HOW WITTGENSTEIN DEFEATED RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT

Transcription

1 PETER W. HANKS HOW WITTGENSTEIN DEFEATED RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT ABSTRACT. In 1913 Wittgenstein raised an objection to Russell s multiple relation theory of judgment that eventually led Russell to abandon his theory. As he put it in the Tractatus, the objection was that the correct explanation of the form of the proposition, A makes the judgement p, must show that it is impossible for a judgement to be a piece of nonsense. (Russell s theory does not satisfy this requirement, (5.5422). This objection has been widely interpreted to concern type restrictions on the constituents of judgment. I argue that this interpretation is mistaken and that Wittgenstein s objection is in fact a form of the problem of the unity of the proposition. 1. INTRODUCTION In 1913 Wittgenstein raised an objection to Russell s multiple relation theory of judgment that was to have a devastating and lasting effect on Russell s later philosophical work. As Wittgenstein put it in the Tractatus, the objection was that the correct explanation of the form of the proposition, A makes the judgement p, must show that it is impossible for a judgement to be a piece of nonsense (Wittgenstein 1961a, 65). The problem for Russell was that the multiple relation theory did not satisfy this requirement. Wittgenstein s objection has been widely interpreted to be a point about type restrictions on judgment. 1 One can judge that an individual possesses a property, or that two individuals bear a certain relation, or etc., but one cannot judge a combination consisting of, e.g., three individuals. Trying to judge a combination of three individuals results in nonsense. The problem for Russell is supposed to be that nothing in his multiple relation theory rules out such nonsensical combinations. Furthermore, Russell cannot add conditions to the analysis of judgment that would rule out nonsensical combinations without undermining the support for the theory of types. 2 This is a natural interpretation of Wittgenstein s objection, and for a long time I accepted it. However, I am now convinced that Synthese (2007) 154: Springer 2007 DOI /s y

2 122 PETER W. HANKS this interpretation is mistaken. The problem Wittgenstein raised for Russell has at best merely an indirect connection to type restrictions on judgment. The real problem that Wittgenstein raised was essentially the same one that was fatal for Russell s theory of propositions. This is the problem of the unity of the proposition. The whole point of the multiple relation theory was to avoid the problems of unity that plagued Russell s account of propositions. But Wittgenstein showed Russell that the very problems that defeated his account of propositions also defeated his account of judgment. In the first part of this paper I will recount Russell s views on propositions and judgment between 1903 and This will be crucial for understanding the effect that Wittgenstein s objection had on Russell. Then I will turn to Wittgenstein s objection and I will standard interpretation in terms of type restrictions and I will present three reasons for doubting this interpretation. Then I will present an alternative interpretation on which the point of the objection has essentially nothing to do with types or type restrictions. I will show that this alternative interpretation makes good philosophical sense and has strong textual support. 2. AN EVENT OF FIRST-RATE IMPORTANCE In early May 1913 Russell began work on a long manuscript titled Theory of Knowledge. 3 This was to be his first major philosophical work after Principia Mathematica. Despite a full load of lectures, students, meetings and visitors, by May 26 he had 240 pages and was optimistic about the book s completion. Then on May 27 he had a visit from Wittgenstein. Wittgenstein came to see me we were both cross from the heat I showed him a crucial part of what I have been writing. He said it was all wrong, not realizing the difficulties that he had tried my view and knew it wouldn t work. I couldn t understand his objection in fact he was very inarticulate but I feel in my bones that he must be right, and that he has seen something I have missed. If I could see it too I shouldn t mind, but as it is, it is worrying, and has rather destroyed the pleasure in my writing. (Russell 2002, 446) Russell kept going, however, and by June 6 he had 350 pages at which point he abandoned the manuscript. The immediate reasons for this had to do with problems with his account of molecular judgments. But it became clear to him as time passed that a more fundamental problem had been raised by Wittgenstein.

3 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 123 All that has gone wrong with me lately comes from Wittgenstein s attack on my work Ihaveonlyjust realized this. It was very difficult to be honest about it, as it makes a large part of the book I meant to write impossible for years to come probably... I must be much sunk it is the first time in my life that I have failed in honesty over work. (Russell 2002, 448) Looking back on this incident in 1916 he wrote to Lady Ottoline Morrell: Do you remember that at the time when you were seeing Vittoz I wrote a lot of stuff about Theory of Knowledge, which Wittgenstein criticised with the greatest severity? His criticism, tho I don t think you realised it at the time, was an event of first-rate importance in my life, and affected everything I have done since. I saw he was right, and I saw that I could not hope ever again to do fundamental work in philosophy. (Russell 1998, 282) Wittgenstein s criticism was directed at Russell s multiple relation theory of judgment, the centerpiece of the Theory of Knowledge manuscript. According to the multiple relation theory, when a subject judges that a is F she stands in a many-termed relation to a and F. On this view the logical form of S judges that a is F is Judges(S, a, F). The multiple relation theory first appeared in Russell s writings in Up until then Russell believed in propositions and held that judgment is a two-place relation between subjects and propositions. Russell s propositions were structured entities composed out of objects, properties and relations. In 1903 in Principles of Mathematics Russell wrote that a proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words (Russell 1903, 47). Russell held that propositions are complex entities, composed out of constituents that correspond to the linguistic constituents of sentences. To use Russell s example, the proposition expressed by A is different from B consists of A and the relation of difference and B. Russell insisted, however, that this proposition could not simply be a collection of these entities these constituents, thus placed side by side, do not reconstitute the proposition (Russell 1903, 49). The proposition must be unified in some way; there must be something that binds together A and the relation of difference and B in the proposition that A is different from B. Russell thought that the binding force in the proposition that A is different from B is the relation of difference itself. In the proposition that A is different from B, the relation of difference relates

4 124 PETER W. HANKS A to B; the relation of difference itself is the glue that binds A and B together into a unified proposition. The [relation of] difference which occurs in the proposition actually relates A and B, whereas the [relation of] difference after analysis is a notion which has no connection with A and B (Russell 1903, 49). Russell distinguishes between the relation as something that relates and the relation as a term, i.e. an independent, self-subsistent entity. 4 The fact seems to be that a relation is one thing when it relates, and another when it is enumerated as a term in a collection (Russell 1903, 140). In the proposition that A is different from B, the relation of difference occurs as a relation that relates, whereas in the set {A, B, the relation of difference} the relation of difference occurs merely as a term. In this set the relation of difference is just another entity alongside A and B. The proposition that A is different from B cannot, therefore, be identified with the set {A, B, the relation of difference}. The proposition has a unity that is lacking in this set owing to the fact that in the proposition the relation of difference occurs as a relation that relates. The unity of the proposition is due to the fact that the relation of difference relates A and B. But what is it for the relation of difference to relate A and B? A and B are related by the relation of difference just in case A is different from B. This proposition must be the fact or state of affairs of A s being different from B. Russell s early view was that true propositions are identical with facts. A true proposition is identical with the fact that it represents. There are two related difficulties that eventually led Russell to abandon this account of propositions in favor of the multiple relation theory. The first is a difficulty about falsity; the second is a difficulty about truth. First, suppose that A is not different from B, i.e. suppose that A and B are numerically identical. Then the relation of difference does not relate A and B there is no fact that A is different from B. It would appear, then, that the proposition that A is different from B does not exist. That would make it impossible to judge that A is different from B, for there would be no proposition there to be judged. And there would be no proposition for the sentence A is different from B to express. Identifying propositions with facts leaves no room for false propositions. The problem about truth is that Russell s account of propositions precluded him from holding a correspondence theory of truth. In a correspondence theory a proposition is true just in case it corresponds to a fact. But in order for the correspondence theory to get

5 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 125 off the ground it must be that propositions are different from facts. Correspondence requires two things to correspond to one another. If one identifies propositions with facts then one cannot hold a correspondence theory of truth for propositions. Russell was forced to say that truth and falsity are unanalyzable, non-relational properties of propositions; in a famous remark he wrote that some propositions are true and some are false, just as some roses are red and some are white (Russell 1904, 523). From the beginning Russell was aware of both of these problems. Up until around 1906 his view on false propositions was akin to his Meinongian view of non-existent entities such as the golden mountain and the Homeric gods. Prior to 1905 and the theory of descriptions he held that the golden mountain subsists because it is referred to in meaningful sentences, e.g. The golden mountain does not exist. Similarly, he held that false propositions, or objective falsehoods as he called them, subsist but do not exist. 5 For obvious reasons Russell was dissatisfied with this ontology. In My Mental Development Russell wrote that the desire to avoid Meinong s unduly populous realm of being led me to the theory of descriptions (Russell 1944, 13). Russell avoids the commitment to a merely subsistent golden mountain through his contextual definition of the definite description the golden mountain this expression is no longer treated as a unit in logical form and thus does not contribute an entity to propositions. Russell got out of his commitment to false propositions in essentially the same way this is the multiple relation theory of judgment. He makes this explicit in the 1913 manuscript Theory of Knowledge: The theory which Meinong adopts in regard to the logical nature of assumptions and beliefs is a natural one to adopt, and deserves credit for its recognition of the necessity of objects for assumptions and beliefs. His view is, that there is an entity, namely the proposition (Objektiv), to which we may have the dual relation of assumption or the dual relation of belief. Such a view is not, I think, strictly refutable, and until I had discovered the theory of incomplete symbols I was myself willing to accept it, since it seemed unavoidable. (Russell 1913, 108) The theory of incomplete symbols is of course the general strategy of the theory of descriptions. The multiple relation theory is an extension of this strategy to expressions that denote propositions, i.e. that -clauses. According to the multiple relation theory, in the logical form of Othello judges that Desdemona loves Cassio there is no unit corresponding to the expression that Desdemona loves

6 126 PETER W. HANKS Cassio. At the level of logical form this expression is broken up into its components Desdemona, Cassio, and loves. The logical form of Othello judges that Desdemona loves Cassio thus involves a four-place predicate, i.e.: Judges(Othello, Desdemona, Cassio, love) The multiple relation theory also allowed Russell to reinstate the correspondence theory of truth. In effect, he traded in propositions as the primary bearers of truth and falsity for acts of judgment. This allowed him to say that a judgment is true if there is a corresponding fact and false otherwise. In the early 1906 version of the multiple relation theory, which he did not endorse, Russell s idea was that judging a true proposition involves a different relation than judging a false one (Russell 1906). Judging truly puts one into a two-termed relation to a fact; judging falsely puts one into a many-termed relation to objects, properties or relations. Four years later, in 1910, Russell gave up this bifurcated account of judgment in favor of the view that judgment is always a many-termed relation, even when the judgment is true. The theory of judgment which I am advocating is, that judgment is not a dual relation of the mind to a single objective, but a multiple relation of the mind to the various other terms with which the judgment is concerned (Russell 1910, 180). Russell s reason for abandoning the bifurcated 1906 account was that he thought such an account would make it possible to tell whether a judgment is true or false by introspection alone. We cannot maintain this view with regard to true judgments while rejecting it with regard to false ones, for that would make an intrinsic difference between true and false judgments, and enable us (what is obviously impossible) to discover the truth or falsehood of a judgment merely by examining the intrinsic nature of the judgment (Russell 1910, 177). 6 Russell assumes that you could tell by introspection whether your mental state involves a dual or multiple relation something that is not at all obvious. In any case, a unified approach to true and false judgments is preferable to a bifurcated one. The logical form of a propositional attitude report should not depend on whether its embedded clause is true or false. 7 Between 1910 and 1913 Russell introduced a number of refinements into the multiple relation, culminating in 1913 with the inclusion of logical forms as constituents of judgments. Russell s logical forms are very general facts, e.g. the fact that something bears some relation to something. Russell symbolized this as R(x, y). In

7 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 127 the 1913 version of the theory this logical form is included as a constituent of any judgment whose subordinate relational term is a two-place relation. So, for example, the logical form of Othello judges that Desdemona loves Cassio becomes: Judges(Othello, Desdemona, Cassio, love, R(x,y)) This was intended to solve two problems. The first was to account for the ordering of the terms of the judgment and the second was to explain how a subject combines these constituents together in judgment. Russell s idea was that a subject associates the constituents of the judgment with the components of the logical form (Russell 1913, 99, 116). So, Othello associates love with R, Desdemona with x and Cassio with y. This is supposed to fix the order of the constituents of the judgment, thus distinguishing it from the judgment that Cassio loves Desdemona. It is also intended to explain the mental act performed by the subject in combining these constituents together in judgment. But it is not clear that logical forms successfully address either problem. Since the terms following the judgment predicate are unordered both Othello judges that Desdemona loves Cassio and Othello judges that Cassio loves Desdemona would be assigned the same logical form, i.e. Judges (Othello, Desdemona, Cassio, love, R(x,y)). This led Russell to complicate the account even further. 8 Secondly, merely associating terms with positions in a logical form is not sufficient for generating a judgment with a truth-value. 9 This is the unity problem in another guise. Simply pairing up love with R, Desdemona with x and Cassio with y will not give you something that is true or false. Some further act of predicating or applying love to the pair Desdemona and Cassio seems necessary. As we will see later on, this problem is closely related to the one that Wittgenstein raised in his objection. 3. WITTGENSTEIN S OBJECTION When we turn to Wittgenstein s objection we can ignore logical forms and the later refinements in Russell s theory of judgment. As will become clearer later on, this is because Wittgenstein s objection goes right to the heart of the multiple relation theory - the idea that in judgment a subject stands in a multiple relation to the other terms of the judgment. Wittgenstein put his objection in a June 1913 letter to Russell:

8 128 PETER W. HANKS I can now express my objection to your theory of judgment exactly: I believe it is obvious that, from the proposition A judges that (say) a is in a relation R to b, if correctly analysed, the proposition arb.. arb must follow directly without the use of any other premiss. This condition is not fulfilled by your theory. (Wittgenstein 1995, 29) The objection reappears later on in Notes on Logic, from September 1913: Every right theory of judgment must make it impossible for me to judge that this table penholders the book (Russell s theory does not satisfy this requirement.) (Wittgenstein 1961b, 96) And again in the Tractatus: The correct explanation of the form of the proposition, A makes the judgement p, must show that it is impossible for a judgement to be a piece of nonsense. (Russell s theory does not satisfy this requirement.) (Wittgenstein 1961a, 65) As I noted earlier, commentators on these remarks have taken Wittgenstein s point to concern type restrictions on judgment. 10 These restrictions rule out some combinations of terms as unsuitable for judgment. One can combine Desdemona, Cassio and the relation of loving in the judgment that Desdemona loves Cassio. But one cannot judge a combination consisting of, e.g. Desdemona, Cassio and Iago Othello judges that Desdemona Cassio Iago is meaningless. The constituents of a judgment must be of the right number and variety of types (e.g. an individual and a monadic property of individuals, two individuals and a dyadic relation of individuals, etc.). This makes sense of Wittgenstein s remark in the June 1913 letter thatfrom A judges that a is in a relation R to b it must follow that arb arb, i.e. a necessary condition on a subject combining together some entities in judgment is that those entities can combine into a complex that either obtains or does not obtain. In Notes on Logic he puts the point by saying that in judgment one cannot combine together a table, a penholder and a book, and in the Tractatus the point is that it is impossible to judge a nonsense, i.e. a combination of entities that isn t a possible fact. Using the formulation from the 1913 letter, the fact that there are type restrictions on the judgment relation is just the fact that the following implication holds: A judges that arb arb arb

9 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 129 And as Wittgenstein emphasizes, the implication must hold without the use of any other premiss. The problem for Russell is supposed to be that if we analyze A judges that arb in the manner of the multiple relation theory then in order to secure the above implication we have to add additional premises about the types of a, b, and R: [Judges (A,a,b,R )&(a and b are individuals) & (R is a dyadic relation of individuals)] arb arb According to Stephen Somerville (Somerville 1980) and Nicholas Griffin (Griffin 1985, 1985/86, 1991), however, Russell could not add these premises without rendering the support for the theory of types viciously circular. The details of the circularity involve complicated issues about the relationship between the multiple relation theory and the hierarchies of types and orders in the ramified type theory of Principia Mathematica. Nevertheless the basic idea is relatively easy to state. Once Russell had traded in propositions for the multiple relation theory, whether or not an expression or entity belongs to a certain type becomes a matter of the kinds of expressions or entities it can be combined with in judgment. 11 Thus, facts about type distinctions depend on facts about which judgments are possible and which are not. But adding the additional premises to the analysis of judgment makes facts about judgment depend on facts about which expressions or entities belong to which types. The first problem for this interpretation is that, if this really were the objection, then Russell had an obvious reply that would have obviated the need for additional premises. Russell could say that the judgment relation itself places the necessary restrictions on its relata, so that something like Judges(Othello, Desdemona, Iago, Cassio) is ruled out as meaningless. 12 This would be meaningless for the same reason that, e.g., φ(ϕ ˆx) is meaningless since φ ˆx and ϕ ˆx are both propositional functions of individuals, φ ˆx results in nonsense when applied to something that is not an individual. In this way the propositional function φ ˆx places restrictions on the sorts of arguments to which it can be significantly applied. In other words, φ ˆx has a range of significance. Russell could make a similar point about the judgment relation. He could reply to Wittgenstein that the restrictions on the arguments to the judgment relation are such as to ensure that Judges(A,a,b,R) implies arb arb, without the need for any additional premises.

10 130 PETER W. HANKS Here is another way to make the same point. To hold that the judgment relation places type restrictions on its relata is essentially to hold that the judgment relation, or rather various judgment relations, occur at various positions in the type hierarchy. To see this more clearly, let s take a brief look the type hierarchy of Principia. Here I will follow the exposition in (Church 1974). Let i be the type of individual constants and variables. Then if β 1,β 2,...,β m are types, there is a type (β 1,β 2,...,β m ). Monadic predicates whose arguments are individual constants and variables are type (i). Dyadic predicates of individual constants and variables are type (i, i). For example, the predicate R in arb is type (i,i). A dyadic predicate whose arguments are individual constants or variables and monadic predicates of individuals, e.g. the predicate instantiates, as in Russell instantiates humanity, is type (i, (i)). The predicate Judges in Judges(A,a,b,R) is type (i,i,i,(i,i)), a fourplace predicate whose arguments are three individual constants and a dyadic predicate of individuals. Abbreviating a sequence of mi s with the numeral m, this judgment predicate is type (3,(2)). Suppose B judges that A judges that a has R to b. On the multiple relation theory this has the form Judges (B, A, Judges, a, b, R). The judgment predicate in B s judgment, Judges is type (2,(3,(2)),2,(2)). Iterated judgments about judgments will involve successive judgment relations of successively more complicated types. Where f,a 1,a 2,...,a m are variables or constants, in order for f(a 1,a 2,...,a m ) to be well-formed f must be of type (β 1,β 2,...,β m ), where β 1,β 2,.., β m are the types of a 1,a 2,...,a m respectively. This means that Judges(Othello, Desdemona, Iago, Cassio) is not wellformed because Judges is of type (3,(2)) and Cassio is type (1). And if Judges(A,a,b,R) is well-formed, since Judges is type (3,(2)), then a and b must be type (1) and R type (2). This secures the implication to arb arb without the need for any other premises. Each judgment predicate belongs to some type and so it can be meaningfully combined with a collection of expressions when and only when those expressions belong to the appropriate types, i.e. types that allow those expressions themselves to combine into a well-formed sentence with a truth-value. The ease and obviousness of this reply casts doubt on the standard reading of the objection it is inconceivable that Russell would not have thought of it. It might be objected, however, that the same sort of circularity that blocks the use of additional premises also blocks this reply. One might argue that Russell can hardly rule out

11 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 131 nonsensical judgment by appealing to the type hierarchy if the type hierarchy itself is founded on facts about which judgments are possible and which are not. This objection is based on a mistaken conception of the relation between the multiple relation theory and the theory of types. Put crudely, the circularity is supposed to be that facts about what is judgable determine the type hierarchy, but the type hierarchy determines what is judgable. To this Russell could have simply pointed out an equivocation in determines. 13 Facts about what is judgable could determine type distinctions only in an epistemological sense they are our means for discovering where the distinctions between types should be drawn. But facts about what is judgable do not metaphysically determine type distinctions they do not make it the case that an entity belongs to a certain type. They do not make it the case, for example, that a is an individual and R a dyadic relation of individuals. Holding otherwise would commit Russell to a radical and very uncharacteristic idealism. To suppose that what we can or cannot judge metaphysically determines that a and R belong to different types is to hold that our mental capacities have the power to force entities in the world into different logical categories. This kind of view would have been anathema to a realist like Russell. That a is an individual and R a relation is an entirely objective matter that is settled independently of what we are or are not capable of judging. Russell s view must have been that facts about judgment determine the type hierarchy only in the sense that they give us a window on objective facts about where type distinctions in the hierarchy are drawn. This eliminates the supposed circularity, and it shows that there was no barrier to Russell s locating the type restrictions on judgment in the judgment relation itself. The lesson of all of this is that if the standard reading of the objection were correct then Russell would have had an obvious answer to it, and so it cannot explain why Wittgenstein s objection had such a powerful and enduring influence on Russell. It is important to note that all along Russell held that type distinctions metaphysically determine which judgments are possible. The fact that the table, the penholder and the book are all individuals makes it the case that one cannot judge that the table penholders the book. Or to put it the other way around, the fact that the judgment relation itself belongs to a certain type makes it the case that the table, the penholder and the book are not, on their own and in

12 132 PETER W. HANKS the absence of a relation, possible relata of the judgment relation. Russell makes this clear in Principia Mathematica: But conversely, when something which is not a function can occur significantly as argument, a function cannot occur significantly. Take, e.g., x is a man, and consider φ ˆx is a man. Here there is nothing to eliminate the ambiguity that constitutes φ ˆx, there is thus nothing definite which is said to be a man. A function, in fact, is not a definite object, which could or could not be a man; it is mere ambiguity awaiting determination, and in order that it may occur significantly it must receive the necessary determination...(whitehead and Russell 1927, 48, my emphasis) 14 Russell s point is that it is the ambiguity of the propositional function that makes it impossible to say (or judge) that φ ˆx is a man. The character of the propositional function makes it the case that a certain assertion (or judgment) is impossible, not the other way around. The second problem for the standard reading is similar to the first there is another sense in which it cannot explain the effect of Wittgenstein s objection on Russell. In particular, it cannot explain why Wittgenstein s objection eventually forced Russell to give up the multiple relation theory. 15 Suppose that the problem really is one about type restrictions on judgment, and that if Russell had tried to solve the problem by adding premises about types to the analysis of judgment then he would have undermined the support for the theory of types. Even if this were right, it would only have undermined one source of the support for type theory. The hierarchy of logical types was to have both indirect and direct support (Whitehead and Russell 1927, 47). The indirect support came from its ability to resolve the paradoxes. Post-1910 and the multiple relation theory, the direct support (supposedly) came from facts about what can or cannot be judged. If the standard reading were correct, then Wittgenstein s objection would have forced Russell to withdraw the direct support for type theory. But this just means that Russell would have been forced to rest type theory solely on its technical merits. It doesn t show that type theory is inconsistent or completely unmotivated. And more importantly, it doesn t show that there is anything wrong with the multiple relation theory itself. Whatever the problem was that Wittgenstein raised, I think it has to be a problem that was internal to the multiple relation theory, not a problem about the connection between the multiple relation theory and Russell s other commitments.

13 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 133 Defenders of the standard reading might reply that during this period Wittgenstein was pressing another line of argument against Russell s theory of judgment and that Russell eventually abandoned the theory either because of this other objection or because of the cumulative effect of Wittgenstein s attacks. 16 Another important objection that Wittgenstein raised to the multiple relation theory is targeted specifically at Russell s use of logical forms in the 1913 manuscript. This objection is a clear precursor to the Tractarian rejection of logical objects and the doctrine that logical form is implicit in objects, names, facts and sentences. The objection appears in Notes on Logic : There is no thing which is the form of a proposition, and no name which is the name of a form. Accordingly we can also not say that a relation which in certain cases holds between things holds sometimes between forms and things. This goes against Russell s theory of judgment. (Wittgenstein 1961b, 99) 17 As we have seen, in Theory of Knowledge Russell identified the logical form R(x,y) with the very general fact that something has some relation to something. This general fact is named by the expression R(x,y), and it appears as a thing in judgment complexes alongside the subject and the other terms of judgment. Now, the version of the multiple relation theory that appears in Theory of Knowledge does depend crucially on Russell s conception of logical form, and so Wittgenstein s objection to this conception may have been instrumental in Russell s decision to abandon the manuscript. The present defense of the standard reading is that this objection about logical form would have been enough to force Russell to abandon the multiple relation theory itself. Or, if that objection on its own were not enough, then the combined effect of this objection plus the (alleged) problem about types would have been sufficient. But this is implausible. As we have seen, the supposed problem about types is not really a problem for the multiple relation theory itself at all. And the objection about logical forms was specific to the 1913 version of the multiple relation theory. This objection could only have forced Russell to reject that particular version. As we have seen, he had already tried and rejected a number of different forms of the multiple relation theory. This shows that he was ready and willing to amend the theory in the face of new problems. At best, then, the objection about logical form could only have undermined Russell s confidence in the theory s latest version. Even when taken together, these two objections present

14 134 PETER W. HANKS no threat to the basic idea that judgment is a multiple relation, and so they cannot account for Russell s eventual abandonment of that basic idea. A third reason to be suspicious of the standard reading is that, with one interesting exception to which I will return shortly, neither Wittgenstein nor Russell ever mentioned type restrictions or type theory in their numerous published and unpublished discussions of the problems for Russell s theory of judgment. In Notes on Logic the objection to Russell s multiple relation theory appears in section I, Bi-Polarity of Propositions. Sense and Meaning. Truth and Falsehood (Wittgenstein 1961b, 93). Wittgenstein does not discuss types until section VI. In a letter to Russell of July 22, 1913 Wittgenstein apologized for the effect of his objection: I am sorry to hear that my objection to your theory of judgment paralyses you. I think it can only be removed by a correct theory of propositions, (Wittgenstein 1995, 33, my emphasis). In the Tractatus the objection to the multiple relation theory occurs in This is a comment on 5.54, In the general propositional form propositions occur in other propositions only as the bases of truth operations (Wittgenstein 1961a, 64). There is no mention of types or type theory in the 5.54s these remarks occur in the context of Wittgenstein s account of molecular propositions. Type theory is discussed in the 3.3s. There is a 1913 letter from Wittgenstein to Russell, often cited by defenders of the standard reading, in which Wittgenstein discusses his developing views on types. I have changed my views on atomic complexes: I now think that Qualities, Relations (like Love), etc. are all copulae! That means I for instance analyse a subject-predicate prop[osition], say, Socrates is human into Socrates and Something is human (which I think is not complex). The reason for this, is a very fundamental one: I think that there cannot be different Types of things! In other words whatever can be symbolized by a simple proper name must belong to one type. For instance if I analyse the prop[osition] Socrates is mortal into Socrates, Mortality and ( x,y)ε 1 (x, y) I want a theory of types to tell me that Mortality is Socrates is nonsensical, because if I treat Mortality as a proper name (as I did) there is nothing to prevent me to make the substitution the wrong way round.(wittgenstein 1995, 24 5) There is no mention of Russell s theory of judgment in this letter. Furthermore, the letter dates from January 1913, five months before the meeting with Russell in late May in which Wittgenstein raised his objection to the multiple relation theory. (Incidentally, in his next

15 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 135 letter to Russell, dated January 21, 1913, Wittgenstein reports the death of his father.) It is highly speculative to suppose that Wittgenstein was concerned with exactly the same problems in his January letter and in his May meeting with Russell. For this reason, I am dubious of any interpretation of Wittgenstein s objection that places great weight on this letter. Of course, we should make use of any available texts in the effort to understand Wittgenstein s objection. But surely the most weight should be put on those texts in which Wittgenstein or Russell explicitly discuss the problems for Russell s theory of judgment. With one exception, in none of these texts is there any mention of types or type theory. In his letters to Lady Ottoline Morrell about Wittgenstein s objection Russell never mentioned type restrictions. Types are also absent from Russell s published accounts of the problems that Wittgenstein raised for his accounts of judgment and belief. For example, in the lectures on logical atomism he remarks: You cannot make what I should call a map-in-space of a belief.... You cannot get in space any occurrence which is logically the same form as belief. When I say logically of the same form I mean that one can be obtained from the other by replacing the constituents of the one by the new terms. If I say Desdemona loves Cassio that is of the same form as A is to the right of B. Those are of the same form, and I say that nothing that occurs in space is of the same form as belief. I have got on here to a new sort of thing, a new beast for our zoo, not another member of our former species but a new species. The discovery of this fact is due to Mr. Wittgenstein. (Russell 1918, 89 91) The idea that belief cannot be mapped in space is a clear allusion to the multiple relation theory. In the 1913 manuscript Russell presented precisely the thing that he here denies one can provide i.e. a map of a judgment complex (Russell 1913, 118). In his introduction to the Tractatus Russell wrote: What Mr. Wittgenstein says here [i.e. 5.54, 5.542] is said so shortly that its point is not likely to be clear to those who have not in mind the controversies with which he is concerned. The theory with which he is disagreeing will be found in my articles on the nature of truth and falsehood in Philosophical Essays and Proceedings of the Aristotelian Society, The problem at issue is the problem of the logical form of belief, i.e. what is the schema representing what occurs when a man believes. (Wittgenstein 1961a, xxi) The essays to which Russell refers are the 1910 paper in Philosophical Essays (Russell 1910) where he first endorses the multiple relation theory and the earlier 1906 Aristotelian Society paper (Russell 1906) where he considers it but does not endorse it. There is no mention

16 136 PETER W. HANKS of types in this part of Russell s introduction to the Tractatus. There are other places scattered throughout Russell s later writings where he discusses Wittgenstein s influence on his theory of judgment and belief, and none of them brings in types or type theory. 18 As we have seen, Wittgenstein raised more than one problem for Russell s theory of judgment, and so for any one of these passages we cannot be sure that Russell is discussing Wittgenstein s objection about nonsense. What is revealing, however, is that, with the one exception to be discussed below, nowhere in his discussions of the problems for the multiple relation theory or his later theories of judgment does Russell bring up type restrictions. If the problem for the multiple relation theory really was a problem about type restrictions on judgment then it is virtually impossible that Russell would not have explained it as such. The exception occurs in some handwritten notes titled Props that were found along with Russell s 1913 manuscript (Russell 1913, Appendix B.I, ). 19 It is likely that these notes were written almost immediately after Wittgenstein s visit in late May. 20 In these notes Russell tries out the ill-conceived idea of a neutral fact : Three objects x,r,y form one or other of two complexes xry or xry.... It looks as if there actually were always a relation of x and R and y whenever they form either of the two complexes, and as if this were perceived in understanding. If there is such a neutral fact, it ought to be a constituent of the positive or negative fact.... 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. (Russell 1913, 195 8) The reference to types occurs in the penultimate remark: There will only be a neutral fact when the objects are of the right types. This introduces great difficulties. (Russell 1913, 199) These notes are very sketchy, and so it is probably a mistake to give them a lot of weight. Nevertheless, despite Russell s explicit reference to types, I think these notes actually support the interpretation of Wittgenstein s objection that I would like to defend. To see why, let s now turn to this interpretation.

17 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT THE UNITY OF JUDGMENT As I said earlier, the problem that Wittgenstein raised in the objection about nonsense is an internal problem for the multiple relation theory. It is directed at the core of Russell s theory of judgment, the idea that judgment is a multiple relation between a subject and several terms. As a start in deciphering this problem, let s take a look at what Wittgenstein says in Notes on Logic immediately prior to presenting his objection: When we say A judges that, etc., then we have to mention a whole proposition which A judges. It will not do to mention only its constituents, or its constituents and form but not in the proper order. This shows that a proposition itself must occur in the statement to the effect that it is judged. For instance, however not-p may be explained, the question What is negated? must have a meaning. (Wittgenstein 1961b, 96) The last sentence is helpful. Suppose we gave a multiple relation theory of negation, i.e. a theory in which we analyze a does not bear R to b as Not (a,b,r). This treats negation as a three-place relation holding between a, b, and R. Following Wittgenstein s suggestion, let s now ask: in a does not bear R to b, what is negated? Given our multiple relation theory of negation, the answer is that a,b and R are negated but this answer does not make any sense. It makes no sense to negate two objects and a relation. Only propositions can be negated. This shows that a whole proposition has to be mentioned in the analysis of a does not bear R to b its logical form must be Not (arb). Now let s ask the same question about judgment, i.e. in A judges that a bears R to b what does A judge? According to the multiple relation theory, the answer is that A judges a, b, and R. But just as in the case of negation, this answer does not make sense. Judgment is not something that can occur between a subject and two objects and a relation. A committed multiple relation theorist might simply deny this she might insist that our intuitions are not a good guide to the nature of judgment and that in fact it makes perfect sense to say that A judges a, b, and R. Wittgenstein s very next remark in Notes on Logic addresses this reply: In A judges (that) p, p cannot be replaced by a proper name. This is apparent if we substitute A judges p is true and not-p is false (Wittgenstein 1961b, 96). I think Wittgenstein s point is that judging that p is always judging that p is true. This means that we can rephrase the question What

18 138 PETER W. HANKS does A judge? as What does A judge to be true?. And now the answer that A judges that a, b and R are true obviously makes no sense. The collection of a, b, and R is not the sort of thing that can be true or false. Only a proposition can be judged to be true a collection of items, even if they are of right number and variety of types, is not the sort of thing that can be true or false and hence not the sort of thing that can be judged. This shows why Wittgenstein s objection is not really about types or type restrictions. Even if the terms of a judgment meet all the requirements necessary for making up a possible fact, as long as those terms are disunified and separate they are not something that can be judged. When Wittgenstein says that any correct theory of judgment must show that it impossible to judge nonsense, by nonsense he does not mean something that violates type restrictions. Rather, he means something that is not capable of being true or false. And the collection of a, b, and R, considered as a disunified collection, is not something that can be true or false. Against this reading one might point out the example of nonsense provided by Wittgenstein in Notes on Logic, i.e. the table penholders the book. Isn t this nonsense precisely because the table, the penholder and the book are all individuals? Yes the table, the penholder and the book are not of the right types to be combined into a state of affairs. Nevertheless, I think there is a different point behind this example. If the relation R is treated as a term in the judgment complex, i.e. as a separate ontological unit on par with the individuals a and b, then there is no important difference between the collection of the table, penholder and the book and the collection of a, b, and R. To use Russell s terminology, if R appears in the judgment as a term as opposed to a relation that relates then the collection of a, b, and R is not something that can be judged. When R is a term, a R s b is just as nonsensical as the table penholders the book. On the other hand, if R is treated as a relation that relates then this problem disappears. And since R can only relate entities of the appropriate types, type restrictions on the terms of judgment will be met automatically. The real point of Wittgenstein s objection is that what is judged must be a unified proposition, not a mere collection of terms. Once this requirement is met the satisfaction of type restrictions comes for free. This is the sense in which there is an indirect connection between Wittgenstein s objection and type restrictions.

19 RUSSELL S MULTIPLE RELATION THEORY OF JUDGMENT 139 What about the formulation of the objection in the June 1913 letter to Russell? Wittgenstein s point that A judges that a is in relation R to b must imply arb arb is just the idea that what is judged must be the sort of thing that is true or false. The problem for the multiple relation theory is that the collection of terms a, b, and R does not meet this requirement. He goes on to emphasize that this implication must hold without the use of any other premiss (Wittgenstein 1995, 29). This may be an allusion to Russell s use of logical forms in the 1913 version of the theory. In any case, it is important to see that his point is quite general and does not depend on the specifics of any particular version of the multiple relation theory. As in the case of negation, the nature of judgment itself requires that what is judged must be a unified proposition. Hence, A judges that a is in relation R to b must directly and immediately imply arb arb. Any analysis of A judges that a is in relation R to b on which additional premises of any sort at all are required in order to secure this implication would thus fail to capture the nature of the judgment relation. It is worth remarking that Wittgenstein drops the reference to additional premises in his later and presumably more considered statements of the objection in Notes on Logic and the Tractatus. This is another reason to doubt the Somerville/Griffin reading of the objection. If the whole problem for Russell was that he could not add premises about types to the analysis of judgment without undermining the support for the theory of types then it is puzzling in the extreme why Wittgenstein should leave out any mention of additional premises in his later presentations of the objection. This account of Wittgenstein s objection also finds support in Russell s remarks on belief in The Philosophy of Logical Atomism: Suppose I take A believes that B loves C. Othello believes that Desdemona loves Cassio. There you have a false belief. You have this odd state of affairs that the verb loves occurs in that proposition and seems to occur as relating Desdemona to Cassio whereas in fact it does not do so, but yet it does occur as a verb, it does occur in the sort of way that a verb should do. I mean that when A believes that B loves C, you have to have a verb in the place where loves occurs. You cannot put a substantive in its place. Therefore it is clear that the subordinate verb (i.e. the verb other than believing) is functioning as a verb, and seems to be relating two terms, but as a matter of fact does not when a judgment happens to be false. This is what constitutes the puzzle about the nature of belief. (Russell 1918, 90)

20 140 PETER W. HANKS The idea that the subordinate verb must function as a verb is that it must express a relation that relates. The subordinate verb cannot be interpreted as a substantive, i.e. as the name of a relation that occurs as a term. The problem for the multiple relation theory is that loves is treated as a substantive; loves is taken to be a name for the relation of loving. A bit later on Russell writes: There are really two things that one wants to notice in this matter that I am treating of just now. The first is the impossibility of treating the proposition believed as an independent entity, entering as a unit into the occurrence of the belief, and the other is the impossibility of putting the subordinate verb on a level with its terms as an object term in belief. That is a point in which I think that the theory of judgment that I set forth once in print some years ago was a little unduly simple, because I did then treat the object verb as if one could put it as just an object like the terms, as if one could put loves on a level with Desdemona and Cassio as a term for the relation believes. (Russell 1918, 91 92) The second of Russell s two points is, I think, the main thrust of Wittgenstein s objection about nonsense. The reason why Wittgenstein s objection had such a profound impact on Russell should now be clear. Russell himself puts the problem quite clearly in the passage just quoted from The Philosophy of Logical Atomism. Judgment and belief cannot be relations to propositions because of the problems for propositions, i.e. the problems about false propositions and the correspondence theory of truth. These problems were consequences of Russell s account of propositional unity. On the other hand, judgment and belief cannot be multiple relations to the constituents of propositions because what is judged or believed must be capable of being true or false, and mere collections of terms are not true or false because they lack the requisite unity. In the face of this dilemma it is understandable why Russell told Lady Ottoline Morrell that he felt ready for suicide (Russell 2002, 449). The whole point of Russell s multiple relation theory was to avoid the problems for propositions brought on by the need for propositional unity. Wittgenstein s objection showed Russell that the very same demand for unity that plagued his account of propositions also applied to his account of judgment. We can now make sense of Russell s claim that you cannot make a map-in-space of a belief. This is another expression of the dilemma of the previous paragraph. If there were a map of Othello believes that Desdemona loves Cassio it would either have to look like this (Russell 1918, 90):