Originally published in A Modern Introduction to Logic (1931) by Harper Torchbooks Press: Copyright Expired. Out of Print.


by   L. Susan Stebbing
The importance of Russell's theory of incomplete symbols is that it makes us see how indirect is the reference of the sentences we use to the facts we seek to refer to in using them. It is natural to suppose that there is a one-to-one correspondence between the elements of a sentence and the constituents of some fact. Attention to such words as "the", "any", "a", dispels this illusion, but the belief that "this table", as used in "This table is brown", refers directly to a constituent of a fact persists. It was shown in Chapter IX that this belief is false; its persistence is due to the failure to realize how logically inappropriate are our ordinary linguistic expressions.
    It is difficult to give clear examples of logical constructions, for the assertion that, for example, this table is a logical construction is a metaphysical statement. To accept the statement is to accept a certain metaphysical analysis. It should, however, be possible to say what is meant by the assertion that something is a logical construction even if we then go on to deny that such a statement is ever true. I have tried to do this in Chapter IX. Here I am concerned to point out that there are good reasons for supposing that the familiar objects of daily life, including persons, are logical constructions. One of the difficulties in the way of accepting this view seems to me to be due to a misunderstanding of the expression "logical construction". There is no doubt that it is an unfortunate expression, for it certainly suggests that something is constructed, which is not the case, and that logic is adequate to the construction, which is also false. Russell's habit of using "logical fictions" as a synonym for "logical constructions" makes matters worse. The expression "logical fictions" suggests something fictitious.1 But to say that the table is a logical fiction (or construction) is not to say that the table is a fictitious, or an imaginary object; it is rather to deny that, in any ordinary sense, it is an object at all.
    I think a clearer apprehension of what is meant by "this table is a logical construction" may be gained if we consider how Russell seems to have been led to this view. It seems to me that two different lines

1 This has been a common mistake of Russell's critics, and it is a mistake to which much that Russell says lends itself. See A. O. Lovejoy, The Revolt against Dualism, p. 199. Cf. my article on "Substances, Events, and Facts'. Journal of Philosophy, June 9, 1932.


of reflexion converged to this conclusion. On the one hand, Russell was concerned to analyse general propositions; on the other, he sought to discover a simple fact, which he could regard as an indubitable datum. At first sight, the connexion between these two problems seems absurdly remote, but when it is remembered that Russell came to hold that a table is a class of appearances, the connexion seems more obvious. There is not space here to deal fully with these considerations but a few of the more important points may be noted.
    The analysis of general propositions such as Men are mortal has been given in Chapter IX. Here it is sufficient to recall that "men" as used in "men are mortal" refers to each individual man indirectly through the property of being human; hence, its significance does not depend upon acquaintance with each individual man. If the table is a class of appearances, then, in saying "This table is brown" there is a reference to each member of the class although the speaker is acquainted only with one member, namely, the appearance which is sensibly present to him, which Russell calls a 'sense-datum'. This line of reflexion leads to the conclusion that the table is not the sort of object which could be directly presented, so that the table could not be referred to demonstratively. Russell, as was pointed out in Chapter IX, seems to assume that to say that a symbol is incomplete is to say that it does not name a constituent of the proposition in whose verbal expression it occurs, so that, from the fact that the table could not be named, he would derive the conclusion that the table is a logical construction.
    The second line of reflexion arises in the search for an indubitable datum. We may, in any given case, be mistaken in believing that we are seeming a table, for we may be victims of illusions or hallucinations. But even in such cases the percipient is aware of a sensible element, and Russell maintains that with regard to the sensible element, - or, as he would say, the sense-datum - doubt is impossible.1 Sense-data are to be regarded as elements in simple facts, which Russell calls 'facts of sense'. These constitute 'hard data', i.e., data 'which resist the solvent influence of critical reflection'. Tables, persons, and the ordinary familiar things, do not resist this solvent influence. Accordingly, Russell regards the problem of the nature of the external object, e.g., the table, as primarily a problem of justifying an inference. The table, he seems to suppose, is reached by an inference; but all inferences concerning that which is not purely formal, are liable to doubt; hence, he seeks to justify the inference. At one time (viz. in 19122) Russell held that the table was known by description as "The thing having R to this sense-datum" (where 'R' stands for the converse of the relation being an appearance of.) But a description may describe nothing, and yet be significant. His next step was to apply Occam's Razor to cut out the table. His formulation of the Razor - 'Wherever possible logical con-

1 See Our Knowledge of the External World, p. 70; Outline of Philosophy, pp. 4-5.
2 See Problems of Philosophy.


structions are to be substituted for inferred entities'1 is significant in revealing his attitude. The opposition of logical constructions to inferred entities shows that he regarded the problem as essentially one of justifying a risky inference. To this is no doubt due the misleading expression "logical constructions".
    A third consideration may have led Russell to some of his misleading statements about logical constructions. He accepted Whitehead's method of extensive abstraction as a satisfactory method of constructing points. He then assumed that the same method could be used in the same way to construct tables. But in favour of the view that points are constructions reasons may be urged that are lacking in the case of tables. These reasons are the same as those which can be urged in favour of the view that "matter" is a 'convenient expression', which can be regarded as defined for the purposes of physical inquiry. The same does not hold with regard to tables. There can be no doubt that there are tables; the doubt arises with regard to the difficulty of determining what is the correct analysis of propositions in whose verbal expression 'table' occur. By failing to make these considerations clear, Russell has obscured the analysis of The table is a logical construction.
    The point to be emphasized is that every statement which would commonly be said to be a statement about The table can be transformed into a set of statements which can be jointly substituted for the original statement, but no grammatical element in the substituted set will be used with the same meaning as any grammatical element in the verbal expression of the original statement.2 An illustration may suffice to show this. We may say that a College, or the Council of a College, or a Committee, or a Nation, have acted in a certain way. Thus, for example, we may say, 'The Council have elected A as Chairman'. This statement says something about each member of the Council, but it does not say of each member that he elected A. But a set of statements could be found, jointly equivalent to the original statement, which would be each a statement about one individual member. The action of the Council is a logical construction out of a set of facts each of which is a fact about one individual member; but the action of the Council is not the sum of the actions of the members. Mr. Wisdom has pointed out that similar considerations hold with regard to the analysis of such statements as 'France fears Germany'. Such words as "fears", "acts", "are" have systematic ambiguity. Hence we must be careful not to suppose that we are saying precisely the same thing when we say that a Committee acts as we are saying when we say that a person acts.
    There are, further, different types of logical constructions. There are logical constructions out of facts about simple constituents; con-

1 Mysticism and Logic, p. 155. This essay was published first in January, 1914. 2 See J. Wisdom, 'Logical Constructions', Mind, N.S., p. 158. Mr. Wisdom's articles on this, which have not yet been completed, will be found of the utmost use to advanced students.


structions out of facts concerning these facts, and so on. This problem of types of logical constructions is intimately connected with the problem of the nature and kinds of abstraction. Much work requires to be done on this problem, but it cannot be discussed here.
    It remains to remove a common misunderstanding. It has been erroneously supposed that from the two statements I am sitting on this chair and This chair is a logical construction, it follows that I am sitting on a logical construction. The two statements are fundamentally different in logical form. The confusion is as gross as the confusion in supposing that if men are numerous and Socrates is a man, it would follow that Socrates is numerous. It cannot be necessary to argue that this conclusion does not follow. But sometimes, owing to our failure to recognize that a word is systematically ambiguous, we make mistakes which are quite as asbsurd but not so obvious.
    It must be remembered that logical constructions are not incomplete symbols. Nothing that can signficantly be said about a logical construction can be significantly said about an incomplete symbol. The first duty, and the greatest difficulty, of the philosopher is to distinguish statements that are significant from those that are meaningless or non-significant. We saw in Chapter XXIII that 'A class is not a member of itself' is meaningless. But that it is meaningless is by no means obvious. Our difficulty is to know when we are talking nonsense. The recognition of systematic ambiguity sometimes enables us to make this discovery.