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Instance ontology, or particularismthe doctrine that asserts the individuality of properties and relationshas been a persistent topic in Western philosophy, discussed in works by Plato and Aristotle, by Muslim and Christian scholastics, and by philosophers of both realist and nominalist positions. This book by D. W. Mertz is the first sustained analysis that applies the rules and systems of mathematics and logic to instance ontology in order to argue for its validity and for its problemsolving capacities and to associate it with a version of the realist position that Mertz calls "moderate realism."Mertz surveys the history of instance ontology in writings from Plato and Aristotle through Leibniz, followed by modern philosophers such as Bertrand Russell and D. M. Armstrong, among others. He also includes a thorough critique of the recent work of Keith Campbell and other contemporary nominalists. Building on the insights gained through this historical overview, he delves deeper into the logic of instance ontology and uncovers some of its extraordinary problemsolving features: distinguishing legitimate from illegitimate impredicative reasoning; uniformly diagnosing the selfreferential paradoxes; being free from the limitation theorems of Gdel and Tarski; providing a basis for the derivation of arithmetic construed intensionally; and formally distinguishing identity and indiscernibility.
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