Part 24

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.

This is the proposition to which I want to direct attention. And there are two phrases in it, which require some further explanation.

The first is the phrase "would necessarily have been." And the meaning of this can be explained, in a preliminary way, as follows:--To say of a pair of properties P and Q, that any term which had had P would necessarily have had Q, is equivalent to saying that, in every case, from the proposition with regard to any given term that it has P, it _follows_ that that term has Q: _follows_ being understood in the sense in which from the proposition with regard to any term, that it is a right angle, it _follows_ that it is an angle, and in which from the proposition with regard to any term that it is red it _follows_ that it is coloured. There is obviously some very important sense in which from the proposition that a thing is a right angle, it does follow that it is an angle, and from the proposition that a thing is red it does follow that it is coloured. And what I am maintaining is that the metaphorical sense of "modify," in which it is maintained that all relational properties modify the subjects which possess them, can be defined by reference to this sense of "follows." The definition is: To say of a given relational property P that it modifies or is internal to a given term A which possesses it, is to say that from the proposition that a thing has not got P it follows that that thing is different from A. In other words, it is to say that the property of _not_ possessing P, and the property of being different from A are related to one another in the peculiar way in which the property of being a right-angled triangle is related to that of being a triangle, or that of being red to that of being coloured.

To complete the definition it is necessary, however, to define the sense in which "different from A" is to be understood. There are two different senses which the statement that A is different from B may bear. It may be meant merely that A is _numerically_ different from B, _other_ than B, not identical with B. Or it may be meant that not only is this the case, but also that A is related to B in a way which can be roughly expressed by saying that A is _qualitatively_ different from B. And of these two meanings, those who say "All relations make a _difference_ to their terms," always, I think, mean difference in the latter sense and not merely in the former. That is to say, they mean, that if P be a relational property which belongs to A, then the absence of P entails not only numerical difference from A, but qualitative difference. But, in fact, from the proposition that a thing is qualitatively different from A, it does follow that it is also numerically different. And hence they are maintaining that every relational property is "internal to" its terms in both of two different senses at the same time. They are maintaining that, if P be a relational property which belongs to A, then P is internal to A both in the sense (1) that the absence of P entails qualitative difference from A; and (2) that the absence of P entails numerical difference from A. It seems to me that neither of these propositions is true; and I will say something about each in turn.

As for the first, I said before that I think some relational properties really are "internal to" their terms, though by no means all are. But, if we understand "internal to" in this first sense, I am not really sure that any are. In order to get an example of one which was, we should have, I think, to say that any two different qualities are always _qualitatively_ different from one another: that, for instance, it is not only the case that anything which is pure red is qualitatively different from anything which is pure blue, but that the quality "pure red" itself is qualitatively different from the quality "pure blue." I am not quite sure that we can say this, but I think we can; and if so, it is easy to get an example of a relational property which is internal in our first sense. The quality "orange" is intermediate in shade between the qualities yellow and red. This is a relational property, and it is quite clear that, on our assumption, it is an internal one. Since it is quite clear that any quality which were _not_ intermediate between yellow and red, would necessarily be _other_ than orange; and if any quality _other_ than orange must be _qualitatively_ different from orange, then it follows that "intermediate between yellow and red" is internal to "orange." That is to say, the absence of the relational property "intermediate between yellow and red," _entails_ the property "different in quality from orange."

There is then, I think, a difficulty in being sure that _any_ relational properties are internal in this first sense. But, if what we want to do is to show that some are _not,_ and that therefore the dogma that all relations are internal is false, I think the most conclusive reason for saying this is that if _all_ were internal in this first sense, all would necessarily be internal in the second, and that this is plainly false. I think, in fact, the most important consequence of the dogma that all relations are internal, is that it follows from it that all relational properties are internal in this second sense. I propose, therefore, at once to consider this proposition, with a view to bringing out quite clearly what it means and involves, and what are the main reasons for saying that it is false.

The proposition in question is that, if P be a relational property and A a term to which it does in fact belong, then, no matter what P and A may be, it may always be truly asserted of them, that any term which had _not_ possessed P would necessarily have been other than--numerically different from--A: or in other words, that A would necessarily, in all conceivable circumstances, have possessed P. And with this sense of "internal," as distinguished from that which says _qualitatively different,_ it is quite easy to point out some relational properties which certainly are internal in this sense. Let us take as an example the relational property which we assert to belong to a visual sense-datum when we say of it that it has another visual sense-datum as a spatial part: the assertion, for instance, with regard to a coloured patch half of which is red and half yellow. "This whole patch contains this patch" (where "this patch" is a proper name for the red half). It is here, I think, quite plain that, in a perfectly clear and intelligible sense, we can say that any whole, which had not contained that red patch, could not have been identical with the whole in question: that from the proposition with regard to any term whatever that it does not contain _that_ particular patch it _follows_ that that term is _other_ than the whole in question--though _not_ necessarily that it is qualitatively different from it. _That_ particular whole could not have existed without having that particular patch for a part. But it seems no less clear, at first sight, that there are many other relational properties of which this is not true. In order to get an example, we have only to consider the relation which the red patch has to the whole patch, instead of considering as before that which the whole has to it. It seems quite clear that, though the whole could not have existed without having the red patch for a part, the red patch might perfectly well have existed without being part of that particular whole. In other words, though every relational property of the form "having _this_ for a spatial part" is "internal" in our sense, it seems equally clear that every property of the form "is a spatial part of this whole" is _not_ internal, but purely external. Yet this last, according to me, is one of the things which the dogma of internal relations denies. It implies that it is just as necessary that anything, which is in fact a part of a particular whole, should be a part of that whole, as that any whole, which has a particular thing for a part, should have that thing for a part. It implies, in fact, quite generally, that any term which does in fact have a particular relational property, could not have existed without having that property. And in saying this it obviously flies in the face of common sense. It seems quite obvious that in the case of many relational properties which things have, the fact that they have them is _a mere matter of fact:_ that the things in question _might_ have existed without having them. That this, which seems obvious, is true, seems to me to be the most important thing that can be meant by saying that some relations are purely external. And the difficulty is to see how any philosopher could have supposed that it was not true: that, for instance, the relation of part to whole is no more external than that of whole to part. I will give at once one main reason which seems to me to have led to the view, that _all_ relational properties are internal in this sense.

What I am maintaining is the common-sense view, which seems obviously true, that it may be true that A has in fact got P and yet also true that A might have existed without having P. And I say that this is equivalent to saying that it may be true that A has P, and yet _not_ true that from the proposition that a thing has _not_ got P it _follows_ that that thing is _other_ than A--numerically different from it. And one reason why this is disputed is, I think, simply because it is in fact true that if A has P, and _x_ has _not_, it _does_ follow that _x_ is other than A. These two propositions, the one which I admit to be true (1) that if A has P, and _x_ has not, it _does_ follow that _x_ is other than A, and the one which I maintain to be false (2) that if A has P, then from the proposition with regard to any term _x_ that it has not got P, it _follows_ that _x_ is other than A, are, I think, easily confused with one another. And it is in fact the case that if they are not different, or if (2) follows from (1), then no relational properties are external. For (1) is certainly true, and (2) is certainly equivalent to asserting that none are. It is therefore absolutely essential, if we are to maintain external relations, to maintain that (2) does _not_ follow from (1). These two propositions (1) and (2), with regard to which I maintain that (1) is true, and (2) is false, can be put in another way, as follows: (1) asserts that if A has P, then any term which has not, _must_ be other than A. (2) asserts that if A has P, then any term which had not, _would necessarily be_ other than A. And when they are put in this form, it is, I think, easy to see why they should be confused: you have only to confuse "must" or "is necessarily" with "would necessarily be." And their connexion with the question of external relations can be brought out as follows: To maintain external relations you have to maintain such things as that, though Edward VII was in fact father of George V, he _might_ have existed without being father of George V. But to maintain this, you have to maintain that it is _not_ true that a person who was _not_ father of George would necessarily have been other than Edward. Yet it is, in fact, the case, that any person who was not the father of George, _must_ have been other than Edward. Unless, therefore, you can maintain that from this true proposition it does _not_ follow that any person who was _not_ father of George _would necessarily_ have been other than Edward, you will have to give up the view that Edward might have existed without being father of George.

By far the most important point in connexion with the dogma of internal relations seems to me to be simply to see clearly the difference between these two propositions (1) and (2), and that (2) does _not_ follow from (1). If this is not understood, nothing in connexion with the dogma, can, I think, be understood. And perhaps the difference may seem so clear, that no more need be said about it. But I cannot help thinking it is not clear to everybody, and that it does involve the rejection of certain views, which are sometimes held as to the meaning of "follows." So I will try to put the point again in a perfectly strict form.

Let P be a relational property, and A a term to which it does in fact belong. I propose to define what is meant by saying that P is internal to A (in the sense we are now concerned with) as meaning that from the proposition that a thing has not got P, it "follows" that it is _other_ than A.