- It should be possible to read A Theory of Universals1 without having read its predecessor, Nominalism and Realism. A brief recapitulation of the argument of volume I is, however, essential.
- An introductory Part considers the notion of a predicate. In contemporary fashion, predicates are taken to be certain linguistic expressions which are parts of sentences. Under what conditions should we say that different predicate-tokens are tokens of the same predicate-type? For the most part, phonetic-orthographic criteria are inconvenient for philosophical purposes. So it is laid down that such tokens are instances of the same type if and only if they are synonymous. A convention is introduced. Where phonetic-orthographic identity-conditions are intended, the predicate is supplied with double quotation-marks. Where, as is usual, semantic identity-conditions are intended, the predicate is given single quotation-marks only.
- The second Part of volume I is an extended critique of Nominalism, together with Platonic, that is, Transcendent Realism.
- Nominalism is defined as the doctrine that everything there is is a particular and nothing but a particular.
- A Realist is one who denies this proposition, holding that universals2 exist.
- It is argued that in the dispute between Nominalism and Realism the onus of proof lies with the Nominalist. For the distinction between token and type is apparently all-pervasive and prima facie incompatible with Nominalism. Five Nominalist strategies for analysing the proposition that an object, a, has a property, F, are distinguished:
- Predicate Nominalism: a has the property, F, if and only if a falls under the predicate 'F'
- Concept Nominalism; a has the property, F, if and only if a falls under the concept F
- Class Nominalism: a has the property, F, if and only if a is a member of the class of Fs
- Mereological Nominalism: a has the property, F, if and only if a is part of the aggregate (heap) of the Fs
- Resemblance Nominalism: a has the property, F, if and only if a suitably resembles the paradigm case(s) of an F.
- These analyses are criticized in detail in successive chapters. One simple line of criticism, among the many which are brought, is that in each analysis the particular, a, has the property, F, in virtue of its relation to something external to it: predicate, concept, class, aggregate or paradigm. Yet it is intuitively clear that a might be F even if none of these things existed. Transcendent Realism is equally a Relational analysis:
a has the property, F, if and only if a "participates" in the transcendent Form, Fand the same criticism can be brought against it.
- Besides these criticisms of Nominalism, a short chapter recapitulates arguments used by Arthur Pap3, and recently strengthened by Frank Jackson4, to show that the truth of certain statements demands the existence of universals5. Examples are:
Pap's argument for the necessity of attribute variables ('He has the same virtues as his father') is also briefly rehearsed.
- Red(ness) resembles orange(ness) more than it resembles blue(ness), and
- Red(ness) is a colour.
- The second Part of volume I ends with a chapter on Particularism, the doctrine, associated with G.F. Stout and many others, that properties and relations of particulars are not universals6 but are, like the things which have the properties and relations, particulars. It is contended,
- that the arguments for Particularism are inconclusive;
- that Particularism leaves the Problem of Universals7 unsolved, a problem which can only be solved by admitting universal properties and relations over and above the Particularist's properties and relations;
- that once this admission has been made, no coherent account can be given of the relation between particular properties (and relations) and the corresponding universal properties (and relations).
- The third Part of volume I begins by asking whether, since it seems that we are forced to postulate universals8 in any case, we should follow Bertrand Russell and others in giving an account of particulars as nothing but "bundles of universals9". Various reasons, including a traditional line of argument based upon the Identity of Indiscemibles, are given for rejecting this view. It is concluded that, just as the Nominalist errs in trying to reduce universals10 to particulars, so this Universalist view errs in trying to reduce particulars to universals11.
- The question then arises how the irreducible particularity of particulars stands to their irreducible universality (their properties and relations). With Transcendent Realism rejected, some form of Immanent Realism must be accepted. A thing's properties must be brought within the thing. Relational Immanent Realism takes the particularity of a particular to be a substratum standing in an indescribable relation to its properties. An argument, in effect F.H. Bradley's regress12, is advanced against this view.
- It is concluded, therefore, that although particularity and universality are inseparable aspects of all existence, they are neither reducible to each other nor are they related. Though distinct, their union is closer than relation. Scotus talked of a mere "formal distinction" between the thisness13 and the nature of particulars. The situation is admittedly profoundly puzzling, but, it is suggested, the Scotist view is the most satisfactory one which can be found. A comparison which may be useful is the way in which shape and size are united in a particular.
- A state of affairs is then defined as a particular's having a property, or two or more particulars' being related by a relation. We may consider particulars along with their properties, or else in abstraction from all their properties. This yields two conceptions of a particular. It is the latter conception which is involved in the conception of a state of affairs. For the former, or "thick", conception already is the conception of a state of affairs. It seems, therefore, that we can say both that the world is a world of particulars (in the "thick" sense) and that it is a world of states of affairs.
- Some universals14 already involve the notion of a state of affairs. These are the "particularizing" universals15, of which being a man would be an instance in the unlikely event that the predicate 'a man' applies in virtue of something genuinely common to all men. Such universals16 divide their instances into non-overlapping individuals (individual men). A universal of this sort may be said to particularize strongly. Being one kilogram of lead, however, is only a weakly particularizing universal (if it is a universal at all) because its instances overlap. The necessity for the notion of a particularizing universal emerges most clearly when it is noted that being two men and being two kilograms of lead have equal claims with the two previous examples to be universals17. These new universals18 involve the notion of being made up of two instances of the original universals19. That is, they already involve the notion of a state of affairs.
- If we take a particular four-dimensionally ("as a space-time worm"), then it may be said to occupy a certain spatio-temporal position. The question arises whether this "total" position can be identified with the particularity of a particular. Since it is logically possible that there are particulars which are not spatio-temporal, the concepts of particularity and total position cannot be identical. But if everything there is is spatio-temporal, as it is plausible to assert, particularity may in fact be identical with total position. We thus reach the view that it is a particular's total position plus its properties (including its spatio-temporal properties) which constitute a particular in the "thick" sense.
- There is reason to think that more than one particular can occupy the very same total position. Possible examples are the "visual cube" and the "tactual cube". The particular constituted by the sum of all the particulars at a certain total position may be called a concrete particular. Its "parts" may be called 'abstract’ particulars. It appears, then, that different particulars may have the same particularity, viz. the same total position. They must then have different properties. Contrariwise, different particulars may have the very same properties. They must then have different total position. But a certain total position plus a certain set of properties yields an unrepeatable particular ("a substance").
- In the last chapter of volume I a world-hypothesis is advanced. The hypothesis is that the world consists of nothing but particulars having properties and relations (monadic and polyadic universals)20. It is argued in the last Part of volume II that these universals21 themselves have certain properties and relations (the relations constituting the laws of nature). But with this exception, it is suggested, no other sorts of entity need be recognized. This hypothesis is less economical than the Nominalist world-hypothesis: that the world contains nothing but particulars. But it is still economical. It involves rejecting transcendent universals22, realms of numbers, transcendent values, timeless propositions, non-existent objects ("the golden mountain"), possibilia, possible worlds and "abstract" classes.
- A general argument is given against postulating any of these entities. They all lack causal power: they do not act. It is then argued that we have no good reason to postulate anything which has no effect upon the spatio-temporal world.
- It is not argued that statements about numbers, propositions, possibilities, classes, etc. are false. But it is suggested that it should be possible to give an account of the truth-conditions of the statements purely in terms of particulars, their properties and their relations. No detailed account of the truth-conditions is given. All that is proposed is a research-programme, one that is obviously too vast to be carried out in this work. The argument from lack of causal power is simply intended as a reason for thinking that the research-programme is a promising one.
Footnote 3: See "Pap (Arthur) - Nominalism, Empiricism and Universals - I".
Footnote 4: See "Jackson (Frank) - Statements About Universals".
Footnote 12: See Wikipedia: Bradley's regress
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