What should an adequate representation of individuals (elements of the domain of discourse) be like, within vagueness models with degrees? This paper explores the hypothesis that individuals are distinguished by their property values, i.e. the extents to which they satisfy gradable properties.
First, as Lewis (1986) argues, cross-world identity is intuitively implausible between individuals differing in their property values, e.g., their height, weight, etc. ('intrinsic properties'). However, cross-world identity is intuitively plausible between individuals sharing the same property values (the same heights, weights, etc.) , even if they differ along extrinsic, relational properties, e.g., if they are considered 'tall' in one world, but not in another, due to variance in the cutoff point of tall across the two worlds. A representation of individuals by their property values captures the intuitively sharp distinction between these two cases.
Second, this proposal captures the intuitive difference between cases we tend to call 'ignorance' and cases we tend to call 'vagueness' (for Williamson 1994, cases of 'accidental' versus cases of 'inherent' ignorance), which are usually modeled with the same formal means. While vagueness/inherent ignorance (about the truth value of statements like Dan is tall) arises due to partial information regarding cutoff points of vague predicates like tall, accidental ignorance (say, about the truth value of statements like Dan is two meters tall or Dan is taller than Sam) arises due to partial information regarding property values (e.g., the height) of referents of arguments like Dan ('discourse entities'). A representation of individuals by their property values, then, captures the intuitive distinctions between both phenomena.