Property Designators, Predicates, and Rigidity (B. Schnieder)

Published in Philosophical Studies 122 (2005), 227–41.

Abstract: The article discusses an idea of how to extend the notion of rigidity to predicates: predicates stand in a certain systematic semantic relation (which I call signification) to properties, such that this relation may hold rigidly or non-rigidly. The relation of signification can be characterised with recourse to canonical property designators that are derived from predicates (or general terms) by means of nominalization: a predicate signifies that property which the derived property designator designates. Whether signification divides into rigid and non-rigid cases will then depend upon whether canonical property designators divide into rigid and non-rigid ones. But, I shall argue, they do not, and so the only notion of rigidity gained this way is trivial. To show this, I first focus on the kind of canonical property designators which could be thought to be non-rigid, canonical designators such as ‘having the colour of ripe tomatoes’, which themselves contain non-rigid property designators. An argument to the effect that such complex canonical designators are non-rigid is rebutted, five arguments to the effect that they are rigid are formulated, and finally an explanation of their rigidity based on the general nature of canonical property designators is presented.