In the index to Appearance and Reality (First Edition) Mr. Bradley declares that all relations are "intrinsical"; and the following are some of the phrases by means of which he tries to explain what he means by this assertion. "A relation must at both ends affect, and pass into, the being of its terms" (p. 364). "Every relation essentially penetrates the being of its terms, and is, in this sense, intrinsical" (p. 392). "To stand in a relation and not to be relative, to support it and yet not to be infected and undermined by it, seems out of the question" (p. 142). And a good many other philosophers seem inclined to take the same view about relations which Mr. Bradley is here trying to express. Other phrases which seem to be sometimes used to express it, or a part of it, are these: "No relations are purely external"; "All relations qualify or modify or make a difference to the terms between which they hold"; "No terms are independent of any of the relations in which they stand to other terms." (See e.g., Joachim, The Nature of Truth, pp. 11, 12, 46).
It is, I think, by no means easy to make out exactly what these philosophers mean by these assertions. And the main object of this paper is to try to define clearly one proposition, which, even if it does not give the whole of what they mean, seems to me to be always implied by what they mean, and to be certainly false. I shall try to make clear the exact meaning of this proposition, to point out some of its most important consequences, and to distinguish it clearly from certain other propositions which are, I think, more or less liable to be confused with it. And I shall maintain that, if we give to the assertion that a relation is "internal" the meaning which this proposition would give to it, then, though, in that sense, some relations are "internal," others, no less certainly, are not, but are "purely external."
To begin with, we may, I think, clear the ground, by putting on one side two propositions about relations, which, though they seem sometimes to be confused with the view we are discussing, do, I think, quite certainly not give the whole meaning of that view.
The first is a proposition which is quite certainly and obviously true of all relations, without exception, and which, though it raises points of great difficulty, can, I think, be clearly enough stated for its truth to be obvious. It is the proposition that, in the case of any relation whatever, the kind of fact which we express by saying that a given term A has that relation to another term B, or to a pair of terms B and C, or to three terms B, C, and D, and so on, in no case simply consists in the terms in question together with the relation. Thus the fact which we express by saying that Edward VII was father of George V, obviously does not simply consist in Edward, George, and the relation of fatherhood. In order that the fact may be, it is obviously not sufficient that there should merely be George and Edward and the relation of fatherhood; it is further necessary that the relation should relate Edward to George, and not only so, but also that it should relate them in the particular way which we express by saying that Edward was father of George, and not merely in the way which we should express by saying that George was father of Edward. This proposition is, I think, obviously true of all relations without exception: and the only reason why I have mentioned it is because, in an article in which Mr. Bradley criticises Mr. Russell (Mind, 1910, p. 179), he seems to suggest that it is inconsistent with the proposition that any relations are merely external, and because, so far as I can make out, some other people who maintain that all relations are internal seem sometimes to think that their contention follows from this proposition. The way in which Mr. Bradley puts it is that such facts are unities which are not completely analysable; and this is, of course, true, if it means merely that in the case of no such fact is there any set of constituents of which we can truly say: This fact is identical with these constituents. But whether from this it follows that all relations are internal must of course depend upon what is meant by the latter statement. If it be merely used to express this proposition itself, or anything which follows from it, then, of course, there can be no doubt that all relations are internal. But I think there is no doubt that those who say this do not mean by their words merely this obvious proposition itself; and I am going to point out something which I think they always imply, and which certainly does not follow from it.
The second proposition which, I think, may be put aside at once as certainly not giving the whole of what is meant, is the proposition which is, I think, the natural meaning of the phrases "All relations modify or affect their terms" or "All relations make a difference to their terms." There is one perfectly natural and intelligible sense in which a given relation may be said to modify a term which stands in that relation, namely, the sense in which we should say that, if, by putting a stick of sealing-wax into a flame, we make the sealing-wax melt, its relationship to the flame has modified the sealing-wax. This is a sense of the word "modify" in which part of what is meant by saying of any term that it is modified, is that it has actually undergone a change: and I think it is clear that a sense in which this is part of its meaning is the only one in which the word "modify" can properly be used. If, however, those who say that all relations modify their terms were using the word in this, its proper, sense, part of what would be meant by this assertion would be that all terms which have relations at all actually undergo changes. Such an assertion would be obviously false, for the simple reason that there are terms which have relation? and which yet never change at all. And I think it is quite clear that those who assert that all relations are internal, in the sense we are concerned with, mean by this something which could be consistently asserted to be true of all relations without exception, even if it were admitted that some terms which have relations do not change. When, therefore, they use the phrase that all relations "modify" their terms as equivalent to "all relations are internal," they must be using "modify" in some metaphorical sense other than its natural one. I think, indeed, that most of them would be inclined to assert that in every case in which a term A comes to have to another term B a relation, which it did not have to B in some immediately preceding interval, its having of that relation to that term causes it to undergo some change, which it would not have undergone if it had not stood in precisely that relation to B and I think perhaps they would think that this proposition follows from some proposition which is true of all relations, without exception, and which is what they mean by saying that all relations are internal. The question whether the coming into a new relation does thus always cause some modification in the term which comes into it is one which is often discussed, as if it had something to do with the question whether all relations are internal as when, for instance, it is discussed whether knowledge of a thing alters the thing known. And for my part I should maintain that this proposition is certainly not true. But what I am concerned with now is not the question whether it is true, but simply to point out that, so far as I can see, it can have nothing to do with the question whether all relations are internal, for the simple reason that it cannot possibly follow from any proposition with regard to all relations without exception. It asserts with regard to all relational properties of a certain kind, that they have a certain kind of effect; and no proposition of this sort can, I think follow from any universal proposition with regard to all relations.
We have, therefore, rejected as certainly not giving the whole meaning of the dogma that all relations are internal: (1) the obviously true proposition that no relational facts are completely analysable, in the precise sense which I gave to that assertion; and (2) the obviously false proposition that all relations modify their terms, in the natural sense of the term "modify," in which it always has as part of its meaning "cause to undergo a change." And we have also seen that this false proposition that any relation which a term comes to have always causes it to undergo a change is wholly irrelevant to the question whether all relations are internal or not. We have seen finally that if the assertion that all relations modify their terms is to be understood as equivalent to the assertion that all are internal, "modify" must be understood in some metaphorical sense. The question is: What is this metaphorical sense?
And one point is, I think, pretty clear to begin with. It is obvious that, in the case of some relations, a given term A may have the relation in question, not only to one other term, but to several different terms. If, for instance, we consider the relation of fatherhood, it is obvious that a man may be father, not only of one, but of several different children. And those who say that all relations modify their terms always mean, I think, not merely that every different relation which a term has modifies it; but also that, where the relation is one which the term has to several different other terms, then, in the case of each of these terms, it is modified by the fact that it has the relation in question to that particular term. If, for instance, A is father of three children, B, C, and D, they mean to assert that he is modified, not merely by being a father, but by being the father of B, also by being the father of C, and also by being the father of D. The mere assertion that all relations modify their terms does not, of course, make it quite clear that this is what is meant; but I think there is no doubt that it is always meant; and I think we can express it more clearly by using a term, which I have already introduced, and saying the doctrine is that all relational properties modify their terms, in a sense which remains to be defined. I think there is no difficulty in understanding what I mean by a relational property. If A is father of B, then what you assert of A when you say that he is so is a relational property—namely the property of being father of B; and it is quite clear that this property is not itself a relation, in the same fundamental sense in which the relation of fatherhood is so; and also that, if C is a different child from B, then the property of being father of C is a different relational property from that of being father of B, although there is only one relation, that of fatherhood, from which both are derived. So far as I can make out, those philosophers who talk of all relations being internal, often actually mean by "relations" "relational properties"; when they talk of all the "relations" of a given term, they mean all its relational properties, and not merely all the different relations, of each of which it is true that the term has that relation to something. It will, I think, conduce to clearness to use a different word for these two entirely different uses of the term "relation" to call "fatherhood" a relation, and "fatherhood of B" a "relational property." And the fundamental proposition, which is meant by the assertion that all relations are internal, is, I think, a proposition with regard to relational properties, and not with regard to relations properly so-called. There is no doubt that those who maintain this dogma mean to maintain that all relational properties are related in a peculiar way to the terms which possess them—that they modify or are internal to them, in some metaphorical sense. And once we have defined what this sense is in which a relational property can be said to be internal to a term which possesses it, we can easily derive from it a corresponding sense in which the relations, strictly so called, from which relational properties are derived, can be said to be internal.
Our question is then: What is the metaphorical sense of "modify" in which the proposition that all relations are internal is equivalent to the proposition that all relational properties "modify" the terms which possess them? I think it is clear that the term "modify" would never have been used at all to express the relation meant, unless there had been some analogy between this relation and that which we have seen is the proper sense of "modify," namely, causes to change. And I think we can see where the analogy comes in by considering the statement, with regard to any particular term A and any relational property P which belongs to it, that A would have been different from what it is if it had not had P: the statement, for instance, that Edward VII would have been different if he had not been father of George V. This is a thing which we can obviously truly say of A and P, in some sense, whenever it is true of P that it modified A in the proper sense of the word: if the being held in the flame causes the sealing-wax to melt, we can truly say (in some sense) that the sealing-wax would not have been in a melted state if it had not been in the flame. But it seems as if it were a thing which might also be true of A and P, where it is not true that the possession of P caused A to change; since the mere assertion that A would have been different, if it had not had P, does not necessarily imply that the possession of P caused A to have any property which it would not have had otherwise. And those who say that all relations are internal do sometimes tend to speak as if what they meant could be put in the form: In the case of every relational property which a thing has, it is always true that the thing which has it would have been different if it had not had that property; they sometimes say even: If P be a relational property and A a term which has it, then it is always true that A would not have been A if it had not had P. This is, I think, obviously a clumsy way of expressing anything which could possibly be true, since, taken strictly, it implies the self-contradictory proposition that if A had not had P, it would not have been true that A did not have P. But it is nevertheless a more or less natural way of expressing a proposition which might quite well be true, namely, that, supposing A has P, then anything which had not had P would necessarily have been different from A. This is the proposition which I wish to suggest as giving the metaphorical meaning of "P modifies A," of which we are in search. It is a proposition to which I think a perfectly precise meaning can be given, and one which does not at all imply that the possession of P caused any change in A, but which might conceivably be true of all terms and all the relational properties they have, without exception. And it seems to me that it is not unnatural that the proposition that this is true of P and A, should have been expressed in the form, "P modifies A," since it can be more or less naturally expressed in the perverted form, "If A had not had P it would have been different,"—a form of words, which, as we saw, can also be used whenever P does, in the proper sense, modify A.
I want to suggest, then, that one thing which is always implied by the dogma that, "All relations are internal," is that, in the case of every relational property, it can always be truly asserted of any term A which has that property, that any term which had not had it would necessarily have been different from A.