“It is quite conceivable that judgment is a very complicated phenomenon”: Dorothy Wrinch, nonsense and the multiple relation theory of judgement

ABSTRACT

In her paper “On the Nature of Judgment”, published in 1919 in Mind, Dorothy Wrinch aimed at understanding how Russell’s multiple relation theory of judgement might be made to work. In this paper we will focus on Wrinch’s claim that on the theory it is impossible, as it should be, to judge nonsense. After having presented the prima facie objection to the theory created by nonsense and what we can take her solution to such a problem to imply (§1), we will show how Wrinch can resist the two main objections that have been moved to such a solution, whether as explicitly attributed to Wrinch or discussed without mentioning her. The conclusion will be, contrary to what one might be tempted to think, that even if there might be reasons to take the multiple relation theory as doomed, Wrinch was the first to show us that nonsense is not one of those reasons.

KEYWORDS:

• Wrinch
• nonsense
• the multiple relation theory of judgement
• type restrictions
• Russell

According to the so-called multiple relation theory of judgement, attitudes such as judgement and belief are not two-place relations between the subject of the attitude and the object of the attitude, i.e. a unified proposition. Rather, judgement is a multiple relation and it is the subject of the attitude who operates the unifying. For example, according to the traditional, propositional account, Inge's judgement that Adrian loves Beatrix is a relation of judgement between Inge and the proposition that Adrian loves Beatrix. By contrast, according to the multiple relation theory, in its simplest form, the judgement is a relation among Inge, Adrian, Beatrix and something corresponding to the relation of love and it is Inge, with her very act of judgement, who unifies the other relata. The multiple relation theory, in this simple or in more complicated versions, was famously first put forward as an option by Russell in 1906 (“Nature of Truth”, 46), who then explicitly started endorsing it in 1910 (“Nature of Truth and Falsehood”; PM, §II.III), while also immediately starting to refine and modify it (The Problems of Philosophy, §12). Famously as well, Wittgenstein criticized the view in 1913. Russell never finished The Theory of Knowledge, where the theory would have to be spelled out in full detail, but he might still be taken to have defended the view in 1917 and 1918, despite recognizing that the theory had serious problems (Mysticism and Logic, f.41; The Philosophy). In a publication of July 1919, Russell then abandoned the theory explicitly, taking it to be “impossible” (“On Propositions”, 27).¹

Within that very period from Wittgenstein’s objections to Russell’s explicit abandonment of the theory, Dorothy Wrinch was also busy thinking about judgements under Russell’s guidance.² In 1917, she presented in Cambridge, to the Moral Science Club, a paper on the multiple relation theory. Russell sent Wrinch some remarks on her paper (Linsky, “Logic”, 44) and the paper was published in Mind in July of 1919. It is not known what Russell’s remarks were. Neither is it known whether Wrinch and Russell discussed Wittgenstein’s objections. It is known that Russell, Wrinch and a few others discussed together the manuscript of Wittgenstein’s TLP, where his objection to the multiple relation theory appears phrased as follows:

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. (Russell’s theory does not satisfy this requirement.)

But Wrinch’s paper was published a few months before such discussions, which are known to have happened in September 1919 (Senechal, I Died for Beauty, 78). Be that as it may, without attributing it to anybody in particular, in her paper Wrinch discussed the apparent problem created by nonsense, a problem that Russell himself never discussed explicitly. Her solution to this apparent problem for the multiple relation theory will be the focus of this paper. The objective will not be to focus on whether this apparent problem really was Wittgenstein’s point or on whether Wrinch’s solution is genuinely compatible with Russell’s system and further aims about relations, truth, the foundation of type theory, understanding, etc. Rather, the purpose is to understand whether the multiple relation theory of judgement can overcome the nonsense objection in the way Wrinch suggests. After having presented the objection and what we can take her solution to imply (§1), we will then consider two objections that have been moved to such a solution, whether as explicitly attributed to her (§2) or discussed without mentioning Wrinch (§3). The upshot will be that her solution can indeed resist the objections. As Wrinch maintains, “[i]t is quite conceivable that judgment is a very complicated phenomenon” (“Nature of Judgment”, 320), and the multiple relation theory of judgement is known to be subject, at least apparently, to many other objections, some of which are in fact discussed by Wrinch herself in her paper.³ But in this paper we will focus only on nonsense. So, together with Wrinch, I will not argue that the multiple relation theory is surely a genuine contender to the traditional propositionalist view or make the even stronger claim that the theory is true. I will only show that, at least concerning nonsense, Wrinch was the first to show us that the theory “might be made to work” (“Nature of Judgment”, 319).

1. The nonsense objection and Wrinch’s solution

Wrinch’s main aim in her paper is to show how the multiple relation theory can be extended to also account for molecular, universal, and existential judgements (“Nature of Judgment”, 319). Take, for example, Inge’s judgement that if Adrian comes, Beatrix goes. Clearly, Wrinch tells us (“Nature of Judgment”, 320), we cannot account for it in terms of a relation holding among Inge, Adrian, something corresponding to coming, Beatrix, and something corresponding to going, for otherwise we would not be able to distinguish it from Inge’s judgement that Adrian comes or Beatrix goes. Moreover, Wrinch continues, if we want the multiple relation theory to be an “other theory” (“Nature of Judgment”, 319) with respect to the propositional account, we cannot introduce as relata propositional unities corresponding to Arian comes and Beatrix goes. But, she maintains, a suggestion that is compatible with the aims of the multiple relation theory is that “the form of the proposition be introduced” (“Nature of Judgment”, 321): Inge’s molecular judgement can be analysed as having as components Inge, Adrian, something for coming, Beatrix, something for going, the form fx ⊃ gy, and the evaluator (“Nature of Judgment”, 321) or, to use Ostertag’s more up-to-date terminology (“The Analytic Tradition”, 569), the assignment x = Adrian; y = Beatrix; f = coming; g = going. Having introduced the form as a component to account for molecular judgements, concerning atomic judgements, such as Inge’s judgement that Adrian loves Beatrix, Wrinch states that “[s]ometimes one feels a desire for uniformity … and it may seem more suitable that the simple propositions … should have a uniform form with molecular propositions” (“Nature of Judgment”, 321). But she also adds that ‘[t]his argument for uniformity has … little cogency' (“Nature of Judgment”, 321) and that the theory should be judged neither in terms of simplicity nor of uniformity (“Nature of Judgment”, 328), so that she is open to the possibility of taking only some judgements to have forms as components. Still, the form has been introduced as a component for at least some judgement relations, so Wrinch feels the urge to stress how introducing it does not mean introducing propositional unities: the logical form, she writes, “is a very colourless thing indeed. It is a few blank spaces with a bare logical structure uniting them … the kind of way in which it is a unity does not in the least imply any propositional unity” (“Nature of Judgment”, 324).

It is at this very point that Wrinch introduces the notion of nonsense. To keep supporting her claim that the form does not imply any propositional unity, she adds:

[a]ll that is implied is that [the form] is so constructed that if we operate on it, we shall not get nonsense … And this is an interesting point because it has been advanced as a criticism that on this theory it is possible to judge nonsense.

(“Nature of Judgment”, 324)

Wrinch does not go into further detail about the nonsense objection. She moreover takes it to be in need of no argument that “it is essential for any theory of judgment that [to judge nonsense] should be impossible” (“Nature of Judgment”, 324–5) and she does not explain why it might seem that on the theory it is possible to judge nonsense, but the reason is clear. Take again Inge’s judgement that Adrian loves Beatrix. According to the traditional, two-place relation view, the second relatum is a proposition, whose components are Adrian, Beatrix and the relation of love. While Adrian, Beatrix and the relation of love can be put together in a proposition, it is not the case that to any combination there corresponds a proposition. For example, out of Adrian, Beatrix and Carl we cannot obtain a proposition. According to the multiple relation theory, instead, we do not have propositions that create constraints on what combinations can do, so that one might think that on the view when it comes to the relata “anything goes” (Stock, “Wittgenstein on Russell’s”, 71), and so it should be possible for Inge to be related in a relation of judgement to Adrian, Beatrix and Carl. But this is a piece of nonsense.

The key passage in the objection is the move from the fact that on the multiple relation theory we do not have the constraints imposed by propositions to the thesis that on the view when it comes to the relata anything goes and Winch was the first (Griffin, “Russell’s Multiple”, 240) to notice that this is exactly the move that a defender of the multiple relation theory, and Russell in particular, could easily resist. On the simplest version of the multiple relation theory, according to which the relata in the case of Inge’s judgement that Adrian loves Beatrix can be taken to be simply Inge, Adrian, Beatrix and something corresponding to the relation of love,

the difficulty can be got over by simply stating it as a property of judging relations that the types of the constituents do not form an independent set … the nature of J as a judging relation makes the type of suitable arguments for the empty place automatically determinate and gives it in terms of the types of I, a, b … The criticism as to the possibility of judging nonsense we were able to dispose of by a careful statement as to the relations between the types of the constituents of a judgment complex.

(“Nature of Judgment”, 324–8)

Even on the simplest version of the multiple relation theory, it is not the case that anything goes. The constraints that propositionalists see as imposed by there being a proposition as the object of the judgement, can be seen, on the multiple relation theory, as imposed by the logical form of the judging relation itself. If forms are introduced as components (to account, as Wrinch suggests, for molecular judgements), the problem is even easier to solve: it is “clear that it is impossible on this theory to judge nonsense … when the form is introduced” (“Nature of Judgment”, 325). The form which is a component of the judgement relation can be taken to impose the needed constraints.

How do forms impose constraints so as to prevent the possibility of nonsense? As we saw, for Wrinch, the logical form is a few blank spaces with a bare logical structure uniting them. Still, the blank spaces cannot accept everything. Rather, to borrow an image used in another context, each hole in the judging relation is “like a keyhole in which only some things fit … it is more than a gap” (Textor, “Unsaturatedness”, 68). For, Wrinch holds, thanks to Russell’s theory of types, we can take each space to be guarded by one type, so that only things of the right type can fit that space:

Each of the spaces is guarded by one type so that only arguments of certain types can be put in certain spaces (“Nature of Judgment”, 321) … [the form] is so constructed that if we operate on it, we shall not get nonsense; the existence of the types belonging to each space will make that impossible.

(“Nature of Judgment”, 324)

Moreover, since on Russell’s theory of types any relation is anyway so constrained, for somebody defending the theory of types, judgement is not to be seen as in any way special in order to solve the nonsense objection.⁴

Wrinch does not provide us with examples of nonsense ruled out as impossible to judge when the theory of types is taken into account. But at least two and at most three kinds of cases can be taken as considered by Wrinch to be nonsense impossible to judge.

First, if we have as relata Inge, Adrian and Beatrix, the judgement relation imposes that the space left empty in ‘J(I, –, a, b)’ should be occupied by a predicate, or verb, to use her terminology.⁵ Textor has recently phrased the nonsense objection in terms of the need for an explanation of why we need a verb, an explanation “that does not appeal to conventions or arbitrary correlations” (“Judgement, Perception, and Predication”, 292. See also Collins, The Unity, §4). While Wrinch does not consider explicitly the issue as to whether her solution would appeal to conventions or arbitrary correlations, she seems to take the very nature of judgement to make the appearance of arbitrariness fade away. There is no arbitrariness in reserving a place in the judgement relation for a verb because predicating a verb of an ordered array of terms is what judgement is. As she states in another paper on memory and imagination, one thing is to merely have images or objects “to float before the mind” (“Nature of Memory”, 51), another is to have “beliefs … judgments” (“Nature of Memory”, 51). While we can surely entertain, imagine, remember Adrian, Beatrix and Carl, we cannot judge that Adrian, Beatrix and Carl. The “mental events” (“Nature of Judgment”, 327) of judgements, being events of judgements, have to involve “the verb of the proposition” (“Nature of Judgment”, 325) and the form of the judgement relation then has to respect this.⁶

So, first, the judgement that Adrian Beatrix Carl is ruled out as impossible.⁷ But there is more. Not only do we need the right number of relata of the right kinds, we also need them to fill the right spaces: “this relation J is such that the arguments cannot be interchanged freely” (“Nature of Judgment”, 320). Second, also the judgement that Adrian Beatrix loves is ruled out, because something corresponding to an individual cannot fit the hole for something corresponding to a relation and vice versa. As stated in the introduction of PM, “when a function can occur significantly as argument, something which is not a function cannot occur significantly as argument” (50).

These two kinds of case were surely cases Wrinch was thinking about as cases of ruled out nonsense and we do not need any details of the theory of types or to embrace it to agree with Wrinch on these cases. It is sufficient to rely on the much less committal distinction between verbs and relation on the one hand, and singular terms and individuals on the other.

But Wrinch might maybe in fact be taken to have ruled out even more, and this third kind of case would instead depend indeed on the theory of types. Whether she ruled out a third kind of case depends on how we read her “gives it in terms of the types of I, a, b” and “the relations between the types of the constituents of a judgment complex” in the quotation above. One might take this to simply mean that if a and b are individuals, then we need a predicate, and this is the first kind of nonsense we already saw. But we can also instead read it as saying that, according to Wrinch, the hole in ‘J(I, –, a, b)' would be determined by the types of the other relata and then, for example, given the types for Adrian and Beatrix, only a verb whose holes can be fitted by entities of those types would fit the hole in ‘J(I, –, a, b)'. For example, the predicate for set membership would be ruled out.⁸

Whether Wrinch considered as ruled out by type theory all three kinds of case or only the first two,⁹ these three are all the kinds of case of nonsense Wrinch can be taken to have ruled out. In particular, since for Wrinch it is type restriction that establishes when something is nonsense, it cannot happen that something sensical becomes nonsense by substituting something belonging to the same type as what is substituted. Thus, for instance, the example Wittgenstein provides in TLP as an example of nonsense – “to say of two things that they are identical is nonsense” (5.5303) – is not necessarily nonsense for Wrinch. An individual is identical to itself, this is sensical and true, and then we cannot obtain nonsense by substituting a name of one individual for the name of another, if they belong to the same type. All we can obtain is something sensical and false.

How satisfactory is Wrinch’s solution? Few did maintain that Wrinch indeed offered a solution to the problem of nonsense (Griffin, “Russell’s Multiple”, 240; Hanks, “How Wittgenstein”, 129; 143–4, f.12; Linsky, “Logic”, 46).¹⁰ But two objections to her solution can be found: one, put explicitly to Wrinch by Griffin, according to which while her solution works, another, incompatible one is to be preferred (§2); a second one, raised by Trueman to her solution, although Wrinch is not mentioned, according to which the solution she suggests makes the multiple relation theory collapse into the propositional view (§3). In the rest of the paper, we will see that Wrinch has the resources to overcome both objections.

2. Griffin on having to admit nonsense

Griffin maintains that, while Wrinch’s is a genuine solution to the problem of nonsense,¹¹ an alternative solution is to admit nonsense judgements (“Russell’s Multiple”, 240; see also Black, Companion, 302) and Griffin thinks this is to be favoured, as “it is an essential feature of a correct theory of judgment that it permits nonsense to be judged” (“Russell’s Multiple”, 240; see also Lebens, Bertrand Russell, 173–9; Stevens, “Wittgenstein and Russell”, 96). The examples Griffin provides as cases of nonsense that should be allowed to be judged fall into two categories. First:

[j]udgments made by the insane are an obvious class of examples. Someone sufficiently paranoid might believe that he was persecuted by the prime numbers, or that the teapot sneered at him

(“Russell’s Multiple”, 241).

Second, allegedly nonsensical philosophical positions:

it is common for philosophers, Wittgenstein among them, to denounce the views of other philosophers as nonsensical. If nonsense cannot be believed then either the allegedly nonsensical positions are not incoherent as claimed, or else they were never held by anyone. For example, if Ryle was right about mind-body dualism then Descartes' belief that he was a thinking substance was a nonsense judgment; on the verification principle many widely held beliefs are nonsense; similarly the theory of types entails that ‘(∃x)(x ∈ x)' is nonsense

(“Russell’s Multiple”, 241)

The examples Griffin chose makes it clear, though, that he should have in mind a notion of nonsense at least partially different from the one Wrinch was working with, due to type restriction, as Wrinch’s solution to the problem of nonsense in fact allows for the possibility of some of these judgements.¹² As Pap notes within a different context, “the statement ‘my toothaches are always rectangular' does not violate the theory of types” (“Logical Nonsense”, 270, f.2). In the PM theory of types, while it is of course false that toothaches are rectangular, this is sensical, as types do not distinguish kinds of individuals into, for example, animated or not, extended or not, but create a relative hierarchy from individuals to properties and relations of individuals, then to properties and relations of properties and relations of individuals, etc.:

It is unnecessary, in practice, to know what objects belong to the lowest type, … only the relative type of variables are relevant … all that is essential is the way in which other types are generated from individuals, however the type of individuals may be constituted.

(PM, 162)

As Lebens maintains, although he unfortunately does not mention Wrinch in this context,¹³ the multiple relation theory would rule out as nonsense that the teapot sneezed at Inge only if combined with a “particularly robust and ontologically serious type theory” (Bertrand Russell, 176). Only in this case,

[j]ust as a chair can’t marry a table, because of marriage (as that culturally constructed relation is currently configured) has argument places reserved only for human beings, the relational judgment could have certain restrictions on its argument places, to rule out the possibility of type-confused judgments.

(Bertrand Russell, 176)

This is not the PM theory of types Wrinch was working with, which should not be conflated with the much more recent type theoretic semantics with meaning postulates, which can indeed impose, for example, that only singular terms for human beings can fill ‘to marry', or that only terms for animated objects can fit the subject space for ‘to sneeze'. Let’s consider the judgement that the teapot sneered at the subject of the judgement.¹⁴ Any theory of judgement should allow the possibility of judging that the guy sneezed at Inge, and in the paper Wrinch in fact considers how to account for judgements reports that do not involve proper names, but ‘one poet', ‘a rose', ‘everybody', or ‘sweets' (“Nature of Judgment”, 321–2). Since ‘the teapot' is an incomplete symbol involving the same types as the incomplete ‘the guy' and since it is surely sensical to judge that the guy sneered at Inge, the judgement that the teapot sneered at Inge is surely permissible on Wrinch’s type restrictions, which have nothing to do with guys being animated and teapots not being so. Similar considerations apply to many of the cases Griffin presents as potential cases of philosophical nonsense: the judgement that Descartes was a thinking substance is not nonsense for the type restriction Wrinch was working with, and neither, as we saw already, would be Wittgenstein’s example of nonsense in TLP.

These are not all the cases Griffin considers, though. It is true that, as Griffin maintains, the theory of types entails that ‘(∃x)(x ∈ x)' is nonsense, due to ‘∈' not accepting variables of the same type. We saw that there are two ways of interpreting Wrinch’s “gives it in terms of the types of I, a, b”. On the first way, it simply means that if we have individuals we need a predicate. On this interpretation, Wrinch’s solution to the problem of nonsense allows logicians to believe that (∃x)(x ∈ x) and this case is similar to the other Griffin considers. But on the second interpretation, ‘(∃x)(x ∈ x)’ would count as a case of the third kind of nonsense impossible to be judged. Exactly as a and b require that only a verb whose holes can be fitted by entities of their types would fit the hole in ‘J(I, –, a, b)', so the variables in ‘(∃x)(x ∈ x)', being of the same type, put constraints on the hole in the judging relation for the verb such that ‘∈' cannot fit it. Thus, arguably, on this interpretation, for Wrinch, nobody can stand in a multiple relation of judgement with what would correspond to the proposition that (∃x)(x ∈ x), if anything like that can be taken to exist. But would this be a genuine problem for Wrinch’s solution? The problem, according to Griffin, is that that piece of nonsense

was nonetheless believed by numbers of earlier logicians. If nonsensical judgments really are impossible then either no-one ever believed that ‘(∃x)(x ∈ x)' or the theory of types is false. The theory of types … is likely false, yet this refutation seems somewhat swift. The exclusion of nonsensical judgments would be sufficient to refute a number of widely held philosophical doctrines.

(“Russell’s Multiple”, 241)

But Wrinch can indeed allow logicians and anybody else to believe the meta-linguistic ‘that “(∃x)(x ∈ x)”'. The meta-linguistic judgement is not ruled out by type restrictions and Wrinch can hold that this is the only belief one might have concerning ‘(∃x)(x ∈ x)', exactly because it is nonsense and the endeavours of PM can be seen as endeavours at showing that we cannot operate linguistic descent on the perfectly allowable meta-linguitic (false) judgement that ‘(∃x)(x ∈ x)' is true: while we can judge about those signs, even though it might not seem so, we cannot judge what those signs aim at standing for. Since excluding nonsensical judgements is not identical to excluding meta-linguistic judgements such as that ‘(∃x)(x ∈ x)' is true, moreover, refuting type theory is still anything but swift.

Thus, whatever exactly is ruled out by Wrinch’s solution, Griffin does not seem to have provided us with any examples that are able to show once and for all that some judgements ruled out by Wrinch’s solution should instead be allowed. It is then unclear why his solution is to be favoured over Wrinch’s.

3. Trueman on the theory collapsing into the propositional view

Although Trueman does not mention Wrinch, he (“The Prenective View”, 1180–4) discusses the very way out of the alleged problem of nonsense she suggested, and he maintains that such a way out makes the multiple relation view collapse into a two-place propositional view of judgement. Here is his argument to that conclusion.

First, Truman maintains, if the space in ‘J(I, –, a, b)' could be filled by a name or more generally a singular term denoting a dyadic predicate, then substituting a singular term denoting an individual would produce something false, maybe necessarily false, but still sensical. Thus, Trueman maintains, the nonsense objection can be solved with type restrictions only if the hole in ‘J(I, –, a, b)' can only be fitted by a predicate occurring as a predicate, and “[t]o be a dyadic predicate is to have a certain kind of linguistic function … [to] behave in a particular kind of way” (“The Prenective View”, 1183).

What is the linguistic function of a dyadic predicate? This is Trueman’s second point: although he admits that “[i]t is by no means easy to say exactly what kind of function dyadic predicates have” (“The Prenective View”, 1183), he takes the following to be “truistic: part of what it is to have the function of a dyadic predicate is to have two argument places that must be filled or otherwise bound in a complete sentence” (“The Prenective View”, 1183). Thus, Trueman continues, Inge’s judgement that Adrian loves Beatrix is really to be analysed, on the multiple relation theory, as ‘Judges(Inge, Adrian loves Beatrix)' (“The Prenective View”, 1184).

But then, Trueman concludes, in appealing to type restrictions, the multiple relation theory stops being a multiple relation theory: “to recast the multiple-relation theory in this way would be to collapse it back into the dual-relation theory” (“The Prenective View”, 1184), as Inge’s judgement that Adrian loves Beatrix would be a relation holding between Inge and a complex consisting of Adrian and Beatrix related by the relation of love, i.e. a propositional unity.

Wrinch would obviously be dissatisfied with this conclusion. But she did not think that she needed to worry. In her paper, Wrinch did consider explicitly the claims Trueman would later put forward and she held very explicitly that his conclusion can and should be rejected.

Wrinch accepts the second step in Trueman’s argument. She in fact maintains that if the predicate is taken to occur as a predicate, then we would obtain a unity, i.e. a proposition:

Functioning as a verb and not as an ordinary constituent means, it appears, acting as a binder. Acting as a binder of certain constituents means making them a unity. Thus, the criticism seems to be reducible to the criticism that the verb binds the elements of the proposition together into a unity.

(“Nature of Judgment”, 325)

Her acceptance of this step is not surprising: she was probably staying faithful to the Russellian idea that when a predicate occurs as a predicate, it denotes a relation in the act of relating.¹⁵ Still, given the resources she put forward in her paper to deal with other issues, Wrinch had in fact the resources to resist this of Trueman’s steps. As we saw, she in fact added evaluators and also operators (“Nature of Judgment”, 322) like the particularizing operator to render existentially quantified judgements. She thought that evaluators and operators “operate on forms or on partially completed forms” (“Nature of Judgment”, 322) and she also considered explicitly operating on “concepts” (“Nature of Judgment”, 326). Wrinch does not discuss evaluators and operators in relation to how the verb occurs. Still, in considering predicates occurring as predicates as partially filled forms,¹⁶ and in adding an assignment to the spaces left unfilled in the predicate, she could resist Trueman’s claim that when predicates occur as predicates, the argument places are filled or bound: it is one thing to have the evaluation accomplished, i.e. the spaces in the predicate filled by Adrian and Beatrix, i.e. to have that Adrian loves Beatrix, quite another to have the spaces left unfilled together with an evaluation that assigns Adrian and Beatrix to such spaces. Put differently, thanks to her notion of evaluator, Wrinch could maintain that while the linguistic function of a predicate is surely to bound, the predicates as they occur in the scope of ‘to judge' can be taken not to having already done the bounding specified by the evaluator. With her introduction of evaluators, without her realizing this, Wrinch might then be taken to have paved the way for spelling out the Russellian idea that

you have this odd state of affairs that the verb ‘loves' occurs in that proposition and seems to occur as relating … 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.

(The Philosophy, 225)

In any event, Wrinch instead did not reject the second step in Trueman’s argument. Contrary to what Russell thought in 1918, she instead thought that the first step should be completely rejected. For Wrinch, the predicate can and should be taken to occur as an ordinary constituent, i.e. not as having a particular linguistic function:

In the propositional theory of judgment, the verb functions in a special way. But in this theory the verb of the proposition does not function in a special way. And so, an answer to the objection must be attempted; but I think I have a satisfactory answer to make to the criticism. It seems to me that the feeling that it has any cogency as an argument is due to a lingering belief in the unity of propositions. It seems to me that it is only as a deduction from the assumption that propositions are unities that one can hold that the verb must function in a peculiar way … the criticism seems to be reducible to the criticism that the verb binds the elements of the proposition together into a unity. Thus this criticism though it appears to be an objection to the theory and not merely to the assumption on which it is built, viz., that propositions are not unities, is really an objection to our initial assumption, and therefore will not be dealt with here … the objection … [is] due to some remaining vestige of belief in the completeness of propositions.

(“Nature of Judgment”, 325–8)

But if, as Wrinch maintains, the predicate can and should be taken to occur as an ordinary constituent, how is it, then, that if the space in ‘J(I, –, a, b)’ is filled by a singular term for an individual we obtain nonsense and not just simply something (necessary) false? Wrinch would repeat that the space in ‘J(I, –, a, b)' is guarded by types: “only argument of certain types can be put in certain spaces” (“Nature of Judgment”, 321). Put differently, it is types, not the way in which the element occurs or the grammatical shape in isolation from the type, that the spaces and the notion of nonsense are sensitive to and we simply need a predicate (possibly of the right type, given the types of a and b) not a predicate occurring as a predicate.

4. Conclusion

In her paper, Wrinch admits that her considerations “have all the way through been put forward in a very tentative way” (“Nature of Judgment”, 328) and often she does explicitly “leave the further discussion” (“Nature of Judgment”, 324). The problem of nonsense is a case in point. Arguably, Wrinch’s solution raises many questions that Wrinch does not even touch upon. For example, what does it mean, exactly, that “a space is guarded” if it is only “a blank”? Ramsey’s objection to Russell’s multiple relation theory seems to apply to Wrinch too: “to leave it at that … cannot be regarded as satisfactory … it is desirable that we should try to find out more about it” (“Facts and Propositions”, 157). Still, with her tentative claims, Wrinch was the first to state explicitly that nonsense does not have to be taken as a genuine problem for the multiple relation theory, even in its simplest form, according to which the relata in Inge’s judgement that Adrian loves Beatrix can be taken to be simply Inge, Adrian, Beatrix and something corresponding to the relation of love. If forms are introduced as relata, the problem is solved even more easily. Without having to rely on the full theory of types of PM, the theory can indeed rule out as impossible to judge those cases of nonsense that have to be ruled out, while remaining a genuine alternative to the propositional view.

Acknowledgments

Thanks to Landon Elkind and the audience at the 4th TiLPS History of Analytic Philosophy workshop for their useful feedback. Thanks to two anonymous referees for their insightful suggestions. Thanks also to Ray Monk for his “I think you should!” when I told him that I wanted to read further about Russell’s multiple relation theory.

Notes

1 There is no consensus on what the objection(s) raised by Wittgenstein really amount(s) to or on whether and if so when Russell started to perceive Wittgenstein's objection(s) as fatal. The reason Russell adduces in 1919 as to why the theory is impossible is “the rejection of the subject”, (“On Propositions”, 27), his dissatisfaction with any “theory which analyses a presentation into act and object”, (“On Propositions”, 25) but there is no consensus on whether this is the only reason why Russell started to abandon the theory. For these points, see Bostock (Russell’s Logical Atomism, 210–6); Carey (Russell and Wittgenstein); Griffin (“Russell’s Multiple”; “Wittgenstein’s Criticism”); Hanks (“How Wittgenstein”); Landini (“A New Interpretation”); Lebens (Bertrand Russell, §7); McBride (“The Russell-Wittgenstein Dispute”); Pincock (“Russell’s Last”); Sommerville (“Wittgenstein to Russell (July 1913)”); Stevens (“Re-Examining Russell’s Paralysis”; “Russell’s Repsychologising”; “Wittgenstein and Russell”); Zalabardo (“Wittgenstein’s Nonsense”).

2 In 1914 Wrinch attended Russell’s lectures in Cambridge (Senechal, I Died for Beauty, 48). Russell’s lectures were then cancelled, but he started to teach logic and mathematics to a small number of students in London and Wrinch was one of them. It is known that in 1916 Russell discussed with his small class the first volume of PM, in particular the introduction (Senechal, I Died for Beauty, 58), where the multiple relation theory is presented. In 1917 Wrinch did a year of mathematics apprentice in Cambridge formally under Hardy, informally still under Russell (Senechal, I Died for Beauty, 63). In 1918, while Russell was in jail, she brought him books and journal issues in philosophy and psychology (Monk, Bertrand Russell, 525) and they wrote each other various letters and messages and we know that at least one of those messages is about judgement (Senechal, I Died for Beauty, 66).

3 For recent defences of the multiple relation theory of judgement, see Crawford (“Propositional or Non-Propositional Attitudes?”); Hossack (The Metaphysics of Knowledge); Jubien (“Propositions”); Lebens (Bertrand Russell); Moltmann (“Propositional Attitudes without Propositions”). For discussion of Wrinch’s solution to objections other than the one created by nonsense, see Crawford (“Dorothy Wrinch”); Hodes (“Why Ramify?”); Korhonen (“Russell on Negative Judgement”); Lebens (Bertrand Russell, 120; 192–4); Ostertag (“The Analytic Tradition”, 569).

4 Lebens urges that if we take the judgement relata as constrained by types, we end up with the judgement relation itself misbehaving in the hierarchy of types:

a concern about the logical type of the judgment-relation itself. Its logical type will seemingly change in tandem with the logical type of its object-relation. If the object-relation is of type n, then the judgment-relation will have to be of type n+1. But a relation can’t keep shifting its place in the type hierarchy. … it’s not clear that we could make sense of a relation that’s flexible with regard to its logical type, given the strictures of type theory.

(Bertrand Russell, 176)

Wrinch does not even touch upon this issue. But the problem, if genuine, is not one that Wrinch created with her solution to the nonsense objection. Moreover, it is far from clear that this is a genuine problem. First, it is not clear that the judgement relation has to be taken as a relation-term subject to the constraints of the theory of types. So it is not clear that we can speak, as Lebens does, of its logical type changing in tandem with the logical type of its object-relation. Second, the problem might be taken as not genuine even if Wrinch were happy to take the judgement relation to be guarded by types not just in the sense that the gaps in a logical form are guarded by types, but also in the sense that the relation is subject to the type-theoretic constraints as are given in PM for relation-terms. Since she thinks, as we saw, that the theory should be judged neither in terms of simplicity nor of uniformity, maybe she would be happy to hold that we have different judgement relations depending on the types of the relata.

5 This should not be taken to concern only two-place relations. Wrinch was explicit in maintaining that on the multiple relation theory, judgement is a multigrade relation and the point in the text should also be taken to hold “[i]f we had more arguments as, for example, in the judgment ‘a is between b and c' [where] we should have ‘J(I, φ, a, b, c)' and generally ‘J(I, φ, a₁, a₂, a₃ . . . a_n)'”. “Nature of Judgment”, 320.

6 On more recent attempts to defend the multiple relation theory from the objection, as phrased by Collins and Textor, see Sainsbury (“How Can We”); Lebens (Bertrand Russell, §8).

7 While it is not known whether Wrinch ever had access to this example, the considerations in text the apply also to the example that Wittgenstein puts forward in his remark on the multiple relation theory in the Notes on Logic: “Every right theory of judgment must make it impossible for me to judge that this table penholders the book. Russell’s theory does not satisfy this requirement.” Notebooks 1914–1916, 103.

8 There is disagreement about what cases of nonsense Wittgenstein was concerned with in his objections to Russell. Zalabardo, for example, claims that the nonsense relevant to the dispute between Wittgenstein and Russell concerns only cases in which a subordinate verb position is occupied by a particular (“Wittgenstein’s Nonsense”). In his commentary to Wittgenstein’s 5.5422, Black instead for example maintains that on the multiple relation theory there is

nothing to prevent A judging that 2 loves 7, for Russell lays down no condition on the corresponding four-term relation (J, say) that would prevent ‘J(A, 2, loves, 7)’ from making sense. This is W’s objection in 5.442 b. (Russell might have retorted that it is possible to ‘judge a nonsense’ – or, alternatively, might have sought to satisfy W. by imposing further demands on J.).

(Companion, 301–2)

While Black unfortunately does not mention Wrinch, if we can take her to have ruled out also cases of the third kind, her solution can be taken to consist in fact not in imposing demands on J, but in maintaining that loves, like any other relation, is type restricted.

9 In her “Nature of Memory”, Wrinch discusses memories in which there are judgements involved and presents the various forms of these judgements (§3). In that context, Wrinch seems to distinguish the various forms exclusively in terms of the logical form and then the number of properties and relations occurring, not in terms of the types of such relations and properties. Thus that paper seems to foster the claim that only cases of the first two kinds are to be taken as impossible to judge nonsense for Wrinch. Thanks to an anonymous referee for suggesting discussing this passage of Wrinch’s “Nature of Memory” in this context.

10 Also Bostock (Russell’s Logical Atomism, 212) and Pincock (“Russell’s Last”, 119) acknowledge that this is a solution, although they do not mention Wrinch. We do not know whether Russell himself found Wrinch’s solution convincing, but Linsky maintains:

although there is no record of a response from Russell … his close association with Wrinch suggests that he at least encouraged her to publish her thoughts in defense of his position even if he did not accept them in full.

(“Logic”, 46)

Similarly, Lebens maintains:

Wrinch … had been Russell’s research assistant while he was incarcerated for his anti-war agitations. At that time, Russell was still grappling with the [multiple relation theory of judgment] … Though circumstantial, this historical consideration suggests that her work on this topic might bear some relation to Russell’s own deliberations.

(Bertrand Russell, 192)

11 As Hanks (“How Wittgenstein”, 144, f.12) notes, in another paper Griffin (“Wittgenstein’s Criticism”, 136) instead maintains that the one suggested by Wrinch is not a genuine solution to the problem created by nonsense, although, as Hanks notes, Griffin does not explain why he maintains so.

12 Griffin maintains that Russell could not endorse his preferred solution due to his commitment to understanding as a prerequisite of judgement (“Russell’s Multiple”, 240–3). Since here we are not primarily interested in the role of the view in Russell’s further aims and system, there is no need to consider this point. For a classic discussion of the role of understanding in Russell’s development of the theory, see Carey (Russell and Wittgenstein, §2); Pears (“The Relation”); Pincock (“Russell’s Last”).

13 Lebens does consider Wrinch’s account of molecular proposition (Bertrand Russell, §9), but he does not discuss Wrinch when he deals with nonsense (Bertrand Russell, 1; 173–9), but he somehow seems to be in perfect agreement with the way in which I reconstructed Wrinch’s point about nonsense. Lebens distinguishes between believing bla-bla-bla, which he takes to be impossible and thinks it is ruled out by the multiple relation theory, and believing, for example, that my toothbrush is trying to kill me which he thinks should be possible.

14 The case of prime numbers is arguably a bit more complicated, given the nature of numbers according to PM. This issue is orthogonal, though, to the problem at hand.

15 The only philosopher from the early twentieth century who mentioned Wrinch’s paper is Susanne Langer, who mentioned the paper exactly as an example of defence of the thesis that “the verb acts as a sort of logical glue-holding the separable elements of the propositional concept together, and making them the inseparable elements of a proposition”. “A Logical Study”, 121. While Langer’s paper is not on judgement or the multiple relation theory, it is historically interesting to note that on the very same page Langer maintains that “[t]hat verbs have a psychological force is evident from their indispensability in judgment”.

16 i.e. as more of Fregean unsaturated concepts than relating relations where the relating has already happened. While he does not speak about Wrinch in this context, on Wittgenstein’s nonsense objection, Russellian relations as always relating and Fregean unsaturated concepts, see Lebens (Bertrand Russell, 99–101; 148–56) and references there.