Philosophical Studies

by G. E. Moore

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.

That is to say, this proposition asserts that between the two properties "not having P" and "other than A," there holds that relation which holds between the property "being a right angle" and the property "being an angle," or between the property "red" and the property "coloured," and which we express by saying that, in the case of any thing whatever, from the proposition that that thing is a right angle it follows, or is deducible, that it is an angle.