CHAPTER VCHARACTERISTICS(I) DIVISION INTO QUALITIES AND RELATIONS1. McTaggart's Classification.Characteristics, according to McTaggart, are of two kinds, viz., Qualities and Relations. Both these terms are indefinable, but both are perfectly familiar and intelligible. In § 80 he remarks that qualities are qualities of something, whilst relations are relations between something and something; but this does not constitute a definition of the difference between the two. At most these two prepositions, "of" and "between", serve to direct our attention to a distinction with which we are all quite familiar. It must be noted that the two occurrences of the word "something" in the phrase "between something and something" may, on McTaggart's view, stand for one and the same term; for he holds that a term may be related to itself. It would not, therefore, have been possible for him to say that a qualitative fact is one which either has only one logical subject or is a conjunction or disjunction of facts each of which has only one logical subject, whilst a relational fact is one which has more than one logical subject and is not a conjunction or disjunction of facts each of which has only one logical subject. Anyone who denied that a term could be related to itself might put the distinction between qualitative and relational facts in this way, and he might then describe a quality as a "monadic adjective" and a relation as a "polyadic adjective". This is, of course, the line taken by Johnson. In § 85 McTaggart points out that, corresponding to a term A and a relation R, there may be a number of different relational facts. There might, for example, be the fact that A has R to B and the different fact that A has R to C. He calls such facts "Relationships". Now he holds that each relationship "generates" a certain quality, corresponding to it, in each term that enters into the relationship. Suppose, for example, that there is the relational fact that A is jealous of B on account of C. This generates in A the quality of being jealous of B on account of C; it generates in B the quality of being an object of jealousy to A on account of C; and it generates in C the quality of being something in respect of which A is jealous of B. McTaggart calls all qualities which are generated by relationships "Relational Qualities". Qualities which are not so generated he calls "Original Qualities" (§ 86). In addition to generated qualities there are generated relationships. If a term has a certain quality, this fact generates a relationship between this term and this quality. For example, the fact that x is red generates the relational fact that redness inheres in x. Again, every relationship generates another relationship. If there is the fact that x stands in the relation R to y, then there is also the fact that x is a term in this fact. Now the latter is a fact about the relation of x to the firstmentioned relationship. It is therefore a second relationship (§ 87). In pursuing this subject in the second paragraph of § 87 McTaggart lands himself in a confusion. He proceeds to talk of generated relations. But he has not shown that any relations are generated; at most he has shown that some relationships are generated. And he has carefully distinguished between relationships, which are facts, and relations, which are not facts but characteristics. This confusion might be avoided by defining a "generated relation" as the relating relation of any generated relationship. Thus inherence would be a generated relation, because all relationships of the form "q inheres in x" are generated from facts of the form "x has the quality q". Similarly, the relation of referent to, which holds between a term and a relation that relates that term to something, would be a generated relation. For all relationships of the form "x has the relation of referent to R" are generated by facts of the form "x has the relation R to y". If we adopt this suggestion, we must notice that it will not be true that there is an endless series of generated relations, even if there be an endless series of generated relationships. Starting with the relationship "that x has R to y", there will be the series "x has the relation of referent to R", "x has the relation of referent to the relation of referent to R", ... and so on. But, even if these be different relationships, there is no new relation generated after the first term of the series. McTaggart defines "Generated Characteristics" as generated qualities and generated relations. All other characteristics he calls "Original Characteristics". He points out in § 89 that the qualities of any term can be divided into two classes. In the first class will be included all its original qualities, all those relational qualities which are immediately generated by its original relationships, and nothing else. This class he calls the "Primary Qualities " of the term. (This usage must not, of course, be confused with the ordinary distinction of primary and secondary qualities, which dates from Locke and has no connexion whatever with McTaggart's distinction.) Suppose, for example, that x is red and is to the right of y. Then the original quality of redness and the relational quality of being to the right of y, which is immediately generated by the original relationship that x is to the right of y, will be primary qualities of x. All the other qualities of a term are called "Repeating Qualities". The repeating qualities of x in our example would include, for example, the quality of being inhered in by redness, the quality of being referent to the relation of to the right of, the quality of being inhered in by the quality of being inhered in by redness, the quality of being referent to the relation of referent to the relation of to the right of, and so on. The whole classification of characteristics may now be summed up in the table given below.
2. Critical Comments on the above Classification.I have now stated and explained McTaggart's way of classifying characteristics, and have refrained almost wholly from criticism. It is now time to consider critically certain points in it. The most important questions which arise are the following.
2.1. Arguments against Relations. According to McTaggart (Chap. VIII) the classical arguments against relations reduce to two. The first is Leibniz's contention that they do not inhere in their terms in the way in which qualities do. This is true, but plainly irrelevant. Why should relations be expected to behave exactly like qualities? When Leibniz says that, for an attribute to have "one leg in one term and another leg in another term", would be "contrary to the nature of attributes", and uses this as an argument against there being relations, he plainly commits a petitio principii. For a relation would be an attribute of this kind, so that Leibniz's "argument" is just a picturesque way of asserting the dogma that all attributes must be qualities. The second argument against relations is that of Bradley. The argument is that, if A is to be related by R to B, A must be related by a relation R_{1} to R, and R must be related by a relation R_{2} to B. On the same grounds A must be related by a relation R_{11} to R_{1}, R_{1} must be related by a relation R_{12} to R, R must be related by a relation R_{21} to R_{2}, and R_{2} must be related by a relation R_{22} to B. Similar remarks will apply to all these four relational facts, and so at the next stage there will be eight relational facts, at the next to this sixteen, and so on without end. Bradley's contention is that this series could not have a first term unless it had a last term, which it plainly does not. McTaggart admits that there is this endless series in connexion with any relational fact, but he denies that it is vicious. His answer amounts to saying that the first term, i.e., that A has R to B, is a fact in its own right, and that the rest of the series consists merely of further consequences of this fact. I think it might fairly be said that, whilst Leibniz's argument depends on insisting that relations shall behave as if they were qualities, Bradley's argument depends on insisting that they shall behave as if they were particulars like the terms which they relate. It is plain that Bradley thinks of A and B as being like two objects fastened together with a bit of string, and he thinks of R as being like the bit of string. He then remembers that the objects must be glued or sealed to both ends of the bit of string if the latter is to fasten them together. And then, I suppose, another kind of glue is needed to fasten the first drop of glue to the object A on the one side and to the bit of string on the other; and another kind of glue is needed to fasten the second drop of glue to the object B on the one side and to the string on the other. And so on without end. Charity bids us avert our eyes from the pitiable spectacle of a great philosopher using an argument which would disgrace a child or a savage. There are two remarks which it seems worth while to add before leaving the topic of Bradley and relations. (i) All our characterizing judgments either assert qualities of terms or relations between terms. They therefore presuppose that the categories of "termcharacterisedbyquality" and "termsinrelation" are understood by those who utter and those who hear such judgments. If we now begin to raise the questions "How do qualities characterise terms?" and "How do relations relate terms?", we can attempt to answer them only by making judgments which, like all judgments, will presuppose these general categories. It is therefore inevitable that all attempts to answer such questions will issue in vicious circles or in vicious infinite regresses. Therefore the fact that they do issue in such circles and regresses is no proof whatever that there is anything wrong with these general notions. If we take a concrete case of Bradley's regress, and translate the symbols into words, the point becomes quite plain. Let us start with the fact that A is father of B. Here we have a perfectly intelligible statement, involving the nonformal relation of fatherhood. At the next stage we get the fact that A is referent to fatherhood, and the fact that B is relatum to fatherhood. The "relations" introduced at this stage are purely formal. At the next stage we get the fact that A is referent to referent to, that fatherhood is relatum to referent to, that fatherhood is referent to referent to, and that B is relatum to referent to. Thus no new "relations" are introduced at this or at any subsequent stage. The fact that at every stage after the first the relating relations are purely formal and are merely repeated shows that we are now embarked on the selfevidently impossible task of explaining, by means of particular relational judgments, that general relational form which is presupposed by all relational judgments whatever. (ii) I am inclined to think that Bradley's real objection to relations is to be found in the second part of Appearance and Reality, and that it is very much more respectable than the tiresome and trivial arguments by which he supports it in the first part would suggest. It seems to me that there is one simple alleged fact which Bradley regards as absolutely fundamental. The alleged fact is that there is something both logically and psychologically prior to terms and relations. This something may be called "Unities". Both terms and relations are abstractions made from unities. Unities are presented as such directly in senseawareness or in feeling. They are, and are felt to be, in some sense complex and differentiated. Directly we start thinking about them we substitute for them a diagrammatic scheme of independent terms and mutual relations. We cannot help doing this; but we are mistaken if we identify the scheme with the original unity of which it professes to be the analysis. Consequently the notion of terms which could exist independently of each other and of the wholes in which they are parts, and which could then, by "coming into relations", constitute these wholes, is a complete perversion of the real order. Any term less than the whole is an abstraction, and a partly misleading abstraction, from the whole. If I had to make up an argument in support of this view, I should put it somewhat as follows. "You must admit that your knowledge of particular terms and particular relations is ultimately derived from unities with which you are directly acquainted. You must admit that it is only from your acquaintance with unities which you have subsequently 'analysed into' terms in relations that you know what is meant by 'terms standing in relations to form unities'. Now the only unities that you are acquainted with are the sensefields which you sense and your own field of consciousness. And here the terms which you profess to distinguish on inspection and introspection seem clearly to be such that they could not have existed out of the very same unity in which you find them. What right then have you to assume that there can be unities composed of terms which could have existed outside these unities? Is it not likely that the whole notion of terms which are to some extent independent of their actual relations, and of wholes which are merely certain of the numerous possible alternative arrangements of such terms, is unjustifiable?" It would take us too far afield to deal adequately with this argument; but I suspect that it is much nearer to Bradley's real thought about Relations than are the dialectical fireworks which he discharges at them in Part I. 2.2. Can Qualities be dispensed with if Relations be accepted? In § 83 McTaggart mentions the suggestion that perhaps qualitative facts could be analyzed away without remainder into relational facts. He takes this suggestion to be that there is a plurality of ultimate relations of exact likeness. To say of the two sensibilia A and B that both are red would be to say that they have to each other a certain one of these ultimate relations of exact likeness. He dismisses the whole suggestion almost without discussion, on the ground that no positive reason has ever been given for doubting that there are qualities, and that it is obvious that relations of exact likeness are not ultimate but depend on the possession of common qualities. The following comments may be made on these statements. (i) If all Judgments which appear to ascribe a quality to a particular really assert that it stands in some relation to some other particular, it is not at all obvious that the relation would be that of exact likeness of a specific kind. Take, for example, the judgment that x is red. If this is to be arlalysed in the way suggested, I should think that the following would be the most plausible account of it. I have sensed certain sensibilia, r_{1}, r_{2}, ... etc., which all resembled each other fairly closely in hue. I have also sensed other sensibilia which resembled each other fairly closely in hue, but did not in the least resemble these. There was in fact a group, b_{1}, b_{2}, ... etc., which answered to this condition. There was also a group, g_{1}, g_{2}, ... etc., and a group y_{1}, y_{2}, ... etc. Each of these groups consisted of sensibilia which were very similar to each other in hue, whilst the sensibilia in any one of these groups were wholly dissimilar in hue from the sensibilia in any other of these groups. I was taught to give the name "red" to all the members of the first group and to any other sensibile which should resemble one of these in hue at least as closely as the least similar of them resembled each other. My judgment that x is red would then be analyzed as follows: "x resembles in hue one of the sensibilia which I was taught to call 'red ' at least as closely as the least similar of these resembled each other". (ii) It does not seem to me to be either selfevident or capable of proof that exact likeness of a speeific kind consists in or depends on the possession of a common quality. I should think it certain that recognition of likenesses and unlikenesses precedes recognition of common qualities. And it does not seem altogether unreasonable to suggest that the notion of common qualities may be a convenient fiction to systematise and abbreviate the statement of a complicated set of interrelated facts about likenesses and unlikenesses. (iii) Suppose that all statements of the form "x has the quality q" correspond to facts of the form "x has the relation R to something". If R be a symmetrical relation, as it would be if it were a relation of likeness, the following consequence would result. It would be logically impossible for one statement of the form "x has q" to be true unless at least one other statement of the same form about another particular y were also true. It would, for example, be logically impossible that there should have been only one noise or only one coloured sensibile. If this is felt to be an objection, it might perhaps be evaded in the case of the coloured sensibile by pointing out that the latter has parts which are also coloured sensibilia, so that there could not, on any view, be one coloured sensibile without there being many. But this argument could hardly be applied to a noise. Even if every noise has parts, as McTaggart would have to hold, it seems impossible that every noise should have parts which are noises. Thus the difficulty may be put in this way. It seems logically possible that the statement "This is a noise" should have been true even though nothing but this had been a noise. If, however, the statement that this is a noise means that this has a certain relation S to something, and if this relation S be symmetrical, it is logically impossible that this should have been a noise if nothing but this had been a noise. We shall have the very paradoxical position that this, which was not a noise, will become a noise when and only when another sensibile begins to exist which has to it the symmetrical relation S. So far as I can see, the only way of evading this paradox would be to say that "x is a noise" means "x is the sort of thing that could stand in the relation S to something", and does not mean "x does in fact stand in the relation S to some thing". Now this amended interpretation seems to imply that certain particulars could, whilst others could not, stand in the relation S. Many people would hold that a fact of this kind cannot be ultimate. They would say that there must be some actual difference between the natures of those terms which could and those which could not stand in a given relation S. This seems to mean that there must be some quality q, such that particulars which had q, and only such particulars, could stand in the relation S. If this be admitted, we are forced back to the admission of qualities. 2.3. Can a Term be related to Itself? Is it true that a term can be related to itself? The alleged examples fall into two classes. (It could not, of course, be asymmetrical. For to say that R is "asymmetrical" is to say that xRy is incompatible with xR*y, where R* is the converse of R, for all values of x and of y. It would therefore entail that xRx is incompatible with xR*x. But obviously xRx, so far from being incompatible with xR*x, is logically equivalent to it. So it is impossible that any term should stand in an asymmetrical relation to itself.Now, as regards the symmetrical relations, like identity, I do not believe that they ever relate a term to itself. If they did, where would be the "duality of aspect" which even McTaggart insists upon? Contrast for example, "A is identical with A" and "A respects A". In the latter case there is a duality of aspect, for it is one fact to be a respecter of A and it is another fact to be respected by A. But no such duality of aspect could arise with a symmetrical relation, like identity. Take, for example, "Tully is the same as Cicero" and "1 + 1 = 4½". The first means: "There was a man who had the property of being called Tully and the property of being called Cicero, and neither property belonged to more than one man". The second means: "There is a number which has the relation of sum to 1 and 1 and has the relation of squareroot to 4, and neither property belongs to more than one number". If this kind of analysis be right, identity is not a relation between a term and itself; in fact there is no relation of which the word "identity" is the name. What is meant by sentences that contain the word "identity" can be expressed by sentences which do not contain it or any synonym for it, but do contain some symbol for the coinherence of different attributes in a single term. The second class of relations between a term and itself is not open to the above criticisms. But at this point I think it is important to distinguish between direct and indirect relations. Sometimes the fact that x has a certain relation T to y is simply the fact that there is some term w such that x has a certain relation R to w and that w has a certain relation S to y, whilst x has neither R nor S to y. In such a case we should call T an "indirect" relation between x and y. We should call T the "relational product" of "R into S", and should denote it by R  S. The relation of uncle to nephew is an example of an indirect relation, since it is the relational product of the relation of brotherorsister into the relation of parent. Not no one could possibly object to a term x standing in a relation R to some term w which stood in some relation S, which was not merely the converse of R, to x itself. Yet this means that x stands to itself in the indirect relation R  S. An example would be if x loved his mother, since x would then have to himself the relation which is the relational product of loving into parenthood. Now there is a special case of indirect relations, which is important for the present purpose. This is the case where x has a part w which stands in a certain relation S to x. Here the relation of x to itself is indirect, since it is the relational product of the relation of having a part into the relation S. But in this particular case we are rather liable to overlook the fact that the relation of x to itself is indirect, and to talk as if it were direct. Thus we might well say that a certain organism was poisoning itself, when what we really meant was that it had a part, e.g., a decaying tooth, which was poisoning it. Now it seems to me that McTaggart's second class of examples all come under this heading if we accept his views about the nature of cognition and emotion. Take, for example, the fact which is expressed by the sentence "A is feeling contempt for himself". On McTaggart's view the feeling of contempt would be a particular which is part of that more inclusive particular which is the self A. It counts as a feeling of contempt because of its peculiar emotional quality. And it counts as a feeling of contempt for A because it stands to A in(the relation of perception to perceptum. Thus the relation of A to itself is the indirect relation which is the relational product of the two relations of "having a part" and "being a perception of" . McTaggart has produced no instance which, on his own views, could consistently be regarded as an example of a direct relation between a term and itself. And it seems to me highly doubtful whether a direct relation between a term and itself is possible. 2.4. Generated Characteristics. 2.41. Qualities generated by Relationships. 2.42. Relationships generated by Qualities.
Next let us represent the form of a dyadic relational fact by a
pair of intersecting circles. Thus:
The fact that A loves B is to be represented by putting "A" into the lefthand compartment, "B" into the righthand compartment, and "L" into the middle compartment. Thus: Now how are we to represent the fact that redness inheres in A? Since it is of the relational form, we shall use the figure of intersecting circles. We shall put "red" into the lefthand compartment, and "A" into the righthand compartment. What shall we put in the middle compartment? Plainly the blank form of a qualityfact. The diagram will thus be 2.43. Relationships generated by Relationships. How should we then represent the fact that loving relates A to B? Remembering that the fact that A loves B is represented by the diagram we can see that the derived fact should be represented by the following diagram: Here the two empty intersecting circles in the innermost compartment represent the form of unity of a relational fact which is dyadic, whilst the three intersecting circles represent the triadic nature of the derived relationship. As at present advised, then, I agree with McTaggart's contention that any original fact, whether qualitative or relational, is at the basis of an endless ascending hierarchy of facts which are not qualitative, and which may, in a slightly extended sense, be called "relational". This is quite consistent with my denial of his contention that every relational fact gives rise to derivative qualities in each of its terms. Again, I agree with McTaggart in holding that there is nothing vicious in an endless series of this kind. Lastly, it seems to me certain that no human being ever makes judgments which refer to facts beyond the second or third stage of such a hierarchy. We have a general rule for writing down the sentences which would express such judgments if they were made, and we may write down very complicated sentences in accordance with this rule when we want to give examples. But we are not really making the judgments which these sentences would properly express. 3. The "Nature" of a Term.I should proceed as follows. I should define the "Complete Original Fact" about a term as the conjunctive fact whose conjuncts are all the original atomic facts, whether qualitative or relational, about the term. By "atomic" I mean for the present purpose facts which are neither conjunctions nor disjunctions of other facts. I should define the "Nature" of a term as the class of all its original qualities. We then get three useful and unobjectionable notions, viz.,
Finally, it must be remarked that the "nature" of a continuant is often taken to consist of its permanent dispositional properties, e.g., its melting point, its modes of reaction in presence of certain other continuants, etc. Thus, it would be said to be a part of the nature of silver to dissolve in nitric acid, and part of the nature of gold not to dissolve in nitric acid but to dissolve in aqua regia. I deal with this subject in Section 3 of Chap. XIV of the present work.
