- Volume II is divided into four Parts. In the first Part, Predicates and Universals1, it is argued that predicates (predicate-types) are correlated with universals2 in a many-many rather than a one-one manner. Given a predicate applying to certain particulars, it may apply in virtue of many, one or no universals3. Given a universal there may be many, one or no predicates corresponding to it. It is the mistaken identification of universals4 with meanings, the meanings of predicates, which has prevented the realization that no simple correlation of predicates and universals5 can be found.
- It is argued in particular that if 'P' and 'Q' are distinct predicates, each applying in virtue of genuine universals6, then 'P v Q', '~P' and '~Q' do not so apply. There are no disjunctive or negative universals7. It is argued, however, that provided there is a particular to which both 'P' and 'Q' apply, then there is a universal, P&Q. There are conjunctive universals8. P and Q are proper parts of this conjunctive universal.
- But how is it determined when we have arrived at genuine generic identities, genuine universals9? It is argued that we have nowhere to begin but with the classifications which we naturally make. Natural science may then take us beyond these classifications to more deeply hidden classings and sortings which, it is our hope, approach more closely to an isolation of genuine universals10. Formal identity criteria for universals11 may be given. They are identical if and only if they bestow identical causal powers upon the particulars which fall under them. But the identification of universals12 must be a posteriori.
- In the final chapter of the first Part, it is argued that non-synonymous predicates may apply to the very same particulars in virtue of the very same universals13. Such predicates may stand to such universals14 in different fashions. Predicates may be said to "name", to "analyse" or else to be "external" to the universals15. All this casts light upon the nature of the so-called "contingent identification of properties", for example, colour with light-waves and mental states with physical states of the brain.
- The second Part of the volume, Properties and Relations, tries to advance first the theory of properties, and then the theory of relations, in a more direct manner. In the chapter on properties it is denied, pace Aristotle, that we need to recognize special sorts of monadic universals16 associated with stuffs and kinds (being gold and being an electron). An account of such universals17 can be given in terms of instantiated conjunctions of properties, and an instantiated conjunction of properties is a property.
- A classification of various categories of property is then made, including the important category of structural property. The properties (and relations) which go to make up a structural property do not qualify the very same particular which the structural property qualifies, but, rather, proper parts of that particular. In ch. 18 §v18 it is suggested that the "foundation in things" for the notion of number lies in non-relationally structural properties possessed by the particular which is the aggregate (not the class) of the things numbered.
- In ch. 19 ("Armstrong (David) - Relations") it is first argued that we do not need to recognize relational properties as anything over and above (non-relational) properties and relations. The question is then taken up whether all properties may not dissolve ad infinitum into structures of propertied-things-in-relation, so that there are no irreducible properties. It is concluded that this is possible, although it does not have to be so. The familiar distinction between internal and external relations is then drawn. It is argued that internal relations are reducible to properties of the "related" things. It is then tentatively suggested that all genuine (i.e. external) relations holding between first-order particulars are spatio-temporal relations. Finally, it is argued that particulars are never reflexively related. Any relation must relate at least two distinct particulars.
- The third Part of volume II, The Analysis of Resemblance, tries to give an account of various sorts of resemblance. The resemblance of particulars involves no especial difficulties. It is a matter of the resembling things' having certain properties. But certain cases of the "resemblance of universals19", for example that of the lengths among themselves and the colours among themselves, raise great difficulties. Difficulties are found in various projects:
- to reduce such resemblances to the resemblance of (first-order) particulars;
- to account for the resemblances in terms of common properties or relations of the universals20 involved (second-order properties and relations);
- to account for the resemblances by drawing the distinction between determinable and determinate properties; and, finally,
- in the attempt to give a subjectivist account of such resemblances.
- It is then argued that there are no determinable universals21, only determinates. The problem arises, what unifies classes of universals22 such as the determinate lengths or the determinate shades of colour. It is suggested that the unifying factor is a series of partial identities holding between different members of the class in question. The conjunctive properties P&Q and Q&R are partially identical. But in the case of the lengths, colours, etc., it is argued that the properties involved are structural properties. Hence the partial identities concerned are identities of parts of such structures. This solution can be rather easily applied to the case of the lengths. But it meets epistemological difficulties in the case of the colours, which appear to be simple and unstructured. It is suggested that the colours are in fact structural properties, although we are unable to perceive this structure.
- In the fourth and final Part of volume II, Higher-order Universals23, it is argued that there are second-order (and perhaps higher-order) universals24: properties and relations of properties and relations. But a thesis of Formalism is upheld. It is suggested that higher-order universals25 are restricted to formal or topic-neutral universals26, such universals27 as being complex as opposed to being a colour,
- The investigation of higher-order properties is of rather a tentative sort. In the case of higher-order relations, it is suggested that these are restricted to the relations between universals28 of (non-logical) necessitation, probabilification and exclusion. It is further suggested that these relations constitute the laws of nature. A law of nature, on this view, is something more than a mere uniformity in nature. It is a uniformity springing from a relation holding berween the universals29 involved. In this way, it is suggested, a Realism about universals30 is able to give a non-sceptical answer to the problem of what constitutes a law of nature. Causal connection is seen as a particular case of nomic connection.
Footnote 18: "Armstrong (David) - Properties", Section “Numbers and Properties”.
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