Essence and Modality

object x may have a property F either by exemplifying F or by being determined by F. Mally's idea is that every group of properties determines an abstract object, but that such an abstract object need not exemplify the properties which determine it. For example, the properties goldenness and mountainhood determine an abstract object which exemplifies neither of these two properties. The intuition here is that the properties determining an abstract object are part of its nature and govern the conception of that object. Indeed, for Mally, there is nothing more to the nature of an abstract object than the properties by which it is to be conceived. In what follows, we shall say that an abstract object encodes property F instead of saying that F determines x. Since encoding is a way of having a property, it constitutes a kind of predication. That is why we introduce 'xF' as an atomic mode of predication, to express the fact that x encodes F. We rigorously distinguish this from the traditional form of predication, namely, that x exemplifies F ('Fx'). (More generally, we read 'F'xl ... xn' as xl ... xn exemplify or stand in the relation F".) For example, on this view, Sherlock Holmes encodes the properties of being a detective, living in London, etc. These are the properties by which we conceive of him, and thus are part of his nature, but on the present view, he does not exemplify these properties. He exemplifies, by contrast, properties like being fictional, being admired by modern criminologists, etc., as well as a variety of properties that things have in virtue of being abstract (more on this below). In general, fictional objects will be said to encode the properties attributed to them in their respective stories. To take another class of examples, mathematical objects will encode the mathematical properties attributed to them in their respective theories. By contrast, they exemplify properties like being abstract, not having mass, not having a texture, being conceived by Euler, etc. Note that by thinking of encoding as a second mode of predication, predication in ordinary language becomes ambiguous relative to a logic that distinguishes xF and Fx. The principal axiom for abstract objects, described in more detail below, is a comprehension principle that asserts the conditions under which abstract objects exist and encode properties: for any expressible condition 4 that is satisfiable (in Tarski's sense) by properties F, there exists an abstract object that encodes exactly the properties F satisfying (. Consider, then, the second-order, modal language that can be formed with Fnl ... xn and xF1 as a basis, and where the other logical notions are (not), -+ (if-then), V (every), and D (necessarily). Identity is not primitive in this language, but will instead be defined below for both objects and relations. The language is further enhanced with Mind, Vol. 115 . 459 . July2006 ? Zalta 2006 This content downloaded from 207.46.13.121 on Wed, 05 Jul 2017 18:02:39 UTC All use subject to http://about.jstor.org/terms