The Principles of Mathematics (1903)

§ 47

Philosophy is familiar with a certain set of distinctions, all more or less equivalent: I mean, the distinctions of subject and predicate, substance and attribute, substantive and adjective, this and what[39]. I wish now to point out briefly what appears to me to be the truth concerning these cognate distinctions. The subject is important, since the issues between monism and monadism, between idealism and empiricism, and between those who maintain and those who deny that all truth is concerned with what exists, all depend, in whole or in part, upon the theory we adopt in regard to the present question. But the subject is treated here only because it is essential to any doctrine of number or of the nature of the variable. Its bearings on general philosophy, important as they are, will be left wholly out of account.(§ 47 ¶ 1)

Whatever may be an object of thought, or may occur in any true or false proposition, or can be counted as one, I call a term. This, then, is the widest word in the philosophical vocabulary. I shall use as synonymous with it the words unit, individual, and entity. The first two emphasize the fact that every term has being, i.e. is in some sense. A man, a moment, a number, a class, a relation, a chimaera, or anything else that can be mentioned, is sure to be a term; and to deny that such and such a thing is a term must always be false.(§ 47 ¶ 2)

It might perhaps be thought that a word of such extreme generality could not be of any great use. Such a view, however, owing to certain wide-spread philosophical doctrines, would be erroneous. A term is, in fact, possessed of all the properties commonly assigned to substances or substantives. Every term, to begin with, is a logical subject: it is, for example, the subject of the proposition that itself is one. Again every term is immutable and indestructible. What a term is, it is, and no change can be conceived in it which would not destroy its identity and make it another term[40]. Another mark which belongs to terms is numerical identity with themselves and numerical diversity from all other terms[41]. Numerical identity and diversity are the source of unity and plurality; and thus the admission of many terms destroys monism. And it seems undeniable that every constituent of every proposition can be counted as one, and that no proposition contains less than two constituents. Term is, therefore, a useful word, since it marks dissent from various philosophies, as well as because, in many statements, we wish to speak of any term or some term.(§ 47 ¶ 3)

§ 47 n. 1. This last pair of terms is due to Mr Bradley.

§ 47 n. 2. The notion of a term here set forth is a modification of Mr G. E. Moore's notion of a concept in his article On the Nature of Judgment, Mind, N. S. No. 30, from which notion, however, it differs in some important respects.

§ 47 n. 3. On identity, see Mr G. E. Moore's article in the Proceedings of the Aristotelian Society, 1900--1901.