Return to the matter of the unity of the proposition again. At one stage in his career, Russell was much concerned with this, and one possibility he considered was that it was the copula, ‘is’, that binds the constituents together. (So, in Fregean terms, there is just one concept, which is the copula.13) He then explains why the copula cannot be on a footing with the other constituents:14
It might be thought that ‘is’, here, is a constant constituent. But this would be a mistake: ‘x is α’ is obtained from ‘Socrates is human’, which is to be regarded as a subject-predicate proposition, and such propositions, we said, have only two constituents [Socrates and humanity]. Thus ‘is’ represents merely the way in which the constituents are put together. This cannot be a new constituent, for if it were there would have to be a new way in which it and the two other constituents are put together, and if we take this way as again a constituent, we find ourselves embarked on an infinite regress.
Russell is using an argument used earlier to great effect by Bradley.15 Again, addressing the problem of the unity of the proposition, Bradley starts by supposing that a proposition has components A and B. What constitutes them into a unity? A natural thought is that it is some relation between them, C. But, he continues:16
[we] have made no progress. The relation C has been admitted different from A and B . . . Something, however, seems to be said of this relation C, and said, again, of A and B . . . [This] would appear to be another relation, D, in which C, on one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process . . . [W]e must have recourse to a fresh relation, E, which comes between D and whatever we had before. But this must lead to another, F; and so on indefinitely. . . [The situation] either demands a new relation, and so on without end, or it leaves us where we were, entangled in difficulties.
And Bradley is, in fact, aware that this is not just a problem concerning the unity of the proposition. It is much more general. Thus, in discussing the unity of the mind, Bradley writes:17
When we ask ‘What is the composition ofMind,’ we break up that state, which comes to us as a whole, into units of feeling. But since it is clear that these units, by themselves, are not all the ‘composition’, we are forced to recognize the existence of the relations . . . If units have to exist together, they must stand in relation to one another; and, if these relations are also units, it would seem that the second class must also stand in relation to the first. If A and B are feelings, and if C their relation is another feeling, you must either suppose
13 A discussion of this view, in the context of its regress, is given in Gaskin (1995).
14 Eames and Blackwell (1973), p. 98.
15 In fact, it had been used some 600 years earlier by Jean Buridan in his Questiones in Metaphysicam Aristotelis (Bk V, q. 8). (See Normore (1985), p. 197f.) It should therefore be called the Buridan/Bradley regress.
16 Allard and Stock (1994), p. 120.
17 Allard and Stock (1994), pp. 78–9.