Herberg Hochberg

In his classic 1905 paper "On Denoting" Russell formulated a correspondence theory of truth, as well as a theory of reference and an analysis of intentional contexts that supposedly avoided (i) non-existent facts (Meinong's non-subsisting objectives), (ii) reference to fictional or non-existent objects (Hume's and Meinong's notorious golden mountain), and (iii) Fregean senses for singular terms. Shortly after that he set out the multiple relation analysis of belief to dispense with propositional entities (Fregean thoughts, Meinongian contents). This culminated in his Theory of Knowledge manuscript of 1913. The literary items directly bearing on Wittgenstein's rejection of both Russell's 1913 account of logical form and his use of it to analyze intentional contexts are quite well known - the letter from Wittgenstein to Russell, those from Russell to Ottoline Morrell in 1913-1916, Wittgenstein's entries in his notebooks, the "Notes on Logic" given to Russell in September 1913, and the passages in the Tractatus .¹ However, neither these documents nor Russell's analysis, nor his reasons for abandoning the later sections of his 1913 manuscript, are clear, in spite of recent commentaries by David Pears

^* From Theoria, LXIII, 1, 2000. pp. 3-40. Professor Hochberg has recently published a detailed examination of the philosophy of Gustav Bergmann: The Positivist and the Ontologist: Bergmann, Carnap and Logical Realism. Rodopi Press. 2001.
¹ In the letter to Russell, Wittgenstein wrote "...I can now express my objection to your theory of judgement exactly: I believe it is obvious that from the proposition "A judges that (say) a is in a relation R to b", if correctly analyzed, the proposition "aRb .v. ¬aRb" must follow directly without the use of any other premiss. This condition is not fulfilled by your theory." L. Wittgenstein, Notebooks: 1914-16, trans. G. Anscombe (New York: 1969), 121. The corresponding passage in the Tractatus is 5.5422, and the most detailed exposition of the point occurs in the "Notes on Logic" printed as an appendix to the Notebooks, 96.

and others.² In the earlier versions of his multiple relation theory of judgment, which focused on atomic contexts like (1) 'Ottoline understands that Wittgenstein is mad' and (2) 'Ottoline believes that Wittgenstein likes Russell', Russell did not take logical forms as constituents of judgment facts. To avoid propositional entities,

² I speak of his abandoning the later sections of the manuscript since he published what are commonly assumed to be the missing first six chapters as papers in 1914 and 1915 in The Monist. The commentaries we shall consider are D. Pears, "Russell's 1913 Theory of Knowledge Manuscript," Rereading Russell: Essays on Bertrand Russell's Metaphysics and Epistemology, ed. C. W. Savage and C. A. Anderson, Minnesota Studies in the Philosophy of Science, v. 12 (Minneapolis: 1989), 169-182; and G. Landini "A New Interpretation of Russell's Multiple Relation Theory of Judgment," History and Philosophy of Logic, 12 (1991), 37-69. I do not bother with N. Griffin's pretentious, inadequate, and verbose treatments of Russell in various works, including Russell's Idealist Apprenticeship (Oxford: 1991). In the book he notes that the foundationalism of "Russell, Moore, Ayer, and the positivists" while "played out" nevertheless allowed Russell to achieve results that "though definitely mistaken, were not misguided by the standards of the time" (40), and, chastizing Russell, Griffin amusingly, if arrogantly, denies the antecedent: "Moreover, if Russell really has shown what he says he has shown, that the Euclidean axioms are independent of the general functions of space and time...then he has shown that the Euclidean axioms are not a priori. For a geometrical proposition is a priori if it is necessary for (a certain type of) experience, and it is necessary (for a certain type of experience) if it is true of any intuition which fulfils the 'general philosophical functions' of space. The Euclidean axioms are false of some such intuitions, and therefore are not a priori. The fact that Russell did not avail himself of this argument suggests that he was no longer confident that he had exhaustively specified the general functions of space and time." (174) More likely Russell did not "avail himself" of Griffin's argument since he would have recognized it for what it is. For further comments on Griffin's Russell scholarship see my review of his book in Canadian Philosophical Reviews, April, 1992.

Meinongian objectives and content properties of mental acts, he construed such judgment facts as involving a relation between a subject, Ottoline, and the objects of the judgment, Wittgenstein and the property of being mad in the one case; Wittgenstein, the relation likes, and Russell in the other.
Assume that Russell and Ottoline are both thinking that Wittgenstein is mad. In an unproblematic sense, one may say that there is something that they have in common or that they have a common characteristic. Propositions, mental contents, objectives and intentional attributes have been invoked by various philosophers to account for what is involved in our unproblematically speaking of there being something in common, irrespective of whether what they think is true. On one view two persons are taken to be related to a proposition or to an "objective", and the common property is then construed in terms of their standing in the same relation to the same "thing". Variants of such views are commonly attributed to Frege and Meinong and can be read into Carnap's early work on semantics. On another view the two persons are taken to have or exemplify a basic intentional attribute or mental content in virtue of which they have the same thought. Such a view, appealing to content properties, rather than propositional entities, is also attributed to Meinong and was implicitly held by Moore in Some Main Problems of Philosophy. It is also, if not clearly, found in J. Searle's writings on intentionality. Such content properties, in turn, are sometimes taken to refer to facts (Moore) or be intrinsically connected to conditions of satisfaction (Searle).³

³ On Searle and Moore see "On Nonsense on Reference," in H. Hochberg, Russell, Moore, and Wittgenstein: The Revival of Realism (Frankfurt: 2001). For Russell's concern with mental

On a correspondence account of truth, which Russell held, propositions or contents (content properties) require a connection to a fact whose existence grounds their truth. Transcribing the statement 'Ottoline judges that Wittgenstein is mad' by 'J(o, M, w)', Russell took Ottoline's judging that Wittgenstein is mad to be a fact linked to the purported fact that is its truth maker, Wittgenstein's being mad, since Wittgenstein and being mad are constituents of both the judgment fact, as truth bearer, and the purported fact that is its truth maker. Every constituent of the latter is also a constituent of the former. Russell's propositional functions enabled him to handle non-atomic contexts. Consider 'Ottoline judges that something is F' and 'Ottoline judges that a is not F'. They are easily transcribed by 'J(o, ($y)fy, F)' and 'J(o, ¬Fy, a)', respectively, with '($y)fy' and '¬Fy' as signs for Russellian propositional functions.⁴
In the 1913 manuscript Russell introduced logical forms as further constituents of multiple relation facts with contents that involved a relation:

acts, along lines obviously influenced by Moore, see B. A. W. Russell, The Problems of Philosophy, (London:1956), 41-42, 99.
⁴ Russell considered non-atomic judgments in Principia, but there he was not concerned with the analysis of the judgment facts, but their contents. Thus he spoke of the judgment "all men are mortal" and "any judgment (x).f x" (not of the judgment facts) and was concerned to point out that such judgments did not correspond to one complex but to complexes as "numerous as the possible values of x." A. N. Whitehead and B. A. W. Russell, Principia Mathematica, v. 1, 2^nded., (Cambridge: 1950), 46. His basic concern in Principia was with the different "types" of truth involved in various kinds of judgment in connection with his consideration of the liar paradox.

Thus, if we call the subject S, and the relating relation (of which "understanding" is the one presupposed by all the others) U, and the objects x, R, y (taking the case of a proposition asserting a dual relation for the sake of illustration), and g the form of dual complexes, the total complex which occurs when the subject has the relation U to the objects in question may be symbolized by

U(S, x, R, y, g).⁵

Such a form is needed since, in order to understand "A and B are similar", we must be acquainted with "the general form of symmetrical dual complexes."⁶ And, more is required:

But these separate acquaintances, even if they all coexist in one momentary experience, do not constitute the understanding of one proposition "A and B are similar", which obviously brings the three constituents and the form into relation with each other, so that all become parts of one complex. It is this comprehensive relation which is the essential thing about the understanding of a proposition. Our problem is, therefore, to discover the nature of this comprehensive relation.⁷

⁵ B. A. W. Russell, Theory of Knowledge, the Collected Papers of Bertrand Russell, v. 7 (London: 1984), 115.
⁶ Russell, 1984, 112.
⁷ Russell, 1984, 112.

Thus, while the form plays a unifying role for some terms, since it is the form of the complex which will exist if the proposition is true, something is needed "so that all become part of one complex" in the "understanding of a proposition." That is, something is needed to unify the constituents in the judgement itself. A problem is posed by taking the understanding relation to unite the objects that provide the content. For such a relation does not merely relate the objects A, B, similarity, and the form of dual relations, but combines them along with the understanding subject into a complex - a judgment or understanding fact. This is the problem Wittgenstein would find in Russell's new solution of the problem. For Wittgenstein the inclusion of the form did not provide a basis for the understanding relation to unify or "synthesize" the appropriate constituents, those other than the judging subject. But Russell seems to have been aware of the need to do something further prior to Wittgenstein's raising the issue. For immediately after raising the problem himself, Russell asks several questions, the second is:

(2) Can we, by bringing in the "form" or in any other way, make the "proposition" an entity, i.e. not a mere incomplete symbol, but something which can subsist on its own account, and not only as a fictitious constituent of certain mental complexes? ⁸

The question is striking since one of the motives for introducing the multiple relation theory was to avoid

⁸ Russell, 1984, 113.

appealing to propositions to supply the content for judgments. ⁹ This points to an odd feature of the 1913 manuscript. In the opening chapters, assuming with the editors, as is generally done, that the first six chapters of Part I, which were published in The Monist, are the missing chapters not found with the manuscript, he rejects propositions as he had in other works of the period. Even in the early part of the manuscript proper (as found among his papers), Chapter I of Part II, prior to raising the question, he rejects propositions for a similar reason:

And this in turn, since it is repugnant to admit the reality of false propositions, forces us to seek a theory which shall regard true and false propositions as alike unreal, i.e. as incomplete symbols. ¹⁰

But, in answering the question about subsistent propositions he surprisingly writes:

(2). Can we give a definition of a "proposition" which neither brings in anything

⁹ Russell still recognized propositional entities in 1905 in "On Denoting." I believe that this is clear from the fact that the scope differences he employs there for different readings of 'George IV wished to know whether Scott was the author of Waverley' require a proposition (a sentence as a linguistic subject) as a term of the intentional verb 'wished to know whether'.
¹⁰Russell, 1984, 109. Earlier, 25, he says: "But for reasons which I have set forth elsewhere, it would appear (1) that no reality is a proposition...(3) that the unreal is simply nothing..." This passage belongs to one of the articles printed in The Monist, while some passages quoted above and the present passage both occur later in Part II, Chapter I.

mental nor makes the proposition an incomplete symbol? At an earlier stage, we provisionally decided this question in the negative, but it is now time to reconsider it. It is to be borne in mind throughout the discussion that false propositions must be allowed for as well as true ones.
We arrived at the proposition, in the first place, as something which a number of mental events have in common. If two men judge that A and B are similar, or if one man makes this judgment on two occasions, it is obvious that the difference between the two events is only on the subjective side, and that on the objective side there is a similarity consisting not only in the fact that the same objects are concerned, but also in the fact that the different judgments bring the objects into the same relation to each other. The objective side, it would seem, remains unchanged if a person doubts or desires or wills that A and B are similar. In the former case, of two judgments, we changed only the subject, not the relation of the subject to the objects, while in this case we change also the relation of the subject to the objects; but when we abstract from both the subject and from its relation to the objects, what remains seems to be exactly the same in the case of doubt or desire or will as in the case of judgment. It is this common element that we call the "proposition", and wish, if possible to isolate from its subjective context. ... the total complex

which occurs when the subject has the relation U to the objects in question may be symbolized by

U(S, x, R, y, g).
If we now proceed to the "form" which results from varying U and S, i.e. to

"there is a U and an S such that U(S, x, R, y, g)"
we arrive at something which is the same for all subjects and for all propositional relations which we should regard as concerned with the same proposition. Thus there is no formal obstacle to defining this as the proposition.¹¹

The proposition, "defined" as the "form" which "results" from abstracting or generalizing, is thus represented by an existentially quantified sentence, with quantifiers expressed in English, and with (bound) variables replacing the attitudinal verb and the sign representing the person having the attitude. This fits with Russell's considering logical forms, such as the form of a dual relation (something has some relation to something), to be existentially general facts, a matter we shall explore later in considering Pears' discussion of the 1913 manuscript. The main point is that Russell reintroduces propositions as forms or existential facts (but not as logical forms) for two reasons. First, as we noted, the need to "unify" the terms in the "content" of the judgment. Second, as we will

¹¹ Russell, 1984, 114-115. The use of the numeral '2' shows he is responding to the question of that number. Russell uses the letters 'x', 'R', and 'y' in the manuscript as both variables and indefinite constants.

later see, he takes propositions and not judgment facts to be the basic bearers of truth and falsity.
While reintroducing propositions as forms, and hence as abstracted from and dependent on judgment facts of which they are the forms, rather than as traditional Fregean thoughts or propositional entities that are independent of judgment (belief, understanding) facts, Russell recognized an obvious problem with his taking such forms (propositions) to be existentially general facts.

The above definition has some merits and some demerits. Its chief merit is that it provides propositions, both true and false, as fast as we can think of them, and that it gives something in common between all the mental events which seem to be concerned with the same proposition. Its chief demerit is that we cannot be sure that there are propositions in all cases in which logic would seem to need them. It is not necessary to our definition that there should actually be a subject which has one of the familiar mental relations to the objects, but it is necessary that there should be some term and some relation by which a complex results having the requisite form and containing the objects in question. It may be possible to prove that there always are such complexes, but I do not at present see how such a proof could be found. In its absence, we cannot know of the existence of propositions other than those that have been actually thought of. ...we must admit, I think, that the objection in question is serious. I cannot, however, think of anything better

10
calculated to fulfill the purposes for which we want propositions, and I therefore propose to continue to use the word in the above sense. ¹²

In thus concluding his answer to the question about the subsistence of propositions, Russell clearly seems not to take the objection as decisive. If it were, it would also be a decisive objection to his construal of logical forms as existentially general facts. His taking existential generalizations that contain constant terms to represent forms must be distinguished from his taking existentially general sentences like 'something has some property' and 'something has some relation to something' to represent pure or logical forms - the forms of monadic exemplification (monadic atomic facts) and dual relation (dyadic atomic facts). Yet his taking propositions to be existential facts (forms) probably stems from his taking logical forms to be existentially general facts, and non-logical forms, like logical forms, are common features of facts. A logical form, like that of dual complexes, is common to every fact of that form, and a proposition, obtained by abstraction, is common to intentional facts with the same content. A logical form is taken to be a fact since:

¹² Russell, 1984, 115-116. Russell's objection to his definition reveals a concern about the identification of logical forms with existentially general logical facts, since that requires that there be instances of relations for there to be logical forms. Thus there must be an exemplified n-term relation for each n-term relational form. This consequence might have provoked Wittgenstein's remarks from 5.55 thru 5.5571 in the Tractatus regarding the possible forms of elementary propositions.

We require of the form that there shall be one form and only one, for every group of complexes which "have the same form"; also, if possible, it would be convenient to take as the form something which is not a mere incomplete symbol. We may secure these desiderata by taking as the form the fact that there are entities that make up complexes having the form in question.¹³

While recognizing propositions as forms, he does not take them to be constituents or terms of judgment facts and does not construe the latter in terms of a dyadic relation between a person and a proposition. Such judgment facts are still construed in terms of a multiple relation, but logical forms are now terms of judgment complexes, like J(o, A, B, similarity, R(x,y)), that serve to unify some of the other terms.¹⁴ Propositions, like (($U)($S)U(S, A, B, similarity, R(x,y)), do not, and, on his multiple relation analysis of judgment, cannot play the traditional role of propositions or Fregean thoughts. J is not a dyadic relation between o and that proposition.
If we think of the proposition as a Principia type propositional function, then with J and o as arguments, J(o, A, B, similarity, R(x,y)) can be taken as the value of the function for such arguments. The relevant sign for the proposition would be a function sign with free variables - i.e. 'U(S, A, B, similarity, R(x,y))' with 'U' and 'S' as free variables.¹⁵ Like the form construed as an existential

¹³ Russell, 1984, 114.
¹⁴ Russell, 1984, 117.
¹⁵ In the Principia notation one would here use circumflexes over the free variables to distinguish the function sign

fact, such a function is not a constituent of the judging complex, and the sign for it does not occur in the sentence obtained by replacing the variables with constants, like 'o' and 'J'. Either with free or bound variables, the sign for the proposition thus resembles a definite description in that it neither stands for a constituent of the judgment complex nor occurs in the analysis of 'o judges that A is similar to B'. As in the case of a definite description, the embedded sentence disappears when contexts like 'o judges that A is similar to B' are analyzed, which suggests that the existence of the represented proposition is somewhat tenuous. In Russell's terminology, the sign is like an "incomplete symbol."¹⁶ Forms, taken as facts, can be seen to play the role of functions. Consider ($R)($x)($y)R(x,y) as the form of dual relations, and hence as the form of the fact expressed by 'similar(A,B)'. As the first is obtained by abstracting (generalizing) from the second, so, by reversing the process, the second can be seen as obtained by "instantiating" or "specifying" the first. This suggests how Russell's accepting propositions fits with his multiple relation theory, since a sentence representing a particular judgment fact is obtained by so "specifying" the variables 'U' and 'S' in '($U)($S)U(S, A, B, similarity, R(x,y))'.¹⁷

from the open sentence. But as the notation is not necessary and as Russell does not use it in the manuscript, I simply use free variables.
¹⁶I will follow Russell's tendency to speak of both signs and purported entities they represent as incomplete symbols. In passages where Russell rejects propositional entities he characteristically speaks of them as incomplete symbols.
¹⁷ We will later see further reasons for his taking logical forms like ($f) ($y) fy to be facts rather than functions, in particular his taking them as terms of a dyadic relation of acquaintance and as truth grounds for logical truths.

Thus such a judgment fact is the value or instance of the form for arguments like o and J.
Later in the manuscript Russell reiterates his objections to recognizing propositions and especially to Meinong's views. But his arguments show that he does not reject propositions taken as the existential facts or forms he accepted earlier in the manuscript. He argues, first, that one need not take atomic propositions as constituent terms in the analysis of molecular propositions.¹⁸ This is just stated, as he proposes to deal with molecular propositions in a later part of the manuscript that was not written. In any case, it does not bear on the acceptance of propositions as forms of facts. Second, he reiterates his argument against objective falsehoods. "Again, it is very difficult to believe that there are objective falsehoods, which would subsist and form part of the universe even if there were no such thing as thought or mind."¹⁹ But, propositions as forms require that there be minds as constituents of intentional facts (thoughts, judgments, etc.), since propositions are forms abstracted from such facts. That is precisely what he took to be the chief "demerit" of his earlier definition of propositions "...we cannot know of the existence of propositions other than those that have been actually thought of."²⁰ Finally, he argues:

¹⁸ Russell, 1984, 153. One must keep in mind the diverse uses of the term 'proposition', by Russell and others - as a synonym for 'statement', as a term indicating what is expressed by a sentence or statement, and as a somewhat neutral term, where it may be the one or the other.
¹⁹ Russell, 1984, 153.
²⁰ Russell, 1984, 116. Accepting propositions under such a condition is like accepting only instantiated universals, a familiar form of realism about universals.

But the chief objection is that the difference between truth and falsehood, on the theory in question, has to be accepted as ultimate and unanalyzable, whereas it seems obvious that the difference between truth and falsehood must be explicable by reference to fact, i.e., to what is actually in the universe whatever we may see fit to believe.²¹

He seeks a theory which

...dispenses with objective falsehoods. And to me, now, it seems obvious, as a matter of inspection, that belief is a multiple relation, not a dual relation, so that belief does not involve a single object called a "proposition."²²

Thus he rejects propositions as entities used in a theory of truth that is an alternative to a correspondence theory and as terms of a supposed dyadic relation in an analysis of sentences expressing intentional facts. But his taking propositions to be existential forms or facts involves neither such an alternative theory of truth nor taking them as terms of dyadic intentional relations. Thus, Russell's accepting propositions as existential facts is compatible

²¹ Russell, 1984, 153.
²² Russell, 1984, 153. In some cases of understanding, the intentional relation is a dual relation, as, for example, in the understanding of a logical form like "something has some relation to something." (Russell, 1984, 131.) But the second term is a logical form and not a proposition taken as an existential fact or form with constituents.

with his arguments against propositions in this part of the manuscript, with one apparent exception: accepting forms that are falsehoods. Yet, such falsehoods, as we noted, are not independent of minds and thoughts, and it is such independence that Russell really objects to. This is clear from the fact that even on the earlier form of the multiple relation theory he recognized belief facts, which replaced propositions, as objective falsehoods. In 1913 he says: "A false belief or a false statement is an entity...".²³ But propositions, as forms, are not taken to be independent of minds and thoughts in 1913, and, as we will see, such propositions become the basic bearers of truth and falsity for him.
Russell's treatment of logical forms suggests a reason he took propositions as existential facts rather than as propositional functions:

If we take some particular dual complex xRy, this has three constituents, x, R, y. If we now consider "something has the relation R to y", we get a fact which no longer contains x, and has not substituted any other entity for x, since "something" is nothing. Thus our new fact contains only R and y. For similar reasons, "something has the relation R to something" contains no constituent except R; and "something has some relation to something" contains no constituent at

²³ Russell, 1984, 109. He goes on to consider the grounds of such falsehood and its bearing on propositional entities, which we will take up below.

all. It is therefore suitable to serve as the "form" of dual complexes.²⁴

This shows that Russell does not take a logical form to be a constituent of the fact of which it is the form, since x, R, and y are the only constituents, which he would later explicitly say in the 1917 logical atomism essays. It also shows that existential forms that are not completely generalized have constituents and that signs for logical forms are arrived at by existential generalization. This suggests a reason for taking propositions to be forms or existential facts. Consider the judgment fact expressed by 'J (o, F, a, ($f)($y)fy)'. We arrive at '($ƒ)($x) ($f) ($S) ($U) U(S, f, x, ƒ)', representing the logical form of such a judgment fact, by successive existential generalizations, with 'ƒ' as a variable for logical forms. A logical form is such a completely generalized fact. By only partially abstracting, we arrive at '($S)($U) U(S, F, a, ($f)($y)fy)'. This suggests that a partially abstract existential generalization is also a common form, although not a logical form, of all intentional facts from which it can be obtained, since it is also arrived at by abstraction. Logical forms, being completely generalized, do not have constituents; "...if a logical form i.e. a fact containing no constants..."²⁵ But ($U)($S) U(S, F, a, ($f) ($y)fy) is not a pure or logical form, it is a proposition or existential fact with constituents.

²⁴ Russell, 1984, 114.
²⁵ Russell, 1984, 131.

A given proposition will be the fact (if it is a fact) of there being a complex of the form of an understanding, where the objects are given, but the subject and the relating relation are arbitrary.²⁶

Such a fact has constituents, the given "objects," since the relevant existential sentence has constants, unlike signs like '($f)($y)(fy)'. One may then ask what distinguishes the proposition that a is F - ($U)($S) U(S, F, a, ($f) ($y)fy) - from the atomic fact that a is F. On Russell's view two things distinguish the proposition from the atomic fact that is its truth maker. The form ($f)($y)fy is a constituent of the proposition (existential fact), but not of the fact that a is F. It is the form of the latter fact, but not a constituent of it. Russell, as we noted earlier, does not take the form of a fact to be a constituent of it. This points to a second difference: the form of the one fact is different from the form of the other.

Russell might have taken propositions in another way. Consider the class of all judgment facts containing F, a, and ($f)($y)fy, i.e. the class that is the "value range" of that function. Such a class may also be taken as a replacement for the classical

²⁶ Russell, 1984, 177. Note that the form (proposition, fact) - ($U)($S)U(S, F, a, ($f)($y)fy) - will itself be of the form ($ƒ)($x)($f)($U)($S)U(S, f, x, ƒ), which is the form "of an understanding" - for example, of the understanding fact,J(o, F, a, ($f)($y)fy). Russell also writes as if such a proposition would have the form of something having some property, determined by the form of its truth maker or content. Since it is a judgment that a is F, what is judged is of the form of something having some property.

proposition and, hence, as the subject of ascriptions of truth and falsity. Thus, if a is F, the class (or function) is true, since every judgment fact that is a member of the class, or value of the function, is a true judgment fact. Such a class, as well as such a function, may be taken to represent the fact that a is F, and since classes are not entities, on Russell's "no class" theory of this period, identifying propositions with such classes would be another way of avoiding propositions as entities.²⁷ But this would not fit with his holding that propositions, not judgment facts, are the basic bearers of truth and falsity.
Just as Russell attempted to avoid Fregean propositional entities and attitudinal relations as dyadic relations relating persons to such entities, he also sought to avoid a basic correspondence relation connecting a judgment fact with the fact that is its truth maker. The link between the two facts is furnished by the logical form of the latter being a constituent of the judgment fact and by their having common constituents. It is as if he recognizes a function that correlates the one fact, the judgment fact, as argument, to the other, its truth maker, as value. Thus one can see a further point to introducing

²⁷ Russell considers appealing to classes in the case of logical forms like ($f)($y)fy but remarks: "...we might of course define the form of a complex as the class of all complexes having the same form. Or, if we wish to avoid classes in so fundamental a question, we can say .... It is, however, obvious that such an explanation will land us in endless regress....the form must be something exceedingly simple." (Russell, 1984, 113-114.) For simplicity, I will follow Russell and sometimes use open sentences, rather than existential quantifications, as signs for logical forms and propositions. This will only be done in contexts where the difference is irrelevant or where there is no ambiguity.

propositions, as existential facts or forms, since the value for such a function is arrived at by ignoring the judging subject and the relation J. But so linking the facts raises a problem posed by non-symmetrical relations.
In the case of the judgment fact J(o, L, w, r), Russell could not, on the basis of common constituents, correlate the judgment with the fact L(w,r) rather than with the fact L(r,w). He had earlier used the order in the expression 'J(o, L, w, r)' to not only express that Ottoline was doing the judging but that she was judging that w stands in L to r. Just prior to 1913, Russell wrote:

The relation 'loving', as it occurs in the act of believing, is one of the objects - it is a brick in the structure, not the cement. The cement is the relation 'believing'. When the belief is true, there is another complex unity, in which the relation which was one of the objects of the belief relates the other objects. Thus, e.g., if Othello believes truly that Desdemona loves Cassio, then there is a complex unity, 'Desdemona's love for Cassio', which is composed exclusively of the objects of the belief, in the same order as they had in the belief, with the relation which was one of the objects occurring now as the cement that binds together the other objects of the belief. On the other hand, when a belief is false, there is no such complex unity....²⁸

²⁸ Russell, 1956, 128.

Thus Russell took the order of the constituents in the belief fact to indicate the order necessary to specify the content of the belief, and hence to determine the fact that is its truth maker, as well as to indicate which term of the belief fact was the judging subject. Recognizing that he was appealing to the order of the constituents in facts to correlate judgment facts with their truth makers, he came to believe that he must account for that order. Russell took the difference between atomic facts that were monadic or involved a symmetrical relation, and hence did not involve order, and ordered facts involving a non-symmetric relation to be based on their different logical forms and different types of constituents. Order is involved in a fact like L(w, r) since it is of the form of a dual relation and contains two constituents of the same logical kind as well as a non-symmetric relation. These considerations led him to analyze order in facts and to modify his theory in 1913 in a far more significant way than his introducing logical forms as constituents of intentional facts and his taking propositions as existentially general forms or facts.
Wittgenstein in asserting that a viable analysis of intentional contexts must prevent judging nonsense, pointed out that Russell presupposes that the signs that replace the free variables 'f' and 'y' in 'J(o, f, y, ($ f)($y)fy)' must be such that they combine into a meaningful sentence. Russell's analysis is then supposedly misleading, for, on it, one simply rewrites 'J(o, Fa)' as 'J(o, F, a, ($f)($y)fy)'. Thus Russell has not really eliminated sentences as terms for the predicate 'J' and thus implicitly acknowledges propositional entities as terms of the relation

J. This points to another problem with Russell's theory. We noted earlier that Russell takes a judgment fact (or a proposition) to determine the fact that is its truth maker in virtue of the constituents of the judgment fact (other than the intentional relation and the intending subject) being the constituents and form of its truth maker. But to transcribe 'J(o, F, a, ($f)($y)fy)' as 'Ottoline judges that a is F' requires one to interpret the sign pattern 'Fa', as well as 'F' and 'a'. We must apparently appeal to a futher "semantical rule" for interpreting sentences in order to take 'Fa' to be used to ascribe the property F to the object a. This is a variant of the point that a sentence is not a class of its constituent terms. Adding the form of monadic predication, ($f)($y)fy, to the members of the class {F, a}, to form the class {F, a, ($f)($y)fy}, does not yield a complex consisting of F and a standing in the form ($f)($y)fy, just as adding the sign '($f)($y)fy' to the class of signs 'F' and 'a' does not form a sentence. Russell, as Wittgenstein saw it, mistakenly assumes that by adding the form ($f)($y)fy to the judgment fact he coordinates the judgment fact, J(o, F, a, ($f)($y)fy) to its purported truth maker, the fact Fa.
Assume we have coordinated the names and predicates to objects, monadic properties, and non-symmetric relations. We must still have interpretation rules for sentences. Suppose we follow Carnap's 1942 uniform use of 'designates', for names, predicates and atomic sentences, as follows: (1) 'a' designates the city of Chicago; (2) 'F' designates the property of being large; (3) 'Fa' designates the state of

affairs of Chicago being large.²⁹ Carnap takes (1)-(3) as semantical rules for a schema.³⁰ But that raises two questions. Does the term 'designates' represent a relation that atomic sentences stand in (or an interpretation function for such sentences), as 'designates' (refers to) represents a relation (or interpretation function) that connects names and predicates to objects and properties? If so, what is the other term of the relation (value for the function) that is correlated with an atomic sentence when the sentence is false?
It is often overlooked that in 1905 in "On Denoting" Russell took his theory of descriptions to provide a way of linking an atomic sentence to its purported truth maker without thereby acknowledging a Meinongian non-existent (non-subsistent) objective in the case of false sentences. Definite descriptions of purported facts supposedly avoided a basic reference relation (function) for sentences and, along with it, the problem posed by false atomic sentences (propositions) as terms (arguments) of such a relation (function): "Thus out of any proposition we can make a

²⁹ R. Carnap, Introduction to Semantics (Chicago: 1959), 24, 50-52 and R. Carnap, "Hall and Bergmann on Semantics," Mind, liv, 214, 1945, 148 ff. Carnap sometimes uses 'proposition' in a version of (3), where that term is understood as "that which is expressed...represented, designated...by a (declarative) sentence... Other terms...'Objectiv' (A. Meinong), 'state of affairs' (Wittgenstein), 'condition'." Carnap, 1959, 235. This use is clearly distinguished from the sense in which a proposition is a sentence; but he also speaks of propositions in a third sense, not clearly distinguished from states of affairs, as designata of sentences that are truth bearers, rather than truth makers. Carnap, 1959, 88.

³⁰ As he treats such rules as conventions that define 'designates' for a semantical system, Carnap never addresses the problem posed by a designation relation, Carnap, 1959, 25.

denoting phrase, which denotes an entity if the proposition is true, but does not denote an entity if the proposition is false."³¹ He simply gave a definite description of a fact; the existence of the fact provided the required truth maker.³² Using definite descriptions in such a way, he did not have to employ a basic relation (refers to, corresponds to, designates) between atomic sentences and their purported truth grounds, in the manner in which Carnap apparently employed such a designation relation in 1942. In 1913, as in 1905, Russell sought to avoid both such a relation between truth bearers and truth makers and the nonexistent facts that such a relation seems to involve.³³ For monadic and symmetric relational contexts he takes certain constituents of an intentional fact to determine its truth maker and seeks to avoid non-existent facts by "defining" such an interpretation function in terms of a relation (consists of) between complexes and their constituents by implicitly using definite descriptions of such complexes. For non-symmetric relational contexts he will explicitly use

³¹ B. Russell, "On Denoting," reprinted in Logic and Knowledge, ed. R. Marsh, (New York: 1971), 48.
³² For his concern with the problem in 1912, see Russell, 1956, 124. Moore employed such a relation (refers to) in his 1910-1911 lectures that became Some Main Problems of Philosophy.
³³ While the 1913 theory does not embrace classical propositional entities, since it is not a person's relation to a propositional entity that is the truth ground for a claim that the person makes a certain judgment, Russell's identification of propositions with forms does appeal to a common feature of the members of a class of intentional facts, and such forms are the basic bearers of truth and falsity. Moreover, as we shall see, such propositions contain only the constituents of intentional facts that are relevant to determining their truth makers. By contrast, a judgment fact like J(o, F, a, fy) contains the extraneous J and o.

definite descriptions of truth makers to state truth conditions, as he did in 1905.
One of the misleading features of Russell's analysis that disguises the need to coordinate truth bearers to truth makers is that a representing complex, whether a particular intentional fact or a proposition, contains all the constituents of the represented complex. In the case of a sentence (or traditional mental content) the representing complex does not share constituents with the represented complex. Since it is easy to overlook the fact that a and F, as they occur in a representing complex, say J(o, F, a, ($f)($y)fy), represent themselves, as they occur in the fact that a is F, one can easily overlook the need to connect the two complexes. Wittgenstein's criticism can be taken to point to the need to connect the representing complex to the represented complex, as well as to Russell's taking the relation J to order the terms of the judgment complex and, by so ordering them, to indicate that F functions as an attribute, and not just as a term of a relation. While contexts like 'J(S, f, y, ƒ)' do not differ from contexts like 'L(x,y)', in that only a certain kind of sign can replace a certain kind of variable, in the former case the connection of the term in the "f-place" to the term in the "y-place" in accordance with the expression in the "ƒ-place" is built into the reading of 'J' and the understanding of the form of the judgment fact. Initially Russell saw no problem with this in view of the logical differences between ($f)($y)fy, F, and a that permitted only one type of combination. But the point Wittgenstein makes is that this presupposes rules of combination that Russell does not explicitely set forth or ground, and this raises a question

about the significance of such rules. Russell will note this in his logical atomism lectures, where he thinks it problematic that belief facts have "two verbs."
In the Tractatus and the Notebooks Wittgenstein appealed to the internal or logical properties of the constituents of atomic sentences and of "thoughts" to connect atomic sentences and thoughts to their correlated situations or possibilities. Supposedly such logical properties were themselves correlated with (or identified with) internal-logical properties of the constituents of such possibilities. The possibilities of combination of the elements in the representing combinations were taken to represent the possible states of affairs determined by the nature or essential properties of constituents. Wittgenstein seems to have thought that by having the possibilities of combination be determined by such logical properties of the combining elements, he avoided recognizing possible facts as entities. For one supposedly did not have to take one combination to represent another over and above the representative roles played by the constituents of the complexes. The object a could be said to have the essential property of possibly being F, instead of being an element of a possible state of affairs, a's being F. But, it is clear that the correlation of constituents still does not suffice to correlate the complexes of which they are constituents, unless it is a logical property of a constituent of a thought or sentence that it not only can combine with another constituent of a certain kind but that the resulting combination represents a state of affairs. It is then gratuitous to claim that correlating constituents suffices to correlate complexes, though the correlation of the complexes depends upon the correlation of their respective

constituents. Wittgenstein's alternative to Russell's analysis of intentional contexts thus suffers from the very problem Pears takes him to have raised against Russell.³⁴ Moreover, Russell's analysis is compatible with assuming that there are such logical properties, for, in effect, he takes such logical differences to determine the place an entity can occupy in a judgment fact.
In taking a fact like J(o, F, a, ($f)($y)fy) or the relevant proposition, ($U) ($S) U(S, F, a, ($f)($y)fy) to represent the fact that a is F, Russell gives intentional relations like J a two-fold role, quite unlike normal relations.³⁵ First, J combines terms like o, a, F, and ($f)($y)fy into a judgment fact. Second, such a fact is the particular judgment fact that it is because it is taken to represent another fact, which is composed of some of the terms standing in J. This second role amounts to taking the

³⁴ Pears, 1989, 174, 180. When Russell adopts Wittgenstein's Tractatarian analysis, as he interprets it in appendix C to the second edition of Principia, he faces exactly the same problem. For he takes the coordination of the elements of a thought to the elements of a fact to suffice for taking the one complex to represent the other. Whitehead and Russell, 1950, 662.
³⁵ Russell clearly recognized the problem in 1913, as well as in the later logical atomism lectures, when he writes:

Thus a first symbol for the complex will be
U(S, A, B, similarity, R(x,y)). This symbol, however, by no means exhausts the analysis of the form of the understanding-complex. There are many kinds of five-term complexes, and we have to decide what the kind is. It is obvious, in the first place, that S is related to the four other terms in a way different from that in which any of the four other terms are related to each other. Russell, 1984, 117.

judgment's meaning or content to be determined by some of its constituent objects and their arrangement in the judgment fact. It is relevant that Russell recognized a problem with his claiming that the meanings of constituent signs determine the meaning of a complex sign in such cases:

There are, however, certain problems remaining. There are purely logical problems, such as: How is the meaning of a complex name such as "aRb" determined when the meanings of the simple constituent names are known? What is meant by "a is part of aRb"? What is meant by "aRb consists of a and R and b united in the general form of a dual complex"?.... These questions, important as they are, I shall not now discuss. Partly they do not belong to the theory of knowledge, partly they belong to a later portion of the subject, partly, wherever they belong, I do not know the answer to them.³⁶

Russell will seek to resolve the problem of meaning for contexts involving monadic properties and symmetrical relations by using existential claims (implicit definite descriptions) to link a judgment fact (or proposition) to a truth maker. By thus avoiding a basic correspondence relation or interpretation function, connecting truth bearers to truth makers, he seeks to avoid representing non-existent facts.

He then draws a diagram showing how the various relations involved are connected to their terms. Russell, 1984, 118.
³⁶ Russell, 1984, 128.

Wittgenstein's logical or internal properties add nothing to Russell's analysis, even though, as noted above, Russell's view is compatible with such properties. That is why only logically proper types of signs can be substituted for the appropriate variables in contexts like 'J(o, f, y, ($f)($y)fy)'. Such internal properties resolve nothing, since Wittgenstein, as he and Pears fail to see, faces the same difficulty that Russell will seek to resolve by his use of definite descriptions. Wittgenstein, in spite of his appeal to internal properties and what he says in Tractatus 5.542, did not manage to correlate complexes merely by correlating their constituents. His atomic sentences implicitly represent possibilities or situations that may then exist or not.
Pears takes Wittgenstein to argue that the addition of a logical form like ($f)($y)fy to the judgment complex does not make the multiple relation analysis more viable.³⁷ This is correct, for one must still treat the relation J as being such that it can only relate certain kinds of terms, and adding a logical form only redundantly specifies that appropriate terms must be of a f-type and a y-type, respectively. The issue is whether imposing the condition that a sentence of the form 'J(S, f, y, ($f)($y)fy)' is well-formed only if the terms replacing the variables are of the requisite logical kinds reveals that Russell's analysis is merely a variant of an analysis employing a sentence as a subject term, as in 'J(S, L(w,r))'. Russell was obviously bothered by this question. But, in spite of his dramatic reaction to Wittgenstein's criticism, he later discussed the relational theory, in its original form, in the 1918

³⁷ Pears, 1989, 179.

lectures on logical atomism. There, as noted earlier, he found it problematic to employ "two verbs" in patterns like 'J(o, L, w, r)', which may be construed as a variant of Wittgenstein's criticism that Russell must assume that the constituents of the judgment fact, other than o and J, can combine into a fact that is the truth ground for the judgment. Ultimately, he explicitly abandoned the theory in "On Propositions: What They Are and How They Mean" of 1919, since he no longer believed in a judging subject, but, as we will see, he seems to have abandoned the theory much earlier for reasons more relevant to those we have discussed.
The change Russell made in 1913 to his relational theory that Pears, following Wittgenstein, focuses on, concerns the introduction of logical forms into the analysis of judgments. Russell thought that the addition of such forms helped unite the relevant constituents in a judgment fact, as he had earlier thought that the ordering of the signs representing such constituents represented their being connected, and did not merely indicate the types of terms required. His explanation of the process of uniting helps us understand why he took logical forms to be existential facts:

The process of "uniting" which we can effect in thought is the process of bringing them into relation with the general form of dual complexes. The form being "something and something have a certain relation", our understanding of the proposition might be expressed in the words "something, namely A, and something, namely B, have a certain relation, namely similarity". ...More simply, in order to understand "A and B

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are similar", we must know what is supposed to be done with A and B and similarity, i.e., what it is for two terms to have a relation; that is, we must understand the form of the complex which must exist if the proposition is true.³⁸

Thus the form allows our thought to unite or synthesize the two terms and the relation. Propositions, as existential facts, do not play such a role, but, are merely common forms of various intentional facts in which such a synthesis takes place. Yet, Russell's holding that logical forms allow us to unite some constituents in a thought does not avoid the problem of having to correlate intentional facts with their truth grounds.
Adding the form of a dual relation as a constituent of a judgment fact obviously does not suffice to distinguish Ottoline judging that Wittgenstein liked Russell from her judging that Russell liked Wittgenstein, since the facts that are the truth grounds for the respective judgments are not thereby distinguished. The constituents L, r, and w and the form R(x, y) are common to both. In 1913 Russell no longer believed that he could simply appeal to the order of the constituents in a fact, for to do so requires an account or analysis of what constitutes such order. As he also came to hold that the linguistic ordering of terms in non-symmetric relational sentences merely reflects an ordering of elements in a fact, he sought to explicate what that ordering is and how it affects the analysis of the form of non-symmetric relational facts.

³⁸ Russell, 1984, 116.

To resolve the problem of order, Russell coordinated to a non-symmetric relation, L for example, two relations, L¹ and L², which were relations between an object and complex or fact. L¹ indicated that an object occupied the initial position in a L-fact; L² indicated it occupied the second position. The fact whose existence would be the truth maker for 'L(w, r)' would now be described by the definite description '(ip)(wL¹ p & rL²p)', and 'E!(ip)(wL¹p & rL²p)' could now be used to assert or judge that w stood in L to r. In place of 'J(o, L, w, r, R(x, y))', Russell now used 'J(o, E!(ip) (wL¹p & rL²))', or, simply, 'J(o, ($p)(wL¹p & rL²p))':

In the case we took, if I have a belief whose objects appear verbally to be R, x₁, x₂, ...x_n, there are really other objects, expressed by inflexions, order of words, etc., and what I am really believing is: "There is a complex g in which x₁C₁g, x₂C₂g, ... x_nC_ng". In the sense already explained, this proposition is non-permutative.... The actual complex g itself, whose existence is affirmed by description in our associated molecular complex, cannot be directly named, ... but a complex name for it must be descriptive.³⁹

³⁹ Russell, 1984, 148. There are problems with Russell's suggesting that there are two associated complexes, with his speaking of there being a non-symmetrical relation which determines and is determined by the relevant positional relations, and with the complex being a term of the

This reveals a radical difference in the analysis of belief contexts involving non-symmetric relations and those involving monadic properties or symmetric relations. In the latter cases, the old multiple relation pattern applies, with the relatively insignificant addition of logical forms as terms. The former cases are treated in a way reminiscent of a propositional analysis: the second subject sign of 'J(o, E!(ip)(wL¹p & rL²p))' is a sentence. Russell's use of such a radically different pattern for non-symmetric relations is a surprising feature of his 1913 analysis.
There is no obvious way to adapt his treatment of such contexts to monadic contexts and contexts with symmetrical relations. He cannot employ positional relations for facts with symmetrical relations, since he would then recognize two facts for each instantiation of such a relation. This he explicitly denied, while he saw no need to revise his earlier pattern for monadic judgments. Thus his new analysis is awkward in that it employs different patterns of analysis for diverse kinds of intentional contexts. That aside, it is interesting that Wittgenstein's criticisms are irrelevant to Russell's treatment of non-symmetric relational contexts. They are irrelevant since Russell employs a sentential expression like 'E!(ip)(wL¹p & rL¹p)' or '($p)(wL¹p & rL²p)' as a subject term in such contexts. This raises a question about how much of the 1913 manuscript Wittgenstein read or discussed with Russell.
G. Landini's recent discussion of Russell's 1913 theory not only misses the point and force of Wittgenstein's

positional relations which are used in the analysis of the order in the fact. These problems are ignored here.

criticism but fails to grasp the crucial feature of the theory. He takes the statement of a truth condition for a non-symmetric relational context, '($p)(aC¹p & bC²p)' for example, to be given a further truth condition. The second truth condition is given by:

'($¹p)(a has C¹ to p & b has C² to p)' is true =df ($¹p)(($¹q)(U(m, a, C¹, p, xRb) corresponds to q) & ($¹r)(U(m, b, C², p, xRb) corresponds to r)).⁴⁰

This requires explaining that he uses 'm' for the mind of the subject and 'xRb' for the logical form of aC¹p. What he writes shows that he fails to grasp both a fundamental problem Russell seeks to resolve and Russell's purported solution. Russell seeks to explain what it is for a proposition to correspond to a complex that is its truth maker. Thus he cannot employ the relational predicate 'corresponds to' as Landini does, and he explicitly avoids doing so. As Russell wrote:

Thus the belief is true when there is a certain complex which must be a definable function of the belief, and which we shall call the corresponding complex, or the corresponding fact. Our problem, therefore is to define the correspondence.
If our complex is one which is completely determined by its constituents, our problem is simple. That is to say, let our belief be
J(S, ƒ, x₁, x₂, ..., x_n)

⁴⁰ Landini, 1991, 55.

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where J is the relation "belief" or "judgment", S is the subject, ƒ the form, and x₁, x₂, ...x_n the objects of the belief; and suppose that ƒ is a form such that there cannot be more than one complex having this form and composed of given constituents; suppose, that is to say, that no complex having this form is homogeneous and unsymmetrical with respect to any of its constituents. Then, if there is any complex whose constituents are x₁, x₂, ...x_n, there can be only one; this one may therefore be defined as the corresponding complex. If there is such a complex, the belief is true; if not, it is false. ...Thus we may say: A non-permutative belief is said to be true when there is a complex consisting of its objects; otherwise it is said to be false.⁴¹
The occurrence of the phrase 'consisting of' makes quite clear what Russell is doing. He sets out the truth grounds for a judgment with an atomic content (or for an atomic sentence) by specifying what fact is involved solely in terms of the latter's constituents and form, and thus does not require a basic ("undefinable") function correlating truth bearers to truth makers. The quotation makes two things explicit. First, he takes a "definable function" to determine the corresponding fact for each non-permutative belief. He thus avoids the problem of a non-existent fact being determined as a value of the function for a false
⁴¹ Russell, 1984, 144-145. I have replaced Russell's use of 'F' by 'ƒ' here. Russell mentions the need to explicate 'correspondence' more than once.

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belief, since such an interpretation function is "defined" in terms of the existence of a fact consisting of specified constituents. Second, he appeals to a relation between a complex and its constituents.
The basic idea had already been expressed, not only in "On Denoting," but in the first edition of Principia, where he and Whitehead write:
In fact, we may define truth, where such judgments are concerned, as consisting in the fact that there is a complex corresponding to the discursive thought which is the judgment. That is when we judge "a has the relation R to b," our judgment is said to be true when there is a complex "a-in-the-relation-R-to-b," and is said to be false when this is not the case. This is a definition of truth and falsehood in relation to judgments of this kind.⁴²
What he clearly does here is try to explain the notion of correspondence between a judgment and a fact in terms of there being a "complex" or fact of a certain kind. However, he faces the same problem he did with the 1905 version of the definition of truth for such judgments or propositions, since he implicitly presupposes, as Moore did, that the judgment represents, whether it is true or not.
Landini treats correspondence as a basic relation and, hence, not only incorrectly interprets Russell, but becomes enmeshed in the very problem Russell sought to avoid. Russell, in 1913, thinks in terms of the truth condition for 'Fa', or U(S, F, a, ($f)($y)fy), as given by something
⁴² Whitehead and Russell, 1950, 43.

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like: ($p)[p consists of F and a with ($f) ($y)fy as the logical form of p] - where consists of is a relation between a fact and its constituents. He is not thinking in terms of something like: ($p)[U(S, F, a, ($f)($y)fy) corresponds to p] - where 'corresponds to' indicates a basic relation between truth grounds and truth bearers. In the case of non-symmetrical relations, as we noted, Russell's positional relations indicate the position of the term in the complex. They thus relate terms to complexes and show that terms are combined in complexes: they take on the role that consists of plays for non-permutative complexes. There is absolutely no indication that Russell employs either a basic correspondence relation or an intentional fact, as Landini does, in stating what must exist for sentences like 'Fa' and 'A is similar to B' to be true.
Introducing a predicate representing a relation to express that a fact contains a term or attribute, say 'C', so that a description like '(ip)(pCa & pCF & p is of the form ($f)($y)fy)' can be employed, one could try to avoid using a representational function or relation to coordinate the complex Fa to the judgment fact J(o, F, a, ($f)($y) fy) or to the proposition ($U)($S)U(S, F, a, ($f)($y)fy). But, an apparent problem can then be raised about contexts like 'pCa'. This is also a question that arises for Russell's treatment of non-symmetrical relational contexts in that we have clauses like 'aL¹p', and we will shortly see that Russell is aware of the problem. The problem concerns whether sentences of such a form represent possible situations. If one takes there to be a function that, for the proposition U(S, F, a, ($f)($y)fy) or judgment fact J(o, F, a, ($f)($y)fy) as argument, determines a complex or fact,

37a being F, it does so whether or not such a fact exists. If it does not, it is a function without a value for certain arguments. Thus, the problems posed by possible facts or situations arise. Employing corresponds to as Landini does implicitely relies on such a function from belief facts to truth makers and thus fails to avoid such entities. Given a truth bearer (a sentence, a belief fact, proposition, etc.) with a non-permutative context, the function determines the fact whose existence makes it true.⁴³ Landini's use of 'corresponds to' and a sign for a truth bearer in the definiens of the truth predicate is simply a variant of Moore's claim that a belief is true if it is directly proven by some fact. The problem this raises becomes apparent when we ask "any fact or some particular fact it purportedly represents?" Obviously not any fact will do. One must specify what fact is the belief's truth maker. As Russell puts it:
Where non-permutative complexes are concerned, the complex formed of the objects of our belief seems as intimately associated with our belief as anything purely objective can be....⁴⁴
⁴³ Moore faced the same problem when he took beliefs to refer to facts and to be true when the facts had "being" and false when the facts had "no being."
⁴⁴ Russell, 1984, 154. For Moore:
Every belief has the property of referring to some particular fact, every different belief to a different fact; and the property which a belief has, when it is true-the property which we name when we call it true, is the property which can be expressed by saying that the fact to which it refers is. (Moore, 1953, 267.)
The problem arises when the belief refers to a fact which has "no being."

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The problem can be resolved, and the unwanted possible facts avoided, by using using a pattern along the lines of '($ p)(pCa & pCF & p is of the form ($f) ($y)fy)' to state the truth ground. I can only briefly indicate the pattern for doing so here. One point involved is that no problem arises from there not being constant signs (atomic sentences for example) representing such situations, as one can only indicate them by description, which Russell explicitly held to be the case for non-symmetric relations. This means that existential claims like '($p)(aL¹p)' will be taken to hold even though there are no sentences like 'aL¹[aLb]', where '[aLb]' is a "complex name" (not a description) of a fact, so that there is no sentence from which '($p)(aL¹p)' is obtained by generalization. A second point is that a relation between a fact and a constituent of it is a purely formal or logical relation that does not introduce possible facts or further facts connecting a constituent to a fact. To introduce a constant sign, like '[Fa]', to denote an existent fact, is to introduce such a sign as an abbreviation for a description. Such a sign is then merely elliptical for '(i p)(pCa & pCF & p is of the form ($ f)($y)fy)', or something like that.⁴⁵ We can take facts to be related to constituents, but not to be terms of further relational facts - facts purportedly grounding the truth of claims like 'the fact that a is F contains a'. Russellian definite descriptions allow us to denote facts and to take a relation like C to be a "formal" or "logical" or
⁴⁵ That Russell was aware of the problem posed by taking a sign like '[Fa]' as a "complex name" is clear from a qutotation cited earlier.

39"internal" relation in an unproblematic and precise sense. The interpretation or coordination or "semantic rule" for a monadic atomic sentence like 'Fa' can be given by a three part conditional, and not Carnap's (3), that functions as both an interpretation rule and as specifying a truth ground:

'Fa' is true º Fa º E!(ip)(pCa & pCF).

For subject signs and predicates we coordinate each to an element or attribute (relation) of respective domains, as in Carnap's (1) and (2). But instead of a domain of possibilities, I am assuming that we have a domain of atomic facts. Thus the interpretation rule for sentences is basically different. In logic texts this is reflected by assigning either truth or falsity to sentence letters. In place of taking a sentence to represent something, as names and predicates are taken, an atomic sentence is understood to assert that there is something and to be true if and only if that something, a fact, exists. Thus sentences are linked to extra-linguistic items, or given an interpretation, in a radically different way than names and predicates.
We can now see that facts are not related, as wholes in further facts, to their constituent parts - that clauses like
⁴⁶ We could simply use '($p)(pCa & pCF)', since no two monadic first level facts will have the same term and attribute. We could also replace C by two more explicit formal relations, is a term in and is attributed in , as holding between a and F, on the one hand, and the fact on the other. In that vein, we can handle relational cases by further formal relations, such as is the initial term in , is the second term in , ...., that are generalizations of Russell's positional relations.

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'pCa' do not indicate further facts and invite a Bradleyian regress. For if 'C' represents a non-formal relation then we will have a further relational fact, with C as the relation and an object and a fact as its terms, and so on and so on. But such a regress does not arise. To specify the fact that would be the supposed term of a further relational fact requires us to describe it as '(ip)(pCa & pCF)'. Thus the sentence that would be true if the purported additional fact existed would be: '(ip)(pCa & pCF)Ca'. But this, by Russell's analysis of definite descriptions, simply asserts that the original facts exists!⁴⁷ Thus given that there is such a fact, it trivially follows that it contains a. No Bradleyian regress thus threatens the recognition of a relation like C, since such a relation can be said to be an internal or formal relation in the sense that 'E!(ip)(pCa & pCF)' entails '(ip)(pCa & pCF)Ca'. That aside, the point here is that however one seeks to resolve the issues raised, it is apparent that Landini overlooks them and neither recognizes the problems introduced by taking corresponds to as a basic relation nor understands that Russell explicitly sought to avoid invoking such a relation. Landini's appeal to such a correspondence relation raises two further difficulties for his analysis.
First, in taking intentional facts to be involved in stating truth conditions, Landini must use a verb like 'believes' as the predicate and as a subject term of a sentence stating a belief fact in analyzing "'A believes that a is red' is true".⁴⁸ He thus violates type rules or
⁴⁷ This is a consequence of a familiar Principia theorem: f (i x)(fx) º E! (i x) fx
⁴⁸ Landini, 1991, 58. His truth condition is '($¹ p)(Bel {m*, Bel, m, a, Redness, fx, f(F, x, g, L)} corresponds to p)',

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introduces a hierarchy of belief predicates for such a simple context. Second, his using '($¹ p)(Bel {m*, Bel, m, a, Redness, fx, f(F, x, g, L)} corresponds to p)' fails in that it is a permutative context containing 'm*' and 'm' as terms for particular minds, even ignoring that a is also a particular. With a text like 'a is human' ('a is a mind'?), the permuting of 'a' and 'm' is only ruled out by fiat. Landini fails to see that he dismisses the very problem that Russell explicitly raised:
One special objection is that ...we have to regard its atomic constituents x₁C₁g, x₂C₂g, etc. as really its constituents, and what is more, we have to regard the corresponding propositions as constituents of the proposition "there is a complex g in which x₁C₁g, x₂C₂g, etc." This seems to demand a mode of analyzing molecular propositions which requires the admission that they may contain false atomic propositions as constituents, and therefore, to demand the admission of false propositions in an objective sense. This is a real difficulty, but as
where m* is "the mind of the person attributing the belief" to a person, m is the latter's mind, fx is the logical form of predication, f (F, x, g, L) is the logical form "which accounts for our understanding of the simplest kind of belief-relation," "'f' represents a kind of mental state such as belief," "'F' represents a mind."
It can be argued that the statement of a truth condition that Landini gives, involving 'corresponds to', does not enable a theory embodying it to satisfy Tarski's Convention-T. Alternatively, if one takes a sentence like 'aLb' to be transcribed by the existential claim '($p)(aL¹p & bL²p)', which also states its truth condition, Convention-T is satisfied.

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it belongs to the theory of molecular propositions we will not consider it further at present.⁴⁹
Russell did not get to the section on molecular propositions, so one can only speculate about how he sought to handle the problem or whether he took it to be insoluble. But, it is worth noting Russell's use of the phrase 'in which' in stating "there is a complex g in which x₁C₁g..." This indicates the appeal to a connection between the complex and the items that form it.⁵⁰ And, he was quite explicit about the analysis of contexts involving non-symmetric relations being construed in terms of existential claims:
When we assert "A is before B", we are asserting "there is a complex in which A is earlier and B is latter." It is impossible to find a complex name which shall name this complex directly, because no direct name will distinguish it from "B-before-A". Complex names, in fact, are only directly applicable to non-permutative complexes, where the mere enumeration of simple names determines the complex meant. Thus the only propositions that can be directly asserted or believed are non-permutative, and are covered by our original simple definition.⁵¹
⁴⁹ Russell, 1984, 154.
⁵⁰ Russell also uses a conjunction of such propositional clauses in descriptions of the complex. Russell, 1984, 146-147.
⁵¹ Russell, 1984, 148.

This also shows that for a non-permutative complex, he thinks of an atomic sentence as a "complex name" and it points to a familiar ambiguity of 'corresponds to'. In one sense 'Fa' corresponds to a complex irrespective of its truth; in another sense it can correspond only to an existent fact. This ambiguity is connected with the problem posed by correlating atomic sentences to truth grounds: the problem of avoiding non-existent facts or possibilities. Russell avoids such entities by using '($p)(p consists of a and F in the form ($f)($y)fy)', rather than '($p)('Fa' corresponds to p)', to specify the truth ground for 'Fa'. He gives truth grounds for permutable contexts, like 'aLb', in the same way, by simply using 'E!(ip)(aL¹p & bL²p)' or '($p)(aL¹p & bL²p)' and not by asserting that a specific judgment fact corresponds to a fact. Moreover, he expresses judgment facts involving permutable contexts by employing such existential statements. He transcribes 'o judges a has L to b' as 'J(o, E!(ip)(aL¹p & bL²p))' or 'J(o, ($p)(aL¹p & bL²p))'. This is clear from:
Owing to the above construction of associated non-permutative complexes, it is possible to have belief which is true if there is a certain permutative complex, and is false otherwise; but the permutative complex is not itself the one directly "corresponding" to a belief, but is one whose existence is asserted, by description, in the belief, and is the condition for the existence

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of the complex which corresponds directly to the belief.⁵²
Thus Russell did not employ the pattern he used for non-symmetric relational judgment facts in the case of symmetrical relational judgments and monadic judgments. Since these latter contexts are non-permutative, he has no need to. But, since he does not use such existential statements in the analysis of judgments with non-permutable contents, as he does in the case of permutable contexts, his analysis faces Wittgenstein's argument.⁵³ He must rely on the intentional relation, J, U, etc., to unify o, F, a, and
⁵² Russell, 1984, 148.
⁵³ As we noted, he can do so by using a relation like C or relations like is a term in and is attributed in, obtaining between complexes and their constituents. This would not have been foreign to Russell, for in an appendix to the second edition of Principia, he spoke of particulars and properties being construed as classes of facts having, respectively, particular-resemblance and predicate-resemblance to a given fact. He could then not only use '$p consisting of F and a in the form fy' to state the truth condition for 'Fa' but use 'J(o, ($p)(p consists of F and a in the form fy))' in place of 'J(o, F, a, fy)'. He could do the same sort of thing for a symmetrical relation. To do so, however, is to give up the pattern of his multiple relation analysis, unless he further construes such patterns in term of something like 'J(o, F, a, p, consisting of, ($R)( $p)(pRx & pRf & pRfy))' with 'R' as an appropriate variable and ($R)($p)(pRx & pRf & pRfy) as the logical form of such existential facts. This is the kind of complexity Landini introduces with his use of a correspondence relation. But, aside from the needless baroque complexity, once the content of the judgment is so fragmented, we face Wittgenstein's objection, since the relation J is used to unify all the terms into the judgment fact as well as all the terms but o into what is judged.

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the form ($f)( $y)fy into a judgment fact, J(o, F, a, ($f)( $y)fy), as well as unify the "objects," F, a and ($f) ($y)fy, of the judgment. In the case of a permutable content, the definite description (or existential claim) connects the "objects" by describing the relevant truth maker. Such definite descriptions do two things. They provide for the unity of content, and thus answer Wittgenstein's objection, and, they resolve the problems posed by specifying truth grounds for atomic sentences (judgments) without recognizing non-existent facts. but they do not appear able to resolve a further, familiar problem. To use 'J(o, E!(ip)(aL¹p & bL²p))', or '($p)(aL¹p & bL²p)', requires specifying what o stands in the relation J to when 'aLb' is false.⁵⁴. Russell canot take the existential sentence to represent either a propositional entity or a possible but non-existent entity. His theories of truth and judgment are designed to avoid doing that.
As we noted earlier, Russell mentioned the problem posed by constituent clauses like 'aL¹p', when 'E!(ip)(aL¹p & aL²p)' is false, but he did not go into the problem. His Principia use of functional abstracts will not help in the present case. We can construe 'o judges that something has L to b' in terms of 'J(o, L, b, ($x) R(x, y))', with 'R' as a dyadic relational variable, since the context is non-
⁵⁴ To use 'J (o, (i p)(aL¹p & bL²p))', in place of 'J (o, E! (i p)(aL¹p & bL²p))', does not help, since we then obtain '($ p) {((aL¹p & bL²p) & (q) (( aL¹q & bL²q) É p=q)) & J(o, p)}'. But with 'p' ranging over existent facts, o can then only judge that a has L to b if it in fact does.

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permutative. But we cannot construe 'J(o, ($ p)(bL¹p & bL²p))' in terms of 'J(o, L¹, L², a, b, ($ p)(xRp & yR¹p))', with ($p)(xRp & yR¹p) as an appropriate logical form, as 'a' and 'b', as well as L¹ and L², can be permuted. Russell appears to have no solution. Landini merely mentions in passing that he "would presumably require...'position relations'" determined by the relation judges (believes). But, in giving a description of such a complex, Landini reverts to using 'L' as a subject term, and not the position predicates 'L¹' and 'L²'. This neither resolves the problems nor fits with what Russell says is really believed.⁵⁵ Such problems may have contributed to Russell's rejecting the later parts of the manuscript.
Pears focuses on the role of acquaintance in Russell's analysis and the question of what logical forms are. The two
⁵⁵ Landini, 1991, 59. For what Russell says about what is "really believed" see earlier quotations above. Landini does consider a context like 'For anything if it is an F then if it is a G then it is an F'. But, as that is a permutative context, since 'F' and 'G' are subject terms in his analysis 'Bel (m, F, G, ($f) ($F)(a) (fa É(Fa É fa)))' the analysis will not do, as the different variables 'f' and 'F' cannot carry the burden of order. (Landini, 1991, 61). Russell seems to have thought no problem arose in such a case. Speaking of "there is a complex g in which x₁C₁g, x₂C₂g, ... x_nC_ng he writes:
... each of these atomic constituents is non-permutative because it is heterogenous. Whether any difficulties arise from the fact that the molecular complex is still permutative with respect to the constituents of its atomic constituents, is a question which must be left until we come to deal with molecular thoughts. But it seems fairly evident that no difficulties can arise arise from this fact. (Russell, 1984, 147.)
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matters are connected. Russell is concerned to answer the somewhat Kantian question: How is the understanding of a sentence possible? In the case of 'Fa' he takes it to be sufficient that we have acquaintance with F, with a and with the form ($f)($y)fy. F and a are objects that are unproblematically terms of the relation of direct acquaintance. But Pears raises a problem that he takes Wittgenstein to have raised: How do we come to understand what it is for an object to exemplify a property by being acquainted with the constituents and the form of a mondadic fact? Following his reading of Wittgenstein, Pears takes Russell to have introduced the form ($f)($y)fy to resolve this problem and argues that it does not do so. It does not do so since to be acquainted with it requires acquaintance with a complex it informs. But, to be acqainted with, and hence understand, a complex presupposes acquaintance with its constituents and its form. Hence, Russell supposedly faces an insoluble problem, since, in the case of acquaintance with a form and acquaintance with a complex of which it is the form, each presupposes acquaintance with the other.
Russell faces no such problem. Even if he holds that acquaintance with a complex implies acquaintance with whatever is involved in its analysis, which Pears attributes to him, no problem arises so long as one understands 'presupposes' or 'implies' in a logical and not a temporal sense. There is no more a problem with talking of acquaintance with logical forms than there is of speaking of acquaintance with universal properties by one who holds that only instantiated properties exist and can be be objects of acquaintance only as instantiated. All Russell need do is hold that to be acquainted with a form is to be acquainted

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with a complex of which it is the form and vice versa. But the criticism itself arises, I believe, from a misunderstanding by Pears. Russell holds that to understand a proposition requires knowledge of the relevant constituents and form. Ignoring questions about propositional entities, we may understand this claim to mean that an atomic sentence like 'Fa' is understood only if the object a, the property F, and the logical form ($f)( $y)fy are known. Assume also that the form is known only if an atomic fact of that form is known. To be acquainted with an atomic fact still does not require prior acquaintance with a form. All that is required is that if there is acquaintance with such a fact, and awareness of it as such, there is also acquaintance with or knowledge of a form. There is no more a problem here than there is in the case of being acquainted with several instantiations of a property. All Pears does is raise a variant of Plato's familiar objection to abstraction, and, hence of the argument for the innate knowledge of the Platonic forms. The logical form must supposedly already be known in order to recognize it as the form of a fact. But it cannot be grasped in experience, i.e., by acquaintance, for in order to experience it one must recognize it as the form it is - hence, it already must be known. Pears' argument is no more viable than Plato's. What gives it some credence is Russell's mingling questions about logical forms of facts with questions about logical truths. Russell was concerned about the truth ground of '($f)($y)fy'. He held that such a ground was not complex, due to his concern about the constituents of such a fact. What he did, as we noted earlier, was take the monadic logical form ($f)($y)fy to be its truth ground, as he took

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the dyadic form ($R)($x)($y)R(x,y) as the truth ground for '($R)($x)($y)R(x, y)', and so on for n-adic relational forms. This helps explain his identifying the logical forms of monadic prediction, dyadic predication, etc. with purportedly simple existentially general facts. As neither forms nor such existentially general facts had constituents, both were simples. Thus, such existential facts cannot contain forms but can be identified with them. Yet, while Russell identifies the predicative forms with existentially general facts, he sees problems with the identification. First, for each such general fact or form to exist, a basic relation and atomic fact of the appropriate logical kind must exist, but it cannot be a matter of logic that they exist. A form must be the form of some fact, but it seems evident to him that a form could be grasped even if there should be no such fact. The form of an n-term relational fact is understood or an object of acquaintance, whether or not there are n terms standing in an n-term relation and whether or not there is such a relation. Second, identifying a logical form with an existential fact raises a problem he noted earlier in connection with his identification of propositions with forms.
But in saying that there are relations of which there are no instances, what we should naturally suppose that we mean would be "there are propositions of the form xRy for values of R for which such propositions are false whatever x and y may be." But with our definition of "proposition", we cannot have any reason to believe that there is a proposition which has never been understood, and we cannot know that a proposition of the form xRy

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has ever been understood, if the R is one of which there is no instance, and with which consequently no human being is acquainted.
This instance suggests, what is also suggested by many other considerations, that our definition of a proposition is inadequate.⁵⁶
Given the problems posed by identifying the form of mondadic prediction with the existentially general fact that something has some property, one may wonder why Russell construes the form as a logically necessary fact. Since he takes such generalized facts to ground logical truths, and completely general facts do not have constituents, we have one motive. In this connection he speaks of the existential quantifier as being "nothing." Not taking the quantifier sign to represent an entity, Russell would have a clear motive for identifying the general fact with the logical form, since there would be no constituent of the fact to distinguish it from the form. He also has a clear cut distinction between "logical facts" and non-logical facts that fits with the notion of logic being a matter of form: logical facts, being forms, are facts that have no constituents. This fits with his taking such forms to be objects of acquaintance, since in cases of acquaintance there must be an object. Hence '($f)($y)fy' must be true. Moreover, there is another reason Russell might have taken logical forms to be facts. He takes the fact that a is F to be composed of the constituents a and F united by the form. We state that a is F by using 'Fa', but we could also use '($f) ($y)(fy & f=F & y=a)'. If we do so and withdraw the
⁵⁶ Russell, 1984, 134.

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clause 'y=a', we are left with '($f) ($y) (fy & f=F)', which says that something has the property F. It is not far fetched to think of this fact being derived from the first by abstracting or removing the object a. What remains is the form and the property F. If we then withdraw the clause 'f = F', we are left with the expression '($f)($y)fy'. This suggests that the existential generalization represents what remains after the other constituent of the fact, the property F, is removed. Hence, what remains, the form, is represented by the existentially general sentence. It is also clear why existential, rather than universal quantifiers, must be used. By abstracting we go from a specific case to an indefinite attribution, not to a universal claim that is a logical falsehood.
Wittgenstein's criticisms aside, one might speculate that problems about logical forms, construed as facts, and the failure of his own theory of descriptions to provide a key to the analysis of intentional contexts with non-symmetric relations were among the reasons Russell abandoned the later chapters of the 1913 manuscript. Pears' claim that Wittgenstein's criticism of Russell's identification of logical forms with existentially general facts played a role could well be right.⁵⁷
⁵⁷ Pears, 1989, 176-178. Russell might have been influenced by Wittgenstein's views, as recorded in the latter's notebooks. Though the entries cited below date from later than Russell's manuscript, the two men had been discussing and communicating about such matters in the period prior to and during Russell's work on the manuscript. Thus, in a letter of January, 1913, Wittgenstein writes:

I now think that qualities, relations (like love) etc. are all

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As we noted, Russell raised problems about that identification in the manuscript, and this would fit with his reporting, in the 1913 letter to Ottoline Morrell, that Wittgenstein had said that he had tried Russell's analysis and that it did not work.
Pears argues that identifying forms with existentially general propositions, and taking these to be simple, makes "their truth unintelligible."⁵⁸ But his argument presupposes that a ground of truth for a logical truth must be a complex, as is a ground of truth for a non-logical truth. Russell is not compelled to agree. On his account there is nothing unintelligible about taking an existentially general fact to be a simple and a ground of truth. The problem stems, in part, from Pears' focusing on Russell's use of the term 'proposition'. This is somewhat misleading, since as Russell says, a logical form is a fact: "if a logical form, i.e. a fact containing no constants..."⁵⁹ The point is that if we state Russell's view more carefully than Pears does, or than Russell himself does in the passage Pears quotes, the proposition would be represented by the expression 'U(S, ($f)($y)fy)', read as 'There is a U and an S such that U(S, ($f)($y)fy)'. The proposition is a complex, and it is true, since the object, the logical form, ($f)($y)fy,

copulae! That means I for instance analyse a subject-predicate proposition,say, "Socrates is human" into "Socrates" and "something is human", (which I think is not complex). Wittgenstein, 1969, appendix iii, 120-121.
In his Notebooks, 17, Wittgenstein writes that he "had thought that the possibility of the truth of the proposition fa was tied up with the fact ($x,f). fx, and, on 22, ("Similarly ($x) fx would be the form of fa, as I actually thought)."
⁵⁸ Pears, 1989, 178.
⁵⁹ Russell, 1984, 131.

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which is its ground of truth, is an object of acquaintance and, hence, exists. Unlike the proposition, which is complex, since it contains the logical form ($f)($y)fy as a constituent, the logical form is simple. The difference between a proposition, whose ground of truth is a logical form (an existentially generalized fact in this case), and a proposition like U(S, F, a, ($f)($y)fy) is two-fold. First, in the former case, a logical form or fact is the only constituent of the proposition, and, second, its being a constituent means that the proposition contains its own ground of truth. One may take that to show, as Russell did, that it is a necessary truth, as the logical form itself is a logical or necessary fact. Pears thus fails to show that Russell's view is unintelligible.
Landini has criticized Pears for confusing facts with propositions, but there is an ambiguity in Russell's view. He speaks of understanding the form ($f)($y)fy, as well as being acquainted with it, and that in such a case understanding, like acquaintance, is a dyadic relation. Such a fact would be represented by 'U(r, ($f)($y)fy)', for example. But, by abstracting from such a fact, we obtain the proposition ($U) ($S)U(S,($f)($y)fy), which is true since ($f)($y)fy is a fact. Just as the sentence 'a is F' expresses the proposition ($U)($S)U(S, F, a,($y)fy) so '($f)($y)fy' should express the true proposition ($U)($S)U(S,($f)($y)fy). As (i) the object is here represented by a sentence and is a fact, (ii) Russell speaks of such facts as "truths," and (iii) U is dyadic here, one easily fuses the fact with the true proposition.⁶⁰ There is

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a further problem with Russell's construing logical forms as purely general facts that he undoubtedly came to notice. He cannot identify a form like (f)(y)fy with a logical fact, since '(f)(y)fy' is false. And he cannot analyze (f)(y)fy, in terms of existential quantification, for he cannot deny that it is simple, by his line of reasoning in the existential case. If he had not taken logical forms to ground logical truths, he would not have to take them to be general facts. He could have taken them as logical universals or functions, a view more in line with his treatment of expressions like 'fy' and '($y)fy' in Principia and his use of the abstraction cap '^'.
Russell may also have come to believe that there was a problem with his use of definite descriptions of facts to state truth conditions for atomic sentences. He sought to use such descriptions not only to specify the order in a fact and to avoid non-existent facts in connection with false atomic sentences, but also to avoid negative facts as truth makers for true negations of atomic sentences. But, it seems that he came to hold, in connection with Wittgenstein's criticisms, that to specify the truth maker for 'Ø L(a, b)' by 'Ø E!(ip)(aL¹p & bL²p)' was to recognize the fact that (ip)(aL¹p & bL²p) does not exist when 'Ø L(a, b)' is true. This is what he later held in arguing for negative facts in 1918. But a page, attached as Appendix B.1 Folio 2 to the 1913 manuscript by the editors, shows him thinking along such lines earlier.
⁶⁰ It is crucial to keep in mind that while propositions are not terms of dyadic intentional relations, forms like ($f)($ y)fy are terms of intentional relations, like U and J, that are dyadic in cases like U(r, ($f)($ y)fy) and in cases of acquaintance.

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"xRy" has different uses:
(1) as the name of the positive fact xRy
(2) as the name of the neutral proposition or of the neutral fact.
(3) as the expression of a judgment. These must be distinguished
(1) Call the positive fact +(xRy), and the negative fact -(xRy).
(2) Call the neutral fact ±(xRy), and the proposition xRy.
... Judgment involves the neutral fact, not the positive or negative fact. The neutral fact has a relation to a positive fact, or to a negative fact. Judgment asserts one of these. It will still be a multiple relation, but its terms will not be the same as in my old theory. The neutral fact replaces the form.⁶¹
The passage reveals Russell's concern with negative facts and a motive for his reconsideration and modification of his theory of judgment. With the neutral fact replacing the form, he has a complex sentential form as a linguistic term in a sentence expressing a judgment. This shows that he was concerned about his theory of descriptions failing to allow him to analyze judgment facts, in addition to believing that it did not enable him to avoid negative facts. His considering a neutral fact as a constituent of a judgment fact and his recognition of negative facts makes it reasonable to think that he saw the problems in the light
⁶¹ Russell, 1984, 197.

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of Wittgenstein's criticism. His neutral fact embodies the same idea that would be transformed into the situations and "possibilities" of the Tractatus, and obviously reflects Wittgenstein's influence. All we need do is recall Wittgenstein's use, in the 1913 "Notes on Logic," of his "a-b" notation, taking 'a' and 'b' as the "poles" of a proposition.⁶² He may even have been referring to Russell's use of definite descriptions to specify truth conditions and to analyze judgments when he wrote: "But it is easy to see that every attempt to replace functions with sense (ab-functions) by descriptions, must fail."⁶³ A passage in the 1921 The Analysis of Mind is relevant to this question:
We may say, metaphorically, that when to-day is Tuesday, your belief that it is Tuesday points towards the fact, whereas when to-day is not Tuesday your belief points away from the fact. Thus the objective reference of a belief is not determined by the fact alone, but by the direction of the belief towards or away from the fact.⁶⁴
This makes it clear that Russell is not only thinking of negative facts, but of a two-fold relation between propositions and facts, in the manner of Wittgenstein's a-b notation. The passage ends with a footnote that contains the
⁶² Wittgenstein, 1969, 97.
⁶³ Wittgenstein, 1969, 97. The Notes on Logic are printed as an appendix to the Notebooks and are dated September, 1913, when he dictated some of them to Russell and supplemented them with a typescript sent to Russell a "few days later." As reported in R. Monk, Wittgenstein: The Duty of Genius , (New York: 1990), 93.
⁶⁴ B.A. W. Russell, The Analysis of Mind (London: 1921), 272.

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only reference to Wittgenstein in the book: "I owe this way of looking at the matter to my friend Ludwig Wittgenstein."⁶⁵
The 1913 manuscript is perplexing due to Russell's ambivalence towards propositions. In earlier versions of his theory he flatly rejected propositions and took specific intentional facts to be the basic bearers of truth and falsity. In 1913 propositions, as forms or existential facts, become the basic bearers of truth and falsity, rather than judgments or statements:
Of course a judgment or a statement may be true or false in one sense ... But it is fairly obvious that the truth or falsehood which is attributed to a judgment or statement is derivative from the truth or falsehood of the associated proposition. We say that two men make the "same" statement, meaning that they assert the same proposition; and it is the proposition that makes both men's statements true or both false .... Thus the opposition of truth and falsehood, in its primary and fundamental sense, is applicable only to propositions, not to particular thoughts or statements.⁶⁶
Russell then repeats his earlier view that propositions are incomplete symbols and that false propositions are unacceptable.⁶⁷ Yet, as we earlier noted that he argues against propositions being mind independent and not against
⁶⁵ Russell, 1921, 272.
⁶⁶ Russell, 1984, 108-109.
⁶⁷ Russell, 1984, 109-110.

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propositions as such, he now argues against propositions by denying that beliefs affirm the reality of propositions, and he rejects propositions as truth makers of beliefs - not as truth bearers.
It is traditional to say that what is true "corresponds" with reality, and what is false does not. The word "correspond" requires investigation, but in any case it seems plain that a false proposition is not itself an actual entity. A false belief or a false statement is an entity; but it seems obvious that they owe their falsehood to the unreality of something which would be real if they were true. Hence if the reality of the proposition were affirmed by the belief, we should have to say that there is such an entity as the proposition when the belief is true, but not when it is false.⁶⁸
This ground for rejecting propositions, given shortly before he takes up the question of their subsistence, in a passage quoted earlier, does not apply to propositions taken as forms that are bearers of truth, not truth makers. He proceeds to give what appears to be a further reason for accepting propositions. He argues that to distinguish 'A precedes B' from 'B precedes A', we must understand what it is for a complex to be logically possible, and : "... the notion of what is "logically possible" is not an ultimate one, and must be reduced to something that is actual before our analysis can be complete."⁶⁹ He then states: "Now although we do not yet know what a proposition is, it is
⁶⁸ Russell, 1984, 109.
⁶⁹ Russell, 1984, 111.

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obvious that what we had in mind, when we said that a complex was "logically possible," may be expressed by saying that there is a proposition having the same verbal form."⁷⁰ One cannot read too much into the expression "verbal form," as he says that it is still in doubt "how propositions are to be explained."⁷¹ A page and a half later he raises the question about the subsistence of propositions. This suggests that he might have thought that propositions were required to explicate logical possibility.
In the 1914 Monist papers Russell rejected propositions, and in the logical atomism lectures he discussed the earlier form of the multiple relation theory and credits Wittgenstein with the discovery that belief facts are of a different "form" from any fact that "occurs in space." One can infer that he had not grasped that fact earlier but had taken properties and relations (verbs) to function as mere terms in such facts.⁷² He also rejects propositions as nothing and speaks of logical forms in terms
⁷⁰ Russell, 1984, 111.
⁷¹ Russell, 1984, 111. Russell's use of the phrase 'same verbal form' may go back to Moore's holding that the only way of referring to the fact that was the truth ground for a proposition, the proposition that-p, was by an expression like 'the fact that-p'.
⁷² Russell's contrast of belief facts with spatial facts clearly derives from Wittgenstein's discussion of "A judges (that) p" in the 1913 Notes on Logic, (Wittgenstein, 1969, 96), where the latter says: "Russell, for instance, imagines every fact as a spatial complex, and since spatial complexes consist of things and relations only, therefore he holds all do." In 1918, as we noted earlier, Russell is bothered by there being two verbs in a judgment fact and that both must occur as verbs. This raises a problem he cannot resolve. B. A. W. Russell, "The Philosophy of Logical Atomism," The Monist, vol. xxviii, 4, 1918, reprinted in Russell, 1971, 225.

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of expressions, not entities, that contain free variables.⁷³ Not able to resolve the problem of the embedded verb and rejecting both a judging subject and mental acts, Russell abandoned his multiple relation theory by 1919 in "On Propositions: What They are and How They Mean." There he suggests an analysis, influenced by Wittgenstein, that is sketched out in the introduction he wrote for the Tractatus.⁷⁴ In his typically generous way, Russell acknowledged his debt and proceeded, in the early 1920s, to develop Wittgenstein's idea into a new analysis of judgment facts in The Analysis of Mind⁷⁵ and in appendix C to the second edition of Principia.⁷⁶ The new analysis is explicitly derived from his construal of Wittgenstein's 5.542 in the Tractatus.⁷⁷
In the later theory Russell takes there to occur a sequence of data, inner items of thought, that represent objects, properties, and relations, while standing in a relation, "predication," that represents exemplification:
⁷³ Russell, 1971, 237-238. Russell does not say that the variables are real but there is no indication that they are apparent.
⁷⁴ Russell, 1922, xix-xx.
⁷⁵ Russell, 1921, 231-278; see especially section IV, 271-278.
⁷⁶ Whitehead and Russell, 1950, 659-666.
⁷⁷ 5.542 reads:
It is clear, however, that 'A believes that p', 'A has a thought p', 'A says p' are of the form ' "p" says p': and this does not involve a correlation of a fact with an object, but rather the correlation of facts by means of the correlation of their objects.
L. Wittgenstein, Tractatus Logico-Philosophicus, trans. D. F. Pears and B. F. McGuiness (London: 1961), 109; for Russell's construal of 5.542 see his "Introduction," xix-xx.

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...when a man believes "Socrates is Greek" he has simultaneously two thoughts, one of which "means" Socrates while the other "means" Greek, and these two thoughts are related in the way we call "predication." ....Call the relation of predication between two thoughts P. (This is the relation which holds between our thought of the subject and our thought of the predicate when we believe the subject has the predicate. It is wholly different from the relation which holds between the subject and predicate when our belief is true.)⁷⁸
Wittgenstein sought to avoid the outright commitment to the possible facts that such inner complexes could be taken to represent, by packing the possibilities into the relevant logical forms of the represented and representing items. Russell saw no problem, since he mistakenly thought, following Wittgenstein, that the representative role of the complex, the thought that Socrates is Greek, is determined by the representative roles of its constituents. He thus overlooked the need to coordinate judgement facts to truth grounds, in addition to coordinating their respective constituents. After attempting to deal with the problem in 1913, Russell simply turned away from it in his later 1925 account.
⁷⁸ Whitehead and Russell, 1950, 662. and on 661:
A word is a class of similar noises. Thus a person who asserts "Socrates is Greek" is a person who makes, in rapid succession, three noises, of which the first is a member of the class "Socrates," the second a member of the class "is," ....

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Propositions, Truth, and Belief: The Wittgenstein-Russell Dispute*

Propositions, Truth, and Belief: The Wittgenstein-Russell Dispute^*