Journal of the History of Philosophy

The Unity of the Proposition LEONARD LINSKY "Es fr~igt sich hier, wie kommt der Satzverband zustande." Wittgenstein 1~ A PERSISTENTTHEME in Russell's Principles of Mathematics ~concerns the unity of the proposition. Propositions are combinations ("complexes") of their constituents , but not all complexes are propositions. For example, classes as many are combinations of their members but they are not propositions, for classes as many are just manyqthey lack the characteristic unity of propositions., Russell says, "In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole. They have, in fact, just so much unity as is required to make them many, and not enough to prevent them from remaining many."s A central concept in Russell's metaphysics of propositions in Principles is the concept of a term. For present-day readers, the term "term" will be understood to refer to words. But that is not Russell's meaning in Principles. "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 is the widest word in the philosophical vocabulary. I shall use it as synonymous with the words unit, individual, and entity .... A man, a moment, a number, a class, a relation, a chimera, or anything else that can be mentioned, is sure to be a term."4 A proposition is a unit--it is one, while the class as many is a mere combination of terms, which combination is not 0nc--not unitary, not a true unit. Of such complexes Russell says, "The combinations are combinations of terms, ' Bertrand Russell, The Prindplesof Mathematics(Cambridge: Cambridge University Press, x9o3; second edition, New York: W. W. Norton &Company, Inc., 1938). , Ibid., 68-69. Ibid., 69. 4 Ibid., 43. [~43] 244 JOURNAL OF THE HISTORY OF PHILOSOPHY 30:2 APRIL 1992 effected without the use of relations."5 What distinguishes complexes which are true unities from those which are mere aggregates lacking unity is "the use of relations." It is because every proposition contains at least one verb that it has its characteristic unity. Verbs, for Russell, in accordance with the ontologizing of grammar in Print/pies, are relations. 6 Russell is certain that the unity of the proposition is effected by relations. That is why he says that the combination of terms which is the class as many and which lacks true unity is "effected without the use of relations." Verbs, however, have a twofold nature, "as actual verb and as verbal noun."v "There is the verb in the form which it has as verb.., and there is the verbal noun indicated by the infinitive or (in English) the present participle. The distinction is that between 'Felton killed Buckingham' and 'Killing no murder' "(sic).s The difference between the verb as "actual verb" and as verbal noun is the difference between a relation as actually relating and the inert relation "in itself." Analysis reveals the difference. Consider, for example, the proposition 'A differs from B'. The constituents of this proposition, if we analyze it, appear to be only A, difference, B. Yet these constituents, thus placed side by side, do not reconstitute the proposition. The difference which occurs in the proposition actually relates A and B, whereas the difference after analysis is a notion which has no connection with A and B. It may be said that we ought, in the analysis, to mention the relations which difference has to A and B, relations which are expressed by/s andfrora when we say 'A is different from B'. These relations consist in the fact that A is referent and B relatum with respect to difference. 'A, referent, difference, relatum, B' is still merely a list of terms, not a proposition. A proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. The verb when used as a verb, embodies the unity of the proposition, and is thus distinguishable from the verb considered as a term, though I do not know how to give a clear account of the...