For a good many years now-dating back at least to the period of the early Russell—unflattering references have abounded to something that is called ‘the subject-predicate logic’.
Yet this is surely a very odd label to attach to any logic? It seems to imply the existence of another logic or other logics concerned (inter alia no doubt) with propositions which contrive to dispense with a subject or with a predicate or perhaps with both. But in what would seem to be the ordinary straightforward meanings of the terms ‘subject’ and ‘predicate’ there are no such propositions; and therefore no such logics. Russell describes the subject-predicate logic as the logic ‘which holds that every proposition ascribes a predicate to a subject’1 and he thinks it obvious that relational propositions do not do this. But there is a perfectly good and well-established sense of the terms in which it seems obvious that they do. Take the proposition (one of Russell's examples) 2 ‘this thing is bigger than that’. Here certainly as Russell says we are asserting ‘a relation of “this” and “that.”’ But are we not also asserting of ‘this thing’ as subject the relational property of ‘being bigger than that’ as predicate? It goes without saying that the fact of the predicate here being a relational property of the subject gives to the proposition a logical form importantly different in certain respects from that of propositions in which the predicate is an attribute of the subject. But it seems confusing to say the least of it in the light of ordinary usage to say that it is a logical form in which there is not a predicate ascribed to a subject.
The confusion in which the subject-predicate terminology has become enveloped in modern times is well illustrated by the statement sometimes made that there are propositions that have neither subject nor predicate. Thus Miss Stebbing tells us that ‘Fire!’ is a proposition which ‘has neither subject nor predicate.’3 It is clear of course that a subject and a predicate do not find linguistic expression in the verbal utterance ‘Fire!’. But if we are talking of propositions we are not talking of verbal utterances as such but of the mentally asserted content that is expressed—adequately or inadequately—through the verbal utterance. Looked at from this point of view it is surely evident that in so far as a proposition is finding expression in the word ‘Fire!’ the characteristic of being a-fire as predicate is asserted of some more or less specific feature of the immediate environment as subject? A proposition one may presume is something capable of being true or false. It is hard to conjecture what could be meant by the ‘truth’ or the ‘falsity’ of something wherein there is nothing about which an assertion is made and wherein about this ‘nothing’ there is nothing asserted.
It looks then as if those philosophers who distinguish a ‘subject-predicate’ logic from other logics must be using their key words in a somewhat esoteric way. And in general terms it is not difficult to know what that way is. The prototype of the subject-predicate logic is taken by its critics to be the traditional formal logic of the schools which it is alleged recognises only one kind of predicate viz. that which is an attribute or quality of the subject. Against this the critics insist that there are irreducibly different kinds of predicate. Most conspicuously and contrary to the assumptions of the traditional logic relational properties cannot be reduced to mere attributes of the subject to which they may be ascribed. But then these irreducibly different kinds of predicate are after all kinds of predicate. In what sense one may reasonably ask is the title ‘subject-predicate logic’ supposed to be more appropriate to a logic which admits only one kind of predicate than to a logic which admits irreducibly different kinds of predicate?
Confirmation that those who denounce a subject-predicate logic really have in mind a subject-attribute logic is plentiful; sometimes in explicit statement more often by implication. Russell himself in the course of arguing for the non-universality of the subject-predicate form of propositions actually uses the term ‘quality’ as though it were a synonym for ‘predicate’. He supposes it to be a proof that there are some propositions not of ‘the form which ascribes a predicate to a subject’ that ‘if we say “this thing is bigger than that” we are not assigning a quality of “this” but a relation of “this” and “that”’4 (italics mine). Clearly such an argument makes its point only if the term ‘predicate’ and the term ‘quality’ are to be regarded as identical.
In ordinary usage—even in ordinary philosophical usage—‘predicate’ is a much wider term than ‘quality’ or ‘attribute’. It remains perfectly good English to say that a relational property is ‘predicated’ of a subject. Would it not therefore be wiser to say ‘quality’ or ‘attribute’ where that is what we mean? I suggest that it would minister appreciably to the clarity of logical discussion if that unhappy piece of nomenclature ‘the subject-predicate logic’ were abandoned—despite such historical justification as can be offered for it—and the much less misleading practice generally adopted of calling the logic which treats all predicates as attributes of the subject ‘the subject-attribute logic’.
When it is appreciated that by ‘subject-predicate’ logic is really meant substantially ‘subject-attribute’ logic it must come as a shock to students of F. H. Bradley to find that the logic of this thinker is often referred to as being of the ‘subject-predicate’ type;5 with the implication of course that it suffers from the defects which almost everyone would now agree to be rightly chargeable against a logic which treats relational properties as mere attributes of a subject. On the face of it the charge in Bradley's case seems monstrous. For so far from there being in Bradley any hint that he thus interprets relational properties the plain fact is that he roundly condemns the traditional logic precisely on the ground that its acceptance of a subject-attribute analysis of propositions imposes disastrous limits upon the proper province of logic by excluding therefrom a whole host of valid inferences.
Nevertheless there must presumably be some ground for this apparently absurd designation of Bradley's logic; apart of course from the purely verbal ground that Bradley (blissfully ignorant of the ambiguity which the future course of logical writings would inject into the use of these terms) formally analyses the general nature of judgment into a ‘subject’ a ‘predicate’ and a relation between them. The ground lies I think in the doctrine common to Bradley with other idealist logicians that the ultimate subject of judgment is always ‘Reality as a whole’. As we saw in Lecture III the total ‘ideal content’ of judgment including what is ordinarily distinguished in logic as the subject can on the idealist view be legitimately (and for some purposes usefully) regarded as predicated of Reality as subject. Now it is clear that Reality as a whole cannot be thought of as standing in relation to something other than itself since there is nothing other than itself. It follows that in so far as the subject of all judgment is Reality the predicate ascribed to the subject can in no case be a relational property. And granted that we accept as exhaustive the disjunction between relational properties and attributes as predicates in propositions this may appear to afford a plausible justification of the view that the idealist logic is of the ‘subject-predicate’ (subject-attribute) type.
Plausible but on deeper consideration surely most inadequate? The whole point of condemning the subject-attribute logic is that its analysis of propositions is of such a kind as to entail the restriction of valid inferences to those which have their source in the relation of an attribute to a subject. But this restriction is not entailed by the analysis of propositions offered by the idealist logic. To suppose that it is is to forget that in addition to the ultimate subject (which is normally only implicit) the idealist analysis of propositions recognises that in almost every case there is also a proximate or immediate (and as a rule explicit) subject distinguishable within the total ideal content predicated of Reality from what is ordinarily called the predicate and constituting ‘the starting-point or point of contact with the ultimate subject’ (i.e. Reality). For the sake of brevity I must here refer the reader to the exposition of this doctrine given towards the end of the third lecture. It should be plain therefrom that the proximate subject of the idealist logic and its corresponding predicate are the subject and predicate which logic ordinarily distinguishes within the judgment and that there is not the faintest reason why for idealist logic what is predicated of this proximate subject should be an attribute rather than a relational property. The view that in judgment we are always ‘characterising Reality’ is wholly consistent with our characterising it on occasion by the presence within it of relational situations in which the proximate subject has ascribed to it relational properties not reducible to attributes (as in the judgment ‘Reality is such that this thing is bigger than that’). Once this is understood it seems to me that no plausible ground remains for calling the idealist logic what it so plainly is not as actually expounded in the works of its leading representatives a ‘subject-attribute logic’.
One further point is worth a brief mention. It is sometimes suggested that there is a close connection if not indeed a relation of entailment between the idealists’ logical doctrine that the ultimate subject of the judgment is Reality and the acceptance by the same philosophers of a metaphysical monism. I can discover no good reason for supposing this. Those who hold the logical doctrine in question can surely in full consistency with it make the judgment ‘Reality is such that there exist within it independent entities whose relation to other entities within it is wholly external’. Here Reality is taken as the ultimate subject yet monism is implicitly denied. Admittedly idealist philosophers do as a rule adopt a monistic metaphysics. But nowhere so far as I am aware is this supposed to be a direct consequence of the view that the ultimate subject of judgment is Reality. Monism requires for its establishment at least the additional premise that all relations are internal; a premise which idealist philosophers have laboured to justify by a vast amount of difficult and quite independent argument.