-111(31)

Publisher: Springer

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Abstract:

An ontology’s theory of ontic predication has implications for the concomitant predicate logic. Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates. PPL, as axiomatized and proven consistent below, is a three-sorted impredicative intensional logic with identity, having variables ranging over individuals x, intensions R, and instances of intensions Ri. The power of PPL is illustrated by its clarification of the self-referential nature of impredicative definitions and its distinguishing between legitimate and illegitimate forms. With a well-motivated refinement on the axiom of comprehension, PPL is, in effect, a higher-order logic without a forced stratification of predicates into types or the use of other ad hoc restrictions. The Russell–Priest characterization of the classic self-referential paradoxes is used to show how PPL diagnosis and solves these antimonies. A direct application of PPL is made to Grelling’s Paradox. Also shown is how PPL can distinguish between identity and indiscernibility.

Keywords: identity vs. indiscernibility; impredicative definitions; instance ontology; intensional logic; moderate realism; self-referential paradox; ‘extended binding’

Document Type: Regular Paper

Affiliations: University of Missouri – St. Louis, 507 Tower, St. Louis, MO 63121-4499, U.S.A.

Publication date: February 1, 1999

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