how wittgenstein defeated russell
TRANSCRIPT
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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
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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.
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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
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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
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RUSSELLS 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 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
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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
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RUSSELLS 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 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:
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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
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RUSSELLS 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 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.
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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
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RUSSELLS 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 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
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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.
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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
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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
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RUSSELLS 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 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
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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.
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RUSSELLS MULTIPLE RELATION THEORY OF JUDGMENT 137
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
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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.
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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)
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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):
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RUSSELLS MULTIPLE RELATION THEORY OF JUDGMENT 141
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.
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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
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RUSSELLS MULTIPLE RELATION THEORY OF JUDGMENT 143
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
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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).
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RUSSELLS MULTIPLE RELATION THEORY OF JUDGMENT 145
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.
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Department of Philosophy
University of Minnesota Twin Cities
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