Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Some preliminary doctrines
- 3 Properties I
- 4 Properties II
- 5 Powers and dispositions
- 6 Relations
- 7 Particulars
- 8 States of affairs
- 9 Independence
- 10 Modality
- 11 Number
- 12 Classes
- 13 Totality states of affairs
- 14 Singular causation
- 15 Laws I
- 16 Laws II
- 17 The unity of the world
- References
- Index
6 - Relations
Published online by Cambridge University Press: 03 February 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Some preliminary doctrines
- 3 Properties I
- 4 Properties II
- 5 Powers and dispositions
- 6 Relations
- 7 Particulars
- 8 States of affairs
- 9 Independence
- 10 Modality
- 11 Number
- 12 Classes
- 13 Totality states of affairs
- 14 Singular causation
- 15 Laws I
- 16 Laws II
- 17 The unity of the world
- References
- Index
Summary
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.
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- A World of States of Affairs , pp. 85 - 94Publisher: Cambridge University PressPrint publication year: 1997