Relations
D. M. Armstrong · Cambridge University Press eBooks · 1997
PROPERTIES AND RELATIONS Properties, as opposed to relations, are monadic universals, the only species of monadic universal, as has been argued (4.3). The term ‘relation’ covers all polyadic universals: dyadic, triadic, … n -adic. Properties then emerge as a limiting case of a universal, though no doubt a limiting case of quite particular importance. Being a universal becomes a determinable with being a monadic, dyadic, … n -adic, universal as its determinates. This in turn suggests that a particular universal can only have one -adicity. The latter conclusion is in any case mandated by the powerful truism that a universal is identical, strictly identical, in its different instantiations. Consider a relation such as is surrounded by . Such relations take a variable number of terms in their different instantiations. (They have been called multigrade relations – Leonard and Goodman, 1940, p. 50 – and also anadic relations – Grandy, 1976.) But it seems that they cannot be universals, because they would differ in their essential nature in these different instantiations. How could a three-term relation be strictly identical with a two-term relation? Indiscernibility of Identicals would seem to forbid it. We may call this result the Principle of Instantial Invariance (see Armstrong 1978b, ch. 19, sec. VII). I will not venture an analysis of is surrounded by . But it will be a ‘second-class’ relation (3.9) that the surrounded particular has to a number of other particulars.