How Wittgenstein Defeated Russell

7/30/2019 How Wittgenstein Defeated Russell

1/26

Synthese (2007) 154: 121146 Springer 2007

DOI 10.1007/s11229-005-0195-y

PETER W. HANKS

HOW WITTGENSTEIN DEFEATED RUSSELLS MULTIPLERELATION THEORY OF JUDGMENT

ABSTRACT. In 1913 Wittgenstein raised an objection to Russells multiple rela-

tion 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 impos-sible for a judgement to be a piece of nonsense. (Russells 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 Wittgensteins objection is in fact a form of the problem of

the unity of the proposition.

1. INTRODUCTION

In 1913 Wittgenstein raised an objection to Russells multiple rela-

tion theory of judgment that was to have a devastating and lasting

effect on Russells 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 (Witt-

genstein 1961a, 65). The problem for Russell was that the multiple

relation theory did not satisfy this requirement.

Wittgensteins objection has been widely interpreted to be a point

about type restrictions on judgment.1 One can judge that an indi-

vidual 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 indi-

viduals results in nonsense. The problem for Russell is supposed to

be that nothing in his multiple relation theory rules out such non-

sensical combinations. Furthermore, Russell cannot add conditions

to the analysis of judgment that would rule out nonsensical combi-nations without undermining the support for the theory of types.2

This is a natural interpretation of Wittgensteins objection, and

for a long time I accepted it. However, I am now convinced that


2/26

122 PETER W. HANKS

this interpretation is mistaken. The problem Wittgenstein raised for

Russell has at best merely an indirect connection to type restric-

tions on judgment. The real problem that Wittgenstein raised was

essentially the same one that was fatal for Russells theory of prop-ositions. This is the problem of the unity of the proposition. The

whole point of the multiple relation theory was to avoid the prob-

lems of unity that plagued Russells 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 Russells views on

propositions and judgment between 1903 and 1913. This will be cru-

cial for understanding the effect that Wittgensteins objection had on

Russell. Then I will turn to Wittgensteins objection and I will stan-

dard 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 books 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 real-

izing the difficulties that he had tried my view and knew it wouldnt work. I

couldnt 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 shouldnt 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 reasonsfor 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.


3/26

RUSSELLS MULTIPLE RELATION THEORY OF JUDGMENT 123

All that has gone wrong with me lately comes from Wittgensteins attack on my

work I have only just 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 dont 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 fundamentalwork in philosophy. (Russell 1998, 282)

Wittgensteins criticism was directed at Russells multiple relation

theory of judgment, the centerpiece of the Theory of Knowledge

manuscript. According to the multiple relation theory, when a sub-

ject 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 Russells writingsin 1906. Up until then Russell believed in propositions and held

that judgment is a two-place relation between subjects and propo-

sitions. Russells propositions were structured entities composed out

of objects, properties and relations. In 1903 in Principles of Math-

ematics Russell wrote that a proposition, unless it happens to be

linguistic, does not itself contain words: it contains the entities indi-

cated 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 Russells 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 prop-

osition that A is different from B, the relation of difference relates


4/26

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 noconnection 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 differ-

ence occurs as a relation that relates, whereas in the set {A, B, therelation of difference} the relation of difference occurs merely asa term. In this set the relation of difference is just another entity

alongside A and B. The proposition that A is different from B can-

not, therefore, be identified with the set {A, B, the relation of differ-ence}. The proposition has a unity that is lacking in this set owingto 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 Ais different from B. This proposition must be the fact or state of

affairs of As being different from B. Russells early view was that

true propositions are identical with facts. A true proposition is iden-

tical 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 rela-

tion 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 rela-

tion 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 proposi-

tion 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 Russells account of propositionsprecluded him from holding a correspondence theory of truth. In

a correspondence theory a proposition is true just in case it corre-

sponds to a fact. But in order for the correspondence theory to get


5/26


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 cor-

respondence theory of truth for propositions. Russell was forced tosay that truth and falsity are unanalyzable, non-relational properties

of propositions; in a famous remark he wrote that some proposi-

tions 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 prob-

lems. 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 objec-

tive falsehoods as he called them, subsist but do not exist.5

For obvious reasons Russell was dissatisfied with this ontol-

ogy. In My Mental Development Russell wrote that the desire

to avoid Meinongs 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 hiscontextual definition of the definite description the golden moun-

tain 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 rela-

tion 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 strat-

egy 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


6/26

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 cor-

responding fact and false otherwise.

In the early 1906 version of the multiple relation theory, which he

did not endorse, Russells 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 relationof the mind to the various other terms with which the judgment is

concerned (Russell 1910, 180). Russells 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 intro-

spection 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 false-

hood 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 refine-

ments into the multiple relation, culminating in 1913 with theinclusion of logical forms as constituents of judgments. Russells log-

ical forms are very general facts, e.g. the fact that something bears

some relation to something. Russell symbolized this as R(x, y). In


7/26


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 judg-

ment. Russells 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 andCassio 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 per-

formed 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 thesame 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 Wittgensteinraised in his objection.

3. WITTGENSTEINS OBJECTION

When we turn to Wittgensteins objection we can ignore logical

forms and the later refinements in Russells theory of judgment. As

will become clearer later on, this is because Wittgensteins objec-

tion goes right to the heart of the multiple relation theory - theidea 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:


8/26

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 the-

ory. (Wittgenstein 1995, 29)

The objection reappears later on in Notes on Logic, from Septem-

ber 1913:

Every right theory of judgment must make it impossible for me to judge that

this table penholders the book (Russells theory does not satisfy this require-

ment.) (Wittgenstein 1961b, 96)

And again in the Tractatus:

5.5422 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. (Russells theory does not satisfy this requirement.) (Wittgenstein 1961a,

65)

As I noted earlier, commentators on these remarks have taken Witt-

gensteins 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 ofloving in the judgment that Desdemona loves Cassio. But one can-

not 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 indi-

viduals, two individuals and a dyadic relation of individuals, etc.).

This makes sense of Wittgensteins remark in the June 1913 letter

that from 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 can-

not 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 isnt 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 thefollowing implication holds:

A judges that aRb aRb aRb


9/26


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 implica-tion 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 mul-

tiple 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 abouttype distinctions depend on facts about which judgments are pos-

sible 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., (x) is meaningless since x

and x are both propositional functions of individuals, x results

in nonsense when applied to something that is not an individual.

In this way the propositional function x places restrictions on the

sorts of arguments to which it can be significantly applied. In other

words, x has a range of significance. Russell could make a similar

point about the judgment relation. He could reply to Wittgensteinthat 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.


10/26

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 essen-

tially to hold that the judgment relation, or rather various judg-

ment relations, occur at various positions in the type hierarchy.To see this more clearly, lets 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

1, 2, . . . , m are types, there is a type (1, 2, . . . , 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 vari-

ables and monadic predicates of individuals, e.g. the predicate in-

stantiates, 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 four-

place predicate whose arguments are three individual constants and

a dyadic predicate of individuals. Abbreviating a sequence of m is

with the numeral m, this judgment predicate is type (3,(2)). Sup-

pose 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 Bs judgment, Judges

is type (2,(3,(2)),2,(2)).Iterated judgments about judgments will involve successive judg-

ment relations of successively more complicated types.

Where f, a1, a2, . . . , am are variables or constants, in order for

f (a1, a2, . . . , am) to be well-formed f must be of type (1, 2, . . . , m),

where 1, 2,..,m are the types of a1, a2, . . . , am respectively. This

means that Judges(Othello, Desdemona, Iago, Cassio) is not well-

formed 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 stan-

dard reading of the objection it is inconceivable that Russell wouldnot 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


11/26


nonsensical judgment by appealing to the type hierarchy if the type

hierarchy itself is founded on facts about which judgments are pos-

sible and which are not.

This objection is based on a mistaken conception of the relationbetween 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 deter-

mines 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 rela-

tion 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 catego-

ries. This kind of view would have been anathema to a realist likeRussell. That a is an individual and R a relation is an entirely objec-

tive matter that is settled independently of what we are or are not

capable of judging. Russells 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 Russells 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 Wittgensteins objection had such a pow-

erful 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 individu-

als 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 judg-ment 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


12/26

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 significantlyas argument, a function cannot occur significantly. Take, e.g., x is a man, and

consider x is a man. Here there is nothing to eliminate the ambiguity that

constitutes x, 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

Russells point is that it is the ambiguity of the propositionalfunction that makes it impossible to say (or judge) that x 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

Wittgensteins objection on Russell. In particular, it cannot explain

why Wittgensteins objection eventually forced Russell to give up

the multiple relation theory.15 Suppose that the problem really isone 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 hier-

archy of logical types was to have both indirect and direct sup-

port (Whitehead and Russell 1927, 47). The indirect support came

from its ability to resolve the paradoxes. Post-1910 and the multi-ple relation theory, the direct support (supposedly) came from facts

about what can or cannot be judged. If the standard reading were

correct, then Wittgensteins 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 doesnt show that type theory is inconsistent

or completely unmotivated. And more importantly, it doesnt show

that there is anything wrong with the multiple relation theory itself.

Whatever the problem was that Wittgenstein raised, I think it has tobe a problem that was internal to the multiple relation theory, not a

problem about the connection between the multiple relation theory

and Russells other commitments.


13/26


Defenders of the standard reading might reply that during this

period Wittgenstein was pressing another line of argument against

Russells theory of judgment and that Russell eventually abandoned

the theory either because of this other objection or because ofthe cumulative effect of Wittgensteins attacks.16 Another important

objection that Wittgenstein raised to the multiple relation theory

is targeted specifically at Russells use of logical forms in the 1913

manuscript. This objection is a clear precursor to the Tractar-

ian 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 thename of a form. Accordingly we can also not say that a relation which in cer-

tain cases holds between things holds sometimes between forms and things. This

goes against Russells theory of judgment. (Wittgenstein 1961b, 99)17

As we have seen, in Theory of Knowledge Russell identified the logi-

cal 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 along-

side 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 Russells conception

of logical form, and so Wittgensteins objection to this conception

may have been instrumental in Russells 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 sup-

posed problem about types is not really a problem for the mul-

tiple relation theory itself at all. And the objection about logical

forms was specific to the 1913 version of the multiple relation the-

ory. This objection could only have forced Russell to reject that par-

ticular 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 faceof new problems. At best, then, the objection about logical form

could only have undermined Russells confidence in the theorys lat-

est version. Even when taken together, these two objections present


14/26

134 PETER W. HANKS

no threat to the basic idea that judgment is a multiple relation, and

so they cannot account for Russells 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, nei-

ther Wittgenstein nor Russell ever mentioned type restrictions or

type theory in their numerous published and unpublished discus-

sions of the problems for Russells theory of judgment. In Notes

on Logic the objection to Russells multiple relation theory appears

in section I, Bi-Polarity of Propositions. Sense and Meaning. Truth

and Falsehood (Wittgenstein 1961b, 93). Wittgenstein does not dis-

cuss 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 proposi-

tions, (Wittgenstein 1995, 33, my emphasis). In the Tractatus the

objection to the multiple relation theory occurs in 5.5422. 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 the-

ory in the 5.54s these remarks occur in the context of Wittgen-steins 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 andSomething 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 Socra-

tes, Mortality and (x, y)1(x,y) I want a theory of types to tell me that Mor-

tality 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, 245)

There is no mention of Russells 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


15/26


letter to Russell, dated January 21, 1913, Wittgenstein reports the

death of his father.) It is highly speculative to suppose that Wittgen-

stein was concerned with exactly the same problems in his January

letter and in his May meeting with Russell. For this reason, I amdubious of any interpretation of Wittgensteins objection that places

great weight on this letter. Of course, we should make use of any

available texts in the effort to understand Wittgensteins objection.

But surely the most weight should be put on those texts in which

Wittgenstein or Russell explicitly discuss the problems for Russells

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 Wittgensteins

objection Russell never mentioned type restrictions. Types are also

absent from Russells 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 ofthe 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, 8991)

The idea that belief cannot be mapped in space is a clear allusion

to the multiple relation theory. In the 1913 manuscript Russell pre-

sented 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, 19067. The problem at issue is the prob-

lem 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 PhilosophicalEssays (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


16/26

136 PETER W. HANKS

of types in this part of Russells introduction to the Tractatus. There

are other places scattered throughout Russells later writings where

he discusses Wittgensteins influence on his theory of judgment and

belief, and none of them brings in types or type theory.18

As wehave seen, Wittgenstein raised more than one problem for Russells

theory of judgment, and so for any one of these passages we can-

not be sure that Russell is discussing Wittgensteins 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 rela-

tion 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 Russells 1913 manuscript (Russell 1913,

Appendix B.I, 19599).19 It is likely that these notes were written

almost immediately after Wittgensteins 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 under-

standing. If there is such a neutral fact, it ought to be a constituent of the pos-

itive 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, 1958)

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 Russells explicit refer-

ence to types, I think these notes actually support the interpretation

of Wittgensteins objection that I would like to defend. To see why,lets now turn to this interpretation.


17/26


4. THE UNITY OF JUDGMENT

As I said earlier, the problem that Wittgenstein raised in the objec-

tion about nonsense is an internal problem for the multiple relationtheory. It is directed at the core of Russells theory of judgment, the

idea that judgment is a multiple relation between a subject and sev-

eral terms. As a start in deciphering this problem, lets 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 constitu-

ents and form but not in the proper order. This shows that a proposition itselfmust 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 Wittgensteins sug-

gestion, lets 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 propo-

sitions 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 lets 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. Wittgensteins 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 substi-tute A judges p is true and not-p is false (Wittgenstein 1961b, 96).

I think Wittgensteins point is that judging that p is always judging

that p is true. This means that we can rephrase the question What


18/26

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 col-lection 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 Wittgensteins 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 non-

sense 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 non-

sense provided by Wittgenstein in Notes on Logic, i.e. the table

penholders the book. Isnt this nonsense precisely because the

table, the penholder and the book are all individuals? Yes thetable, 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 differ-

ence between the collection of the table, penholder and the book

and the collection of a, b, and R. To use Russells 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 Rs 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 Wittgensteins 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 thesense in which there is an indirect connection between Wittgensteins

objection and type restrictions.


19/26


What about the formulation of the objection in the June 1913 let-

ter to Russell? Wittgensteins point that A judges that a is in rela-

tion 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 problemfor 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 pre-

miss (Wittgenstein 1995, 29). This may be an allusion to Russells

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 Wittgensteins objection also finds support in

Russells 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 judg-

ment happens to be false. This is what constitutes the puzzle about the natureof belief. (Russell 1918, 90)


20/26

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 isthat 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 couldput 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, 9192)

The second of Russells two points is, I think, the main thrust of

Wittgensteins objection about nonsense.

The reason why Wittgensteins 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 Philos-

ophy of Logical Atomism. Judgment and belief cannot be relationsto 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 Russells account of

propositional unity. On the other hand, judgment and belief can-

not 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 understand-

able why Russell told Lady Ottoline Morrell that he felt ready for

suicide (Russell 2002, 449). The whole point of Russells multiple

relation theory was to avoid the problems for propositions brought

on by the need for propositional unity. Wittgensteins 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 Russells 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 Othellobelieves that Desdemona loves Cassio it would either have to look

like this (Russell 1918, 90):


21/26


Or like this21:

But it cannot be the first since Desdemona does not love Cassio and

so there is nothing that corresponds to the bottom half of the map.

And it cannot be the second because Desdemona, Cassio and love,

taken separately, are not the sorts of things to which Othello can be

related by the relation of belief. Russell concludes that belief must

be a new sort of thing, a new beast for our zoo, not another mem-

ber of our former species but a new species (Russell 1918, 91), and

he credits Mr. Wittgenstein for the discovery of this fact.Finally, lets return to Russells remarks on neutral facts in

Props (Russell 1913, 1959). In these notes we can see Russell hav-

ing exactly the kind of reaction to Wittgensteins objection that we

should expect him to have if this reading of the objection were cor-

rect. Since a neutral fact is a constituent of the positive or negative

fact,(195), the neutral fact that aRb still exists even if a does not

bear R to b. Neutral facts thus solve the problem about falsity that

defeated Russells early account of propositions. And since neutralfacts are unities, if [j]udgment involves the neutral fact, (197), then

Russell can accommodate the need for unity in judgment. Further-

more, since [t]here will only be a neutral fact when the objects are

of the right types, (199), the satisfaction of type restrictions on the

terms of judgment comes for free. Of course, as Russell notes, this

introduces great difficulties, (199). He doesnt elaborate on these

difficulties, but it is not hard to see what they might be. The whole

idea of a neutral fact is metaphysically suspect. Russell might just

as well have reintroduced Meinongian objective falsehoods.


22/26

142 PETER W. HANKS

5. CONCLUSION

The problem of the unity of the proposition, both in its origi-

nal form and in the form of Wittgensteins objection, resonatedthroughout the rest of Russells philosophical work. In the wake

of Wittgensteins objection Russell spent a long time without a

clear view on judgment. In the 1918 lectures on logical atomism

we see him clinging to the multiple relation theory despite the

strong misgivings engendered by Wittgensteins objection (Russell

1918, 89). By 1919 he had adopted what he took to be the account

of judgment in the Tractatus. Propositions are reinstated, but now

they are mind or language-dependent entities, word-propositionsor image-propositions (Russell 1919, 308). His account of the

unity of these propositions is essentially Wittgensteins picture the-

ory of meaning. Russell coupled this with a rejection of the subject,

another Tractarian doctrine. Subsequent to this his abiding concern

was to reconcile belief sentences with the principle of extensional-

ity (e.g. Whitehead and Russell 1927, Appendix C; Russell 1940,

2517). But these later developments in Russells views are the topic

for another occasion. My objective in this paper has been to correct

a misunderstanding of Wittgensteins objection to the multiple rela-

tion theory and to explain why it had such a devastating effect on

Russell.

NOTES

1 See (Black 1964), (Giaretta 1997), (Griffin, J. 1964), (Griffin 1985), (Griffin

1985/86), (Griffin 1991), (Hyder 2002), (Hylton 1984), (Hylton 1990), (Landini

1991), (Pears 1977), (Pears 1978), (Pears 1989), (Somerville 1980), (Stevens 2003),

(Tully 1988), (Wahl 1986), (Weiss 1995), and (Wrinch 1919).2 The connection between Wittgensteins objection and the foundations for the

theory of types was originally drawn by Stephen Somerville (Somerville 1980)

and has been enthusiastically endorsed by Nicholas Griffin (Griffin 1985), (Griffin

1985/86), (Griffin 1991).3 Published posthumously as (Russell 1913).4 Russell does not use the word term to mean a linguistic expression. Anything

that can be a constituent of a proposition is a term. Whatever may be an object

of thought, or may occur in any true or false proposition, or can be counted as

one, I call a term. This, then, is the widest word in the philosophical vocabulary.

I shall use as synonymous with it the words unit, individual and entity (Russell

1903, 39). I will follow Russell in this use of the word term.5 In On Denoting (Russell 1905) Russell confusingly reversed his earlier termi-

nology, using subsists for the more exclusive property, i.e. the property possessed


23/26


by only those things that actually exist: Thus the present King of France, the

round square, etc., are supposed to be genuine objects. It is admitted that such

objects do not subsist, but nevertheless they are supposed to be objects (Rus-

sell 1905, 38, Russells emphasis). In the earlier Principles of Mathematics and

his series of papers on Meinong (Russell 1904), however, Russell held that the

round square subsists but does not exist. I will stick with the more natural, ear-

lier terminology.6 See also (Russell 1913, 109).7 Russell says as much in The Philosophy of Logical Atomism: The logical form

is just the same whether you believe a false or a true proposition. Therefore in

all cases you are not to regard belief as a two-term relation between yourself and

a proposition, and you have to analyse up the proposition and treat your belief

accordingly (Russell 1918, 89).8 See the discussion of permutative and non-permutative judgment complexes,

(Russell 1913, 144148). (Griffin 1985/86) is helpful in unraveling these portions

of Russells manuscript.9 If I understand him, Hochberg takes this to be the main point of Wittgensteins

objection. See (Hochberg 2000, 6).10 See note 1.11 There is a controversy over whether the hierarchy of types in Principia Math-

ematica should be understood merely linguistically, i.e. as hierarchies of differ-

ent kinds of expressions, or also ontologically, i.e. as hierarchies of expressions

as well as different kinds of entities, e.g. universals. According to the linguistic

interpretation, for Russell all individuals and universals belong to a single, all-

encompassing type. See (Klement 2004) and (Landini 1998) for the linguistic

interpretation, (Hylton 1990), (Linsky 1999), and (Quine 1953) for the ontolog-

ical interpretation. I wish to remain officially neutral on this issue. I can do

so because, on my reading of Wittgensteins objection, the issue of how best to

understand Russells type hierarchy is irrelevant. However, for the purposes of

this paper I will adopt the ontological interpretation. This is required in order

for the standard reading of Wittgensteins objection in terms of type restrictions

to even get off the ground. Since Russell clearly held that judgment is a mul-

tiple relation between subjects and entities, for type restrictions on judgment to

make sense it must be that entities, and not merely expressions, come in differ-

ent types. Stevens adopts the linguistic interpretation and argues that the point

of Wittgensteins objection was that the multiple-relation theory, if it was to be

successful, required the imposition of the type part of the ramified hierarchy onto

Russells ontology in exactly the way that the multiple-relation theory had been

intended to avoid, (Stevens 2003, 26).12 Cf. (Black 1964, 302) and (Wrinch 1919, 325). Citing Wrinch, Nicholas Griffin

acknowledges the cogency of this reply to Wittgenstein: Wrinch is alone in noting

that there are already type restrictions on the terms of the judging relation in this

it doesnt differ from any other relation in Russells formal system. It is clear that

such restrictions could be used to ensure that nonsense could not be judged were it

desirable to ensure this, (Griffin 1985, 240). However, speaking for himself and not

Russell, Griffin endorses a different strategy: An alternative reply, and one which I

would favour, would be simply to admit nonsensical judgments, (Griffin 1985, 240).

Building on the work of Somerville, he goes on to argue that Russell could not make


24/26

144 PETER W. HANKS

this reply without undermining the theory of types: ...if Wittgensteins significance

requirement is let go [i.e. if Russell allows nonsensical judgments] the propositions

which emerge will not be regimented by type theory, (Griffin, 1985, 243). In other

words, Griffin argues that Russell could not have made Griffins preferred reply to

Wittgensteins objection. Of course, this establishes nothing about whether Russell

could have made the reply that Griffin does not prefer, i.e. the one in which type

restrictions are imposed by the judgment relation itself. However, contrary to what

he acknowledges in his comment on Wrinch, in a subsequent paper Griffin suggests

that this reply was unavailable to Russell: The task is to distinguish the garbled

beliefs and exclude them. Now if one simply relies upon the belief-relation to do the

ordering, there seems to be nothing which makes it impossible to believe that loves

Desdemona Cassio, (Griffin 1985/86, 136). But he does not explain why he thinks

this is so.13 I suspect that a similar reply can be made to the circularity posed by

Somerville and Griffin.14 This quotation is part of the direct inspection argument for the type part of

ramified type theory (Whitehead and Russell 1927, 4748). Type distinctions are

drawn by direct consideration of propositional functions, rather than by consid-

eration of what can or cannot be judged. Stevens presses this point against the

Somerville/Griffin interpretation of Wittgensteins objection. See (Stevens 2003,

23). In a similar vein, Weiss argues that Russells account of permutative and

non-permutative complexes in Theory of Knowledge shows that it would be

wrong to think of the multiple relations theory as providing the foundations of

Russells logical theory, (Weiss 1995, 2745).15 Russell did not explicitly renounce the multiple relation theory until 1919 in a

paper titled On Propositions: What They Are and How They Mean, (Russell

1919). One year earlier in The Philosophy of Logical Atomism he was still cling-

ing to the multiple relation theory, but with strong misgivings (see Russell 1918,

8992). As will become clearer later on, as I see it Russells misgivings about the

multiple relation theory in The Philosophy of Logical Atomism are an expression

of Wittgensteins objection about nonsense.16 Thanks to an anonymous referee for suggesting this reply.17 Some have taken this line of attack to be identical to the one contained

in Wittgensteins remarks on nonsense. See (Landini 1991), (Pears 1977), (Pears

1978), and (Pears 1989). While the views expressed in the two objections fit

together as pieces in Wittgensteins early philosophical system, it is quite an inter-

pretive leap to see him making a point about Russells conception of logical form

in his remarks about nonsense. Furthermore, there are strong textual reasons for

thinking that these are two separate points. The objection about logical form and

the nonsense objection appear in different sections of Notes on Logic. And in

the Tractatus the nonsense objection appears in the context of Wittgensteins dis-

cussion of molecular propositions (in the 5.5s), long after his discussions of log-

ical form (in the 2s and 3s).18 See (Russell 1919, 3067), (Whitehead and Russell 1927, Appendix C), (Russell

1940, 2524), and (Russell 1959, 11719).19 Thanks to an anonymous referee for bringing these notes to my attention.20 See the editors notes to Appendix B.I, (Russell 1913, 195).


25/26


21 Cf. a similar diagram in Russells notes appended to the Theory of Knowledge

manuscript (Russell 1913, Appendix A.4, 186). See (Carey 2003) for a discussion

of Russells diagrams of judgment.

REFERENCES

Black, M.: 1964, A Companion to Wittgensteins Tractatus, Cambridge University

Press, Cambridge.

Carey, R.: 2003, The Development of Russells Diagrams for Judgment, Russell23,

2741.

Church, A.: 1974, Russellian Simple Type Theory, Proceedings of the American

Philosophical Association 47, 2133.

Giaretta, P.: 1997, Analysis and Logical Form in Russell: The 1913 Paradigm, Dia-

lectica 51, 273293.

Griffin, J.: 1964, Wittgensteins Logical Atomism, Oxford University Press, Oxford.

Griffin, N.: 1985, Russells Multiple Relation Theory of Judgment, Philosophical

Studies 47, 213247.

Griffin, N.: 1985/86, Wittgensteins Criticism of Russells Theory of Judgment, Rus-

sell5, 132145.

Griffin, N.: 1991, Was Russell Shot or Did He Fall?, Dialogue 30, 549553.

Hochberg, H.: 2000, Propositions, Truth and Belief: The Wittgenstein-Russell Dis-

pute, Theoria 66, 340.

Hyder, D.: 2002, The Mechanics of Meaning, Walter de Gruyter, Berlin.

Hylton, P.: 1984, The Nature of the Proposition and the Revolt Against Idealism,

in R. Rorty, J.B. Schneewind, and Q. Skinner (eds.), Philosophy in History, Cam-

bridge University Press, Cambridge, 375397.

Hylton, P.: 1990, Russell, Idealism, and the Emergence of Analytic Philosophy,

Oxford University Press, Oxford.

Klement, K.: 2004, Putting Form Before Function: Logical Grammar in Frege,

Russell, and Wittgenstein, Philosophers Imprint 4, 147.

Landini, G.: 1991, A New Interpretation of Russells Multiple-Relation Theory of

Judgment, History and Philosophy of Logic 12, 3769.

Landini, G.: 1998, Russells Hidden Substitutional Theory, Oxford University Press,

Oxford.

Linsky, B.: 1999, Russells Metaphysical Logic, CSLI Publications, Stanford.

Pears, D.: 1977, The Relation Between Wittgensteins Picture Theory of Proposi-

tions and Russells Theories of Judgement, Philosophical Review 86, 177196.

Pears, D.: 1978, Wittgensteins Picture Theory and Russells Theory of Knowledge,

in H. Berghel, A. Hbner, and E. Khler (eds), Wittgenstein, The Vienna Cir-

cle, and Critical Rationalism: the Proceedings of the 3rd International Wittgenstein

Symposium, HlderPichlerTempsky, Vienna, 101107.

Pears, D.: 1989, Russells 1913 Theory of Knowledge Manuscript, in C. W. Savage

and C.A. Anderson (eds), Rereading Russell: Essays on Bertrand Russells Meta-

physics and Epistemology, Minnesota Studies in Philosophy of Science, 12, Univer-

sity of Minnesota Press, Minneapolis, 169182.

Quine, W.V.O.: 1953, Logic and the Reification of Universals, in From a Logical

Point of View, Harvard University Press, Cambridge, Mass., 102129.


26/26

146 PETER W. HANKS

Russell, B.: 1903, Principles of Mathematics, Norton, New York.

Russell, B.: 1904, Meinongs Theory of Complexes and Assumptions (III), Mind

13, 509524.

Russell, B.: 1905, On Denoting, Mind14, 479493.

Russell, B.: 1906, On the Nature of Truth, Proceedings of the Aristotelian Society 7,

2849.

Russell, B.: 1910, On the Nature of Truth and Falsehood, in Philosophical Essays,

Simon and Schuster, New York, 1966, 147159.

Russell, B.: 1913, Theory of Knowledge, in E. Eames (ed.), The Collected Papers of

Bertrand Russell Vol. 7, George Allen & Unwin, London, 1984.

Russell, B.: 1918, The Philosophy of Logical Atomism, in D. Pears (ed.), Open

Court, La Salle, Illinois.

Russell, B.: 1919, On Propositions: What They Are and How They Mean, in R.

Marsh (ed.), Logic and Knowledge, Capricorn Books, New York, 1971, 285320.

Russell, B.: 1940, An Inquiry into Meaning and Truth, Penguin, New York, 1962.

Russell, B.: 1944, My Mental Development, in P. Schilpp, The Philosophy of Ber-

trand Russell, Northwestern University Press, Chicago, 320.

Russell, B.: 1959, My Philosophical Development, Simon and Schuster, New York.

Russell, B.: 1998, Autobiography, Routledge, London.

Russell, B.: 2002, The Selected Letters of Bertrand Russell: The Private Years, 1884

1914, N. Griffin (ed)., Routledge, London.

Somerville, S.: 1980, Wittgenstein to Russell (July, 1913). I am Very Sorry to Hear

. . . My Objection Paralyses You, in R. Haller and W. Grassl (eds.), Language,

Logic, and Philosophy: Proceedings of the 4th International Wittgenstein Sympo-

sium, HlderPichlerTempsky, Vienna, pp. 182188.

Stevens, G.: 2003, Re-examining Russells Paralysis: Ramified Type-Theory and

Wittgensteins Objection to Russells Theory of Judgment, Russell23, 526.

Tully, R.: 1988, Forgotten Vintage, Dialogue 27, 299320.

Wahl, R.: 1986, Bertrand Russells Theory of Knowledge, Synthese 68, 383407.

Whitehead A. and Russell, B.: 1927, Principia Mathematica, 2nd Edition, Cam-

bridge University Press, Cambridge.

Wiess, B.: 1995, On the Demise of Russells Multiple Relation Theory of Judge-

ment, Theoria 61, 261282.

Wittgenstein, L.: 1961a, Tractatus Logico-Philosophicus, D. Pears and

B. McGuinness (trans), Routledge, London.

Wittgenstein, L.: 1961b, Notebooks, 19141916, G.E.M. Anscombe (trans), Harper,

New York.

Wittgenstein, L.: 1995, Ludwig Wittgenstein: Cambridge Letters, B. McGuinness and

G.H. von Wright (eds.), Blackwell, Oxford.

Wrinch, D.: 1919, On the Nature of Judgment, Mind28, 319329.

Department of Philosophy

University of Minnesota Twin Cities

Minneapolis MN 55455-0310

USA

E-mail: [email protected]

Documents

How Wittgenstein Defeated Russell