Any characteristic whatever of a term constitutes a "Description" of it. If the characteristic belongs to several terms, it will not be an "Exclusive Description" of any of them. An "Exclusive Description" of a term is a characteristic which belongs to it and to no other term, or it may be a set of characteristics such that all belong to this term and not all belong to any other term. An exclusive description of a term need not be a "Complete Description" of it; for a selection of its characteristics may suffice to distinguish this term from all others.

      Now a description of a term may contain characteristics which involve a reference to particulars that are merely designated by proper names. Suppose, for example, that Julius Caesar is described as the first Roman invader of Britain. The description involves a reference to two particulars, viz., Britain and Rome, which are merely designated. If an exclusive description of a term refers to no merely designated particulars, but consists wholly of universals, it is called a "Sufficient Description". Thus it would be a sufficient description of Christ, on the Christian view of his nature, to say that he is the son of the Most Perfect Being.

      If the Dissimilarity of the Diverse be admitted, it would follow at once that every particular must have an exclusive description. For consider any particular A. Either A is the only particular that there is, or there are others beside it. If it were the only particular, any characteristic of it would be an exclusive description of it. If there be other particulars beside A, none of them can be exactly like A. So a complete description of A would necessarily be an exclusive description of it. And, of course, a selection from the complete description of A might be an exclusive description of it. The question that remains, for those who accept the Dissimilarity of the Diverse, is whether every particular must have a sufficient description. McTaggart professes to show that, if every particular has an exclusive description, every particular must have a sufficient description And, since he accepts the Dissimilarity of the Diverse as self-evident, he claims in this way to prove that every particular must have a sufficient description. This proposition I will call "The Principle of Sufficient Descriptions". He does not, of course, pretend that, in the case of most particulars, any sufficient description is known to us. But he holds that there must be a sufficient description in every case, whether anyone happens to know of one or not.

      McTaggart begins by distinguishing several possible kinds of sufficient description, of various degrees of complexity. He does not follow any systematic order in his account of them. I think that it is possible to classify them, and I shall now do so. In the first place, we must distinguish between sufficient descriptions of the "First", "Second", "Third", and higher "Orders". A sufficient description of a particular A will be "of the First Order" if it contains no sufficient description of any other particular. Thus the description of God as the Most Perfect Being, i.e., the being who has to every other being the relation of greater perfection, is a first-order sufficient description. A sufficient description of A is "of the Second Order" if it contains a first-order sufficient description of a certain particular, and contains no sufficient description which is not of the first order. The description of Christ as the son of the Most Perfect Being, is a sufficient description of the second order, on the usual Christian assumptions. A sufficient description is "of the Third Order" if it contains a second-order sufficient description of a certain particular, and contains no sufficient description which is not of either the first or the second order. The description of the Virgin Mary as the mother of the son of the Most Perfect Being, is a sufficient description of the third order, on the usual Christian assumptions. The general notion of orders of sufficient descriptions should now be clear.

      Now, so far as I can see, first-order sufficient descriptions fall into five groups, some of which can be further subdivided.

      (1) A may be the only instance of a certain original quality, or set of original qualities, or set of original qualities, φ. It might, for example, be the only thing that had a certain shade of a certain colour.

      (2) We might take a certain relation R, and consider the following five possibilities.

(2.1) A is the only particular which has R to anything. For example, God is the only particular that has to anything the relation of creating, according to most theists.

(2.2) A is the only particular which has R to everything. For example, God, in the opinion of most theists, is the only particular which is acquainted with all particulars.

(2.3) A is the only particular which has the relation R to itself . For example, the Devil might be the only particular which hates itself.

(2.4) A is the only particular that has R to anything but itself. For example, if psychological egoism had been true, God would have been the only particular which loves anything but itself.

(2.5) A is the only particular which has R to everything but itself. For example, on another view of the nature of the Devil, he might be the only particular which hates everything but himself.

      (3) In this group we again take a certain relation R. and we now consider the number of things to which A stands in this relation. This again gives five possibilities. A might be the only thing which has R to

(3.1) n particulars,

(3.2) more than n particulars,

(3.3) less than n particulars,

(3.4) at least n particulars, or

(3.5) at most n particulars.

      (4) We now consider a class of particulars having some exclusive common property ψ. We again consider a certain relation R. This gives rise to seven possibilities. A might be the only thing that has R to

(4.1 ) any instance of ψ,

(4.2) every instance of ψ,

(4.3) n instances of ψ,

(4.4) more than n instances of ψ,

(4.5) less than n instances of ψ,

(4.6) at least n instances of ψ, or

(4.7) at most n instances of ψ.

      (5) Even if a particular has no first-order sufficient description of any of these kinds, it may have one which is constructed by combining insufficient descriptions of two or more of these kinds. Thus, there might be several instances of φ, and several instances of particulars which have R to n instances of ψ, but there might be one and only one particular which was an instance of φ and had R to n instances of ψ. There are, for example, plenty of negroes, and plenty of people who are fathers of two red-haired children; but there might well be one and only one particular which is a negro father of two red-haired children.

      I have not gone into all this elaborate detail merely in order to be tiresome. It seems to me important to realise the vast number of different ways in which a particular could be sufficiently described, for this makes the Principle of Sufficient Descriptions less unplausible than it appears at first sight.

      We can now deal with McTaggart's attempted proof of the Principle. This is contained in § 105. I will first try to show by an example that a case is conceivable in which, whilst everything had an exclusive description, there were things that did not have a sufficient description. Imagine a universe consisting of just three minds, A, B, and C. We will suppose that none of them has a sufficient description. Now, suppose it were the case that A is jealous of B on account of C, that B is jealous of C on account of A, and that C is jealous of A on account of B. Then I maintain that each of these particulars would have an exclusive description, in spite of the fact that none of them had a sufficient description. A would have the characteristic of being jealous of B on account of C. Call this φ. B could not have this, since no one can be jealous of himself. C could not have this, since no one can be jealous on account of himself. Hence B and C both have the characteristic non-φ. Now take the characteristic of being jealous of C on account of A. Call this ψ. B has ψ, and, for similar reasons to those mentioned before, C and A have non-ψ. Lastly, if we denote the characteristic of being jealous of A on account of B by χ, it is plain that C has χ and that A and B have non-χ. Thus A is the only particular in the universe which has φ, B is the only one that has ψ, and C is the only one that has χ. By hypothesis A, B, and C are the only particulars in the universe and have no sufficient descriptions Nevertheless, we see that each will have an exclusive description.

      It is clear then that there must be something wrong with McTaggart's argument in § 105, since it claims to show the necessity of something which could conceivably be false. The argument is very obscurely stated and is not at all easy to follow, but I am afraid that there is no doubt that what I am now going to state in my own words is what McTaggart had in mind. Let A be any particular. Then A must have an exclusive description. If possible, suppose that it has no sufficient description. Then (i) every exclusive description of A must describe it by a certain relation R in which it stands to a certain other particular B. And (ii) this other particular B must itself have no sufficient description. For, if B had a sufficient description φ, A could be sufficiently described as the particular which has R to the only instance of φ. Now B in turn must have an exclusive description. Since this cannot be a sufficient description, B must be exclusively described by a certain relation S in which it stands to a certain other particular C. And C cannot have a sufficient description. For, if ψ were a sufficient description of C, A could be sufficiently described as the particular which has R to the particular which has S to the only instance of ψ. By repeated application of the same considerations we arrive at the following conclusion. If every particular has an exclusive description, and if A had no sufficient description, there would have to be an unending series of particulars, B, C, ..., such that none of them had a sufficient description. McTaggart thinks that the endlessness of this series would entail that A had no exclusive description. And so the compound supposition that every particular has an exelusive description and that A has no sufficient description entails the conclusion that A has no exclusive description. It thus contradicts itself, and therefore cannot be true. Therefore the proposition that every particular has an exclusive description is inconsistent with there being any particular which lacks a sufficient description. That is, the proposition that every particular has an exclusive description entails the proposition that every particular has a sufficient description.

      This is McTaggart's argument, fully and formally stated. If I have not misunderstood it, it contains no less than three gross formal fallacies.

      (i) McTaggart assumes that, if A had no sufficient description, any exclusive description of A would have to describe it by a certain relation to a certain other particular, B. This is not so. The relation might be to A itself. Suppose, for example, that the universe consisted of two minds, A and B, each of which respected itself and despised the other. Then the property of respecting A would belong to A and to nothing else. It would therefore be an exclusive description of A. Similarly, the property of respecting B would be an exclusive description of B. Thus A could be exchlsively described without reference to B, and B could be exclusively described without reference to A, even though neither had a sufficient description. It is true, of course, that A also has the property of respecting itself, and that this involves no reference to any merely designated particular. But then it also does not constitute an exclusive description of A, since B also has the property of self-respect. And so it does not constitute a sufficient description of A. It cannot therefore be contended that the exclusive, but not sufficient, description "respecting A" could be replaced by "respecting itself", and that this would be a sufficient description. The first description fails to be sufficient, in McTaggart's sense, because it contains the merely designated particular A; the second description avoids this defect, but fails to be sufficient by failing to be exclusive.

      (ii) McTaggart assumes that, if A has to be described by reference to a particular B which is other than A, and if B has to be described by reference to a particular C whieh is other than B, then C must he other than A. This is, of course, completely fallacious. "C" might be simply another name for the particular of which "A" is a name. Julius Caesar is other than Cicero, and Tully is other than Julius Caesar, but "Tully" and "Cicero" are just two different names of the same eloquent egotist. Thus, even if the series must start, there is no need for it to be endless, except in the sense in which a circle is "endlless". My earlier example of a universe consisting of three minds, A, B, and C, of whom A is jealous of B, on aeeount of C, B is jealous of C on account of A, and C is jealous of A on account of B. illustrates this possibility. Here the exclusive description of each particular involves a reference to two other designated particulars, but there are only three particulars altogether.

      (iii) Even if the series had to start, and had then to continue without end and without recurrence, McTaggart's conclusion would not follow. His conclusion is that A would have no exclusive description. But, so far as I can see, this is a complete non-sequitur. A has the exclusive description of being the only particular that has R to B. How could this be altered by the fact that B has no sufficient description, that its exclusive description must be of the form "having S to C", and that the same must be true, mutatis mutandis, of C and of every particular in a certain endless and non-recurrent series? Even if we accepted both the false premises which McTaggart tacitly assumes, the only conclusion which could legitimately be drawn is the following. "If every particular has an exclusive description, and there were any particular A which lacked a sufficient description, then there must be an endless and non-recurrent series of particulars starting with A and all lacking sufficient descriptions". Of course, if you object to such an unending and non-recurrent series of particulars simply on the ground of its non-recurrent endlessness, you would be justified in concluding from this that, if every particular has an exclusive description, no particular can lack a sufficient description. But McTaggart has not the slightest objection to endless and non-recurrent series of particulars, as such. His argument is that the non-recurrent endlessness of this series would prevent A from having an exclusive description, which it must have. And this it simply false.

      To sum up.

1. There is no reason to accept the Dissimilarity of the Diverse. Therefore
2. there is no reason to accept the premise that every particular must have an exclusive description.
3. Even if every particular had an exclusive description, this would not entail that every particular must have a sufficient description.