forthcoming, in From an Analytical Point of View. Essays in Honor of Edgar Morscher (1941–2023), Otto Neumaier and Peter Simons (eds.), Stuttgart-Bad Cannstatt: Frommann-Holzboog, pp. 87–122.
In this paper we describe the theory of definitions developed for object theory (OT), i.e., the formal, deductive system developed in the monograph Principia Logico-Metaphysica (excerpted online). OT exhibits a number of features which call for great care when stating, and reasoning from, definitions. The features in question include: (a) identity is not a primitive, (b) there are complex terms (descriptions and λ-expressions) that may fail to denote, (c) all terms, including descriptions, are interpreted rigidly, (d) the axiomatization of an actuality operator includes a contingent axiom (and so the modal logic allows for reasoning from contingencies), and (e) the theory of relations in OT is hyperintensional and so one can't substitute necessary equivalents in all contexts. The theory of definitions addresses the issues that arise in connection with (a)–(e) and includes two kinds of definition, namely, definitions by equivalence and definitions by identity, each of which has a distinctive inferential role.