On the identification of properties and propositional functions

Abstract

The theory of properties, relations, and propositions (PRPs) promises to play a significant foundational role in logic, philosophy, semantics, and psychology. There is now a growing recognition of this fact by research ers in these disciplines.' Nevertheless, formalizations of PRP theory run into some technical complexities in connection with the treatment of free and bound terms occurring in PRP-abstracts (see, e.g., Bealer, 1979, 1982, 1983; Zalta, 1980; Monnich, 1983). These complexities can be largely avoided by adopting the thesis that properties and propositional functions are identical (see, e.g., Aczel, 1980 and 1987; M6nnich, 1983; Turner, 1987; Chierchia and Turner, 1988). The purpose of this paper is to present some reasons against this thesis despite its short-term technical advantages.2 Philosophically, the propositional-function thesis seems unacceptable on at least two counts. First, it is highly counterintuitive. How im plausible that familiar sensible properties are functions the color of this ink, the aroma of coffee, the shape of your hand, the special painfulness of a burn or itchiness of a mosquito bite. No function is a color, a smell, a shape, or a feeling. Or consider the fact that navy blue is darker than yellow and that it covers the surface of my pen. No function is darker than another function, and no function covers the surface of my pen. To assert otherwise seems to be a category mistake.3 In addition to intuitive objections to the propositional-function thesis, a second philosophical objection is that the thesis threatens the prospect of certain explanations in epistemology, phenomenology, and philo sophical psychology. For example, how are we to explain what is going on in the interplay of sensation and cognition when a person sees that two objects have some sensible quality in common? Or how are we to explain why various shades of color can look so similar? At best, the identification of properties and propositional functions complicates our epistemology, phenomenology, and philosophical psychology in con nection with these and kindred phenomena. My aim, however, is not to dwell on such philosophical objections to the propositional-function thesis, serious as they are. Rather, my aim is to discuss four logical difficulties facing the thesis. (1) The first problem derives from the fact that functions are usually