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Truth Primitivism and Truth as Correspondence: Some Developments in

Russell’s Theories of Truth

Anssi.korhonen@helsinki.fi

The classical debate on truth gave us the three theories of truth that constitute a large part of the background for contemporary philosophy of truth: the correspondence theory, the coherence theory, and the pragmatist theory. The classical notion of correspondence truth may be found, for example, in Chapter XII of Russell’s The Problems of Philosophy, where we read the following characterizations: ‘a belief is true when there is a corresponding fact, and is false when there is no corresponding fact’; ‘a belief is true when it corresponds to a certain associated complex, and false when it does not’. Whatever else it may involve, the classical notion of correspondence – also known as Cambridge correspondence–at least involves the notion of fact, and does so in a way that renders the theory metaphysically robust rather than innocent.

Russell was one of the chief advocates of the classical notion, but his road to it was far from easy. Originally, he advocated truth primitivism, a position according to which ‘truth and falsehood […] are ultimate, and no account can be given of what makes a proposition true or false’. In this paper, I’ll do several things. Firstly, I’ll provide a sketch of Russell’s version of truth primitivism. This will be done by a comparison with Frege’s views on truth; second, I’ll provide an account of the philosophical reasons that led Russell to reject the earlier account of truth in favour of truth as correspondence. A large part of Russell’s reasons, so I shall argue, had to do with his growing realisations of the implication of truth-primitivism for the problem of the unity of the proposition. Thirdly, I’ll provide an outline of some of the later developments that took place in Russell’s correspondence theories of truth and relate to the multiple-relation theory of judgment and the psychological theory of propositions that he began to work out around 1918–19. The story that is told here focuses on Russell’s attempts to formulate a correspondence theory of truth that (i) accounts for the unity of the proposition and (ii) explains false belief ‘without assuming the existence of the non-existent’.

1. Contemporary philosophy of truth has its origins in the debates on truth that took place in

the early twentieth century and played a prominent role in the development of early analytic

philosophy. To be sure, much of the focus today is on the issue of ‘deflationism’ vs.

‘inflationism’, with the key question commonly formulated in some such terms as ‘Does truth

have a nature?’ ‘Is truth a genuine characteristic?’ and so on. And although people claim to

find the roots of deflationism in Frege and Ramsey, both of whom were major figures in early

analytic philosophy, the focus in the classical debates was elsewhere. But at least we may say

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that our model of what it is to be a substantive or robust theory of truth still comes from the

old debates featuring the familiar trio of theories of truth: the correspondence theory, which

decrees that the truth of what we believe and say consists in the relation of correspondence to

facts; the coherence theory, according to which the truth of a proposition is a matter of its

participation in a system of propositions fulfilling certain conditions; and the pragmatist

theory, which–one version of it, anyway–says that the true is ‘whatever proves itself to be

good in the way of belief and […] for definite assignable reasons’ (William James).

These three theories are the three classical theories of truth, and the arguments built

around them constitute the classical debate on truth. To be sure, the debate, as it is standardly

described, is largely an abstraction, the sort of entity that lives only in textbooks on truth and

epistemology, where the complexities characteristic of philosophers in flesh and blood tend to

get smoothed out. I give you one example here, from Moore’s treatment of truth around 1910;

I shall return to it below, as it is relevant to Russell’s concerns as well. One side of the

classical debate, it is said, is occupied by analytic philosophers defending the correspondence

theory of truth and seeing their task as one of delivering an analysis of a philosophically

pregnant concept in terms of necessary and sufficient conditions:

(*) the belief that p is true if and only if p corresponds with fact.

This is very rough, but even this formulation indicates that advocates of truth as

correspondence saw as their primary task as one of explaining the notions of fact and

correspondence that are in play here, and in a way that throws genuine light on the concept, or

property, of truth; (*) is meant to deliver an analysis of truth in terms of necessary and

sufficient conditions, and this imposes restrictions on whether and when a proposed analysis

is acceptable. These requirements are reflected in some of the standard criticisms of the

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classical correspondence notion of truth: for example, that it is difficult to spell out what the

supposed correspondence is to consist in; that the only notion of fact that is available to us is

conceptually or logically tied to that of a true proposition (statement, etc.), so that (*) will not,

and cannot, give independent insight into the metaphysics of truth; and so on.

These familiar points do reflect views once held by real philosophers. But behind text-

book style generalizations, there is a reality that is rather more varied and heterogeneous.1

Consider what G. E. Moore has to say about truth in his Some Main Problems of Philosophy.2

Starting from a reflection on a particular case, Moore argues that a necessary and sufficient

condition for the truth of a belief is this:

To say that a belief is true is to say that the fact to which it refers is or has being; while

to say that a belief is false is to say that the fact to which it refers is not–that there is no

such fact. (SMPP, p. 267)

Moore then points out that this isn’t quite satisfactory as a definition of truth. One problem is

that according to Moore’s definition, a belief refers to a thing whether or not the belief is true.

If the belief is true, then it refers to a fact which is there, or ‘is present in the Universe’. This

is fine; of course, one can raise all sorts of objections to the idea, but that is immaterial here.

But what does a false belief refer to? As we shall see, this was a major problem for Russell,

and it figures prominently in his thinking about truth and judgment (Moore was not unaware

of it, either). What Moore is immediately concerned with and about, however, is the general

question of what is meant by ‘the fact to which a belief refers’.

1 I said above that I would give just one illustration, but I cannot resist at least mentioning another one, McTaggart’s treatment of truth in Volume I The Nature of Existence (1921). McTaggart is an exception to textbook wisdom in two respects. Firstly, he was an idealist, but nevertheless argued that truth, in the sense in which truth is a characteristic of beliefs, can only be correspondence to a fact. Secondly, he also evaded the analytical task, arguing that the notion of correspondence that is at play here cannot be defined (McTaggart 1921, Chapter II: secs. 9–13).

2 These were lectures that Moore delivered at Morley College, London, in the winter of 1910–1911; they were published in 1953.

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In a given particular case the question is easy enough to answer: the belief that there are

lions refers to the fact that there are lions; the belief that we are now hearing the noise of a

brass-band refers to the fact that we are now hearing the noise of a brass-band; and so on. But,

Moore argues, generalization is not easy. This we see by considering the case of a false belief.

When we say that a belief is false what we mean is not just that “some fact or other is absent

from the Universe” (SMPP, p. 256); what we mean, according to Moore, is that the unique

fact to which the belief refers is absent.

A full definition of truth would thus require that we give a complete and correct analysis

of the event that is happening in someone’s mind when she believes that something is the

case; that is, that we give an analysis or exact definition of what is meant by ‘referring to’, by

talking of the fact to which a belief refers. Moore argues, however, that this is not necessary

for understanding what truth is: “[F]rom the fact that we can’t analyse it, it doesn’t follow that

we may not know perfectly well what the relation is; we may be perfectly well acquainted

with it; it may be perfectly familiar to us; and we may know both that there is such a relation,

and that this relation is essential to the definition of truth” (SMPP, pp. 267–8). And he adds

that we do have this sort of knowledge. Take any belief you like, say, the belief that there are

lions. It’s plain, Moore thinks, that there is one fact, and one fact only, which has being if the

belief is true, and which has no being if the belief is false; and there’s nothing mysterious

about the relation thus characterized. You know full well what belief it is, in the sense that

you know what it is to believe that there are lions. And your knowledge of what belief it is, is

ipso facto knowledge of what the relevant fact is, to wit, the fact that there are lions. And you

see that the relation is such that there are any number of similar belief-fact pairs. And you see,

on reflection that the fact’s being there is both necessary and sufficient for the truth of the

belief, so that a belief is true if there is in the Universe a fact to which it ‘corresponds’ in this

sense. (ibid. pp. 268–9)

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As Moore sees it, then, to grasp this relation of correspondence presupposes that we

grasp the relevant belief-fact connection. And surely this presupposes that we already grasp

what truth is. So, whether or not he believed that one could give a ‘complete and correct

analysis’ of what truth is, he certainly thought that there is a perfectly acceptable

correspondence account of truth that explains correspondence (partly) in terms of truth, rather

than vice versa.

Making full sense of Moore’s conception of truth in SMPP would be a rather delicate

matter–this of course is precisely why text-book wisdom won’t take us very far when our

concern is with the views actually held by actual philosophers. One might even argue that

Moore’s conception exhibits features that make it in some respects similar to present-day

deflationism. But, it also seems, he really was one of the Cambridge friends of

correspondence: a belief is true, if it is, because there is an entity, a fact, to which the belief

stands in an appropriate relation, namely correspondence. Crucially, being one of the

Cambridge friends, he understands ‘fact’ in a metaphysically robust sense:

We may divide all the constituents of the Universe—all things which are, into two

classes, putting in one class those which we can only express by a clause beginning with

‘that’ or by the corresponding verbal noun, and in the other all the rest. Thus we have,

in the first class, such things as ‘the fact that lions exist’ or […] ‘the existence of lions’,

‘the fact that twice two are four’, ‘the fact that I am now talking’, and absolutely all the

immense number of facts which we thus express by phrases beginning with ‘that’. In

short, this class of constituents of the Universe consists of the sort of entities which

correspond (in the sense explained) to true beliefs […]. And this first class of entities–

the class of entities which correspond to true beliefs, certainly constitutes, I think, one

of the largest and most important classes of things in the Universe. (SMPP, p. 296)

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Moore’s views involve complications, but discussing these would be too much of a digression

here. (Very briefly, the interpretative difficulty with Moore’s conception of truth arises from

reconciling his apparently robust understanding of the notion of fact with his insistence that

‘facts’ in his sense are “neither more nor less than what are often called ‘truths’” (SMPP, p.

297)).

Let us now move on to consider Russell. Russell, of course, was another friend of

Cambridge correspondence. In The Problems of Philosophy he summarizes his position on

truth saying that “a belief is true when there is a corresponding fact, and is false when there is

no corresponding fact” (PP, p. 75). What I wish to do now is not so much to dwell on the

details of the classical notion of correspondence as to look at the complex developments

(some of them, anyway) that led Russell to advocate ‘the Cambridge version of

correspondence’.3 Russell was not always a correspondence theorist. As late as 1906 he wrote

to Harold Joachim: ‘I agree of course that the correspondence-theory is absurd, but your

arguments are not those which I should use’.4 This quotation prompts two questions, and it is

with these that I will be concerned here. Firstly, why did Russell think (around 1906) that the

correspondence theory is absurd? Secondly, what made him change his mind on this point?5

2. As Russell’s remark to Joachim indicates, the correspondence theory of truth was by no

means taken for granted by early analytic philosophers. Indeed, if we take a look at late

nineteenth and early twentieth century theorizing about truth, there is a view that was much

more popular, so much so, that it could be regarded, with considerable justification, as the

standard conception of truth in early analytic philosophy. It is the view that truth is an

3 I won’t here pause to consider to what extent the title ‘the Cambridge version of correspondence’ is

justified. 4 Russell’s letter to Joachim, 1 February, 1906; as quoted in Griffin (2007: 225). 5 For Joachim’s reasons for thinking that the correspondence theory is absurd, see Joachim (1906: Chapter I).

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unanalysable, primitive feature of truth-bearing entities. As Candlish and Damnjanovic (2007)

point out, turn of the century philosophers were less concerned with ‘theories of truth’ and the

‘nature of truth’ than they were with the nature of reality, the nature of judgment and the

nature of mind, and their accounts of truth were usually by-products of their commitments

elsewhere. But their relative reticence about truth did have another and rather more interesting

source as well, namely truth-primitivism.

3. A definition of truth in the classical sense should enable us to ‘bring clearly before the

mind the abstract opposition upon which our distinction between true and false depends’

(ONTF, p. 148). In contrast to this, truth-primitivism holds that the distinction does not

depend upon anything and is therefore not amenable to any sort of explanation; truth and

falsity are primitive features of truth-value bearing entities (‘propositions’).

Truth-primitivism is found in the early Moore and the early Russell. It was held by

Frege as well, probably throughout his philosophical career. It doesn’t occupy any prominent

position in their thought, but one context where it can be found – and where it does substantial

philosophical work – is a notorious argument against truth-definitions. Here’s Russell’s

version of the argument, formulated in a paper entitled ‘On the Nature of Truth’ and read to

the Jowett Society at Oxford in June 1905. At the beginning of the paper, Russell levels

various criticisms against the correspondence theory of truth. He then raises a general

difficulty for all purported definitions of truth:

But even supposing some other definition of correspondence with reality could be

found, a more general argument against definitions of truth would still hold good. An

idea is to be true when it corresponds with reality, i.e. when it is true that it corresponds

with reality, i.e. when the idea that it corresponds with reality corresponds with reality,

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and so on. This will never do. In short, if we don’t know the difference between a

proposition’s being true and not being true, we don’t know the difference between a

thing’s having a property and not having it, and therefore we cannot define a thing as

true when it has a certain property such as corresponding with reality. (NT, pp. 493–4)

This argument is from a little known paper by Russell, one that was published only

posthumously. But even if you have not met this particular version of the argument before, it

may still strike you as familiar. If so, that’s probably because you have seen something quite

similar to it in Frege, and even in the same kind of context, namely one where the author is

criticising the definition of truth as the “correspondence of an idea with something real” (CP,

p. 353). Here’s what Frege has to say about such a definition:

[I]n this case it is essential precisely that the reality shall be distinct from the idea. But

then there can be no complete correspondence, no complete truth. So nothing at all

would be true; for what is only half true is untrue. Truth does not admit of more and

less. – But could we not maintain that there is truth when there is correspondence in a

certain respect? But which respect? For in that case what ought we to do so as to decide

whether something is true? We should have to inquire whether it is true that an idea and

a reality, say, correspond in the specified respect. And then we should be confronted by

a question of the same kind, and the game could begin again. So the attempted

explanation of truth as correspondence breaks down. And any other attempt to define

truth also breaks down. For in a definition certain characteristics would have to be

specified. And in application to any particular case the question would always arise

whether it were true that the characteristics were present. So we should be going round

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in a circle. So it seems likely that the content of the word ‘true’ is sui generis and

indefinable. (ibid.)

Frege’s argument has a specific target. But the underlying point is meant to be an entirely

general one that dismisses all putative definitions of truth, this time on the grounds that the

application of a would-be definition to a particular case somehow reintroduces the concept of

truth, so that the definition, being circular, cannot be put to use. Now, one might reply to this

criticism by saying that it confuses the meaning and criterion of truth. Putting that aside,

however, there’s the further complaint that it is far from obvious why the application of a

definition would have to take the form that Frege says it does: why can’t we determine

whether the content <snow is white> ‘corresponds with reality’ simply by finding out whether

snow is white? Similarly, what justifies the immediate transition, as in Russell’s argument,

from ‘an idea corresponds with reality’ to ‘it is true that it corresponds with reality’? And

even if we can give reasons here, it is not obvious that they show that a definition of truth

would generate a vicious regress (as in Russell’s version) or vicious circle (as in Frege’s).

Let’s start by considering Frege’s argument and its conceptual environment a little

further. The argument against truth-definitions is just one of several points that Frege makes

about truth. Here are the others. Firstly, there is a pair of claims about the truth-predicate (or

better, truth-operator) and its redundancy:

It is also worth noticing that the sentence ‘I smell the scent of violets’ has just the same

content as the sentence ‘It is true that I smell the scent of violets’. (CP, p. 354)

… denn was wir mit dem Satze “Der Gedanke, dass 3>2 ist, ist wahr” sagen wollen,

können wir einfacher mit dem Satze ”3 is grösser als 2” sagen. Wir brauchen also hierzu

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das Wort “wahr” gar nicht. Und wir erkennen, dass durch dies Prädikat dem Sinne

eigentlich gar nichts hinzugefügt wird. (NS, s. 251) (…for what we want to say with the

sentence ”the thought that 3 > 2 is true” we could say more simply with the sentence ”3

is greater than 2”; we don’t need the word “true” here at all. And we see that through

this predicate nothing at all is added to the sense.)

Um etwas als wahr hinzustellen, brauchen wir kein besonderes Prädikat, sondern nur

die behauptende Kraft, mit der wir den Satz aussprechen. (NS, p. 251) (To present

something as true, we don’t need a special predicate but only the assertoric force with

which we utter the sentence.’)

An explicit truth predicate (or truth operator) affects neither the sense (content) nor the force

of a sentence. It makes no difference to sense, if instead of ‘I smell the scent of violets’ I say

‘it is true that I smell the scent of violets’, and hence what is said using the latter sentence can

be said more simply by means of the former. And to present something as true, that is, to

assert it, a truth operator or predicate is neither necessary nor sufficient. Truth and assertion

are closely interwoven, but the connection is not effected through an explicit use of ‘true’; and

even if we use one (‘it is true that I smell the scent of violets’), assertion doesn’t reside in it

but in the force with which we utter the sentence.

This pair of claims seems to make Frege an early advocate of the redundancy

conception of truth. This association would be mistaken, however, as is shown by Frege’s

second point about, namely that there is an exceedingly close connection (we might say: an

internal one) between predication and truth:

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All the same it is something worth thinking about that we cannot recognize a property

of a thing without at the same time finding the thought that this thing has this property

to be true. So with every property of a thing there is tied up a property of a thought,

namely truth. (CP, p. 354)

And this in turn leads straight away to the third point. This is Frege’s account of judgment,

which provides the necessary rationale and clarification of what he says in the previous

quotation. To recognize a property of a thing is to judge that the thing has that property. But

judgment is the acknowledgement of the truth of a thought (CP, p. 356); hence, we cannot

recognize a property of a thing without finding the thought that this thing has this property to

be true. Frege argues that we cannot do the former without ‘at the same time’ doing the latter,

but in fact the connection is tighter than what this formulation suggests: we cannot do the

former without doing the latter because to do the former is just to do the latter: to recognize

that a thing has a property is (identity) to acknowledge the truth of the thought that the thing

has the property.

Frege’s argument against truth-definition is a corollary to his conception of judgement.

A definition of truth, Frege writes in ‘Thoughts,’ is a specification of certain characteristics.

Thus we have, schematically:

(Tr) A is true =df A has the characteristic F.

(Tr), according to Frege, cannot provide an independent insight into the concept of truth, or

something’s being true, an insight that could be put to use to find out whether a particular

thought is true. To do that, we would have to determine whether is F. But to ‘recognize’

that is F (or isn’t F), is to judge that is F (or isn’t F); and to judge that is F (or isn’t F)

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is to recognize the truth of the thought that is F (or the truth of the thought that isn’t F).

So, what the truth-driven conception of judgment brings out is the primacy (in some sense yet

to be specified) of truth over property-possession, and it is this that undermines the possibility

of truth definitions, rendering all putative such definitions viciously circular. It isn’t enough

for Frege’s argumentative purposes just to say – as he does in the above quotation – that ‘with

every property of a thing there is tied up a property of a thought, namely truth’. Given a

sufficiently liberal ontology of truth-bearers, even a correspondence theorist might agree with

this. The real bottom-line presupposition underlying the argument is the identification of facts

with true propositions; or more accurately, as it’s not specifically the notion of fact that calls

for clarification here, the ontological grounding of property possession in true propositions–of

course, property possession includes relations as well.

Although the point is metaphysical, Frege usually formulates it in epistemic terms: to

judge that something is the case, or is a fact, is to acknowledge the truth of a proposition, just

as Frege says. Another way is metaphysical: a thing’s having a property consists in the truth

of the proposition that the thing has the property. This is approximately how Russell puts the

point in the quotation above, where he argues that ‘if we don’t know the difference between a

proposition’s being true and not being true, we don’t know the difference between a thing’s

having a property and not having it’; the point is not really about our knowledge (or

understanding) but about the ontology of predication.

4. Let’s now consider the early Russell’s version of truth-primitivism in more detail. Truth

cannot be defined, and hence whatever nature there’s to the concept, this must be directly

apprehended; at least these were the options available to Russell. The point is epistemological,

or methodological, but it does have ontological consequences. Consider Russell’s best-known

allusion to truth primitivism, his comparison of truth and falsehood with the colours of roses:

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It may be said–and this is, I believe, the correct view–that there is no problem at all in

truth and falsehood; that some propositions are true and others false, just as some roses

are red and others white. […] Thus the analogy with red and white roses seems, in the

end to express the matter as nearly as possible. What is truth, and what falsehood, we

must merely apprehend, for both seem incapable of analysis. (CPBR, pp. 473–4)

The last sentence formulates truth-primitivism: truth and falsehood cannot be analysed, but

must be accepted as ‘indefinable’, and hence the only way to grasp the difference between the

two is to ‘see’ it, the way that we just see the difference between the colours of roses.

Now, whether or not the analogy actually presupposes this, it at least strongly suggests

that the two cases share a common structure; that truth is a property of a true proposition in

the way that a determinate colour is a property of a rose of that colour. Nevertheless, much of

what the early Russell says about truth elsewhere implies a rather different conception, one

according to which truth in the fundamental sense is not a property of propositions but is to be

understood some other way. And I think this different conception was his real view on truth.

Or, to put the point more cautiously, there were quite fundamental elements in his

metaphysics of propositions awareness of which drew him towards the not-a-property-

conception of truth. Much of what he says on the topic is quite confused and shows him in the

process of struggling towards a coherent position, rather than possessing one, but at least the

direction in which his thinking about truth was moving is sufficiently clear to permit

articulation. Again, comparison with Frege will be helpful.

5. Frege had a simple argument for the conclusion that truth (in the fundamental sense) is not

a property of truth-bearers (what he called ‘thoughts’): since truth is content-redundant, ‘the

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thought that 5 is a prime number’ says no more than ‘5 is a prime number’; hence in ascribing

truth to a thought we aren’t predicating truth of a thought–but are in fact passing from sense to

reference (SM, 164). Thus, although judgment is acknowledging the truth of a thought, this

does not take the form of acknowledging that a thought has the property of truth, but

possesses the sui generis form of an assertion.

Russell couldn't use this straightforward argument, because he didn’t think that ‘it is

true that...’ and ‘... is true’ are content-redundant.6 Nevertheless, he did accept Frege’s

conclusion that truth in the fundamental sense is not a property of truth-bearers (but is to be

understood some other way).

This conception informs Russell's argument against truth-definitions, but it's more

explicit in PoM. The metaphysical import of Russell's truth-primitivism centres around the

notion of external relation. Whatever else may be involved in it, the ‘externality’ of relations

at least rejects the idea that the holding of a relation implies complexity in its relata; the idea,

that is, that when a relation–any relation–holds between (distinct) entities, that’s because the

respective qualitative natures of the entities make it so. As against this, Russell held that the

holding of a relation is just a brute fact involving, apparently, nothing beyond the relation and

its relata. In this framework, it’s natural to analyze even property-possession in terms of

external relations. Consider a rose (call it Rose), which is of a specific colour (say red). In

Russell’s view, that’s not because Rose has the property of being red but because an

appropriate external relation holds between two entities, Rose and redness.7

6 ‘Consider […] what it is we mean when we judge. At first sight, we seem to mean that a certain proposition

is true; but “p is true” is not the same as proposition as p, and therefore cannot be what we mean’ (MTCA, p. 463). Cf. PoM, §478: ‘[I]t seems doubtful whether the introduction of truth-values marks any real analysis. If we consider, say, “Caesar died,” it would seem that what is asserted is the propositional concept “the death of Caesar;” not the “truth of the death of Caesar.” This latter seems to be merely another propositional concept, asserted in “the death of Caesar is true,” which is not, I think, the same proposition as “Caesar died.”’

7 This analysis is not absolutely forced on Russell, though, and in PoM he appears to be somewhat of two minds on the issue. In §216 he states explicitly that ‘the so-called properties of a term are, in fact, only other terms to which it stands in some relation; and a common property of two terms is a term to which both stand in the same relation’. That all propositions are relational in character is also implied by his well-known view, introduced in PoM, that the unity of a proposition is a matter of ‘relating relations’. In §53, on the other hand, he

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Given the relational analysis of property possession and predication, the question

whether truth is a property of true propositions becomes this: if a proposition, p, is true, is that

because p stands in some external relation to truth?

To answer the question, let’s start by considering another one, which Russell raises in

§52 of PoM: what logical difference is expressed by the grammatical difference between

verbs (as in ‘Fenton killed Buckingham’) and verbal nouns (as in ‘killing no murder’). ‘By

analyzing this difference’, Russell argues, ‘the nature and function of the verb will appear’.

Since he holds that this ‘nature and function’ is intimately connected with truth, there’s a

chance that by considering the former we will come to see what he thought about the latter.

Besides truth, there’s another concept that is closely related to the distinction between

verbs and verbal nouns, that of assertion. Russell explains:

By transforming the verb, as it occurs in a proposition [“Caesar died”], into a verbal

noun [‘the death of Caesar’], the whole proposition can be turned into a single logical

subject, no longer asserted, and no longer containing in itself truth or falsehood. (ibid.)8

So, the proposition indicated by “Caesar died” is asserted and contains its own truth or

falsehood, whereas “the death of Caesar” is a mere logical subject, which is not asserted but

is, rather, an entity, about which something can be asserted (for example, that it’s true). Now,

states that subject-predicate propositions are distinguished by their non-relational character. As far as I can see, the latter view is not inconsistent with Russell’s other metaphysical commitments including the vexing issue of unity. Nevertheless, in the text I will assume that Russell accepted the relational analysis of predication.

8 Russell’s explanation of the difference is somewhat careless. Propositions in his sense don’t consist of linguistic expressions but their worldly entities–entities that may be regarded, among other things, as the meanings of linguistic expressions. Thus it’s not verbs and verbal nouns that occur in propositions but entities indicated by such expressions. Speaking the way he does, Russell is just using a shorthand formulation, as it would be both tedious and unnecessary to formulate the point in precise terms, provided that the basic point about what sort of entities the constituents of propositions are is kept in mind.

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the problem here is that assertion, though Russell needs the concept, turns out to be deeply

problematic within Russell’s metaphysical-cum-logical framework.9

The problem here arises from Russell’s deep-seated conviction that absolutely every

entity there is, is capable of being a logical subject; that is, for every entity, there are

propositions that are about it. The problem with the proposition indicated by “Caesar died” is

that it seems to break this rule: once you turn it into a logical subject (to speak somewhat

loosely) the proposition ceases to be asserted: for instance, if I say, ‘Caesar died is a

proposition’, I don’t assert that Caesar died.

From a Fregean perspective, this problem is resolved by insisting that an asserted

proposition can, indeed, be made into a logical subject. The presence or absence of assertion

doesn’t affect propositional identity, and hence what’s asserted in one context may very well

be unasserted in another. On the other hand, that a proposition occurring as a logical subject

isn’t asserted is only to be expected, as long as we keep in mind what assertion is: to assert

something is to present it as true, and if I say (assert) ‘Caesar died is a proposition’, I don’t,

indeed, assert that Caesar died.

So, Frege indicates a way out of the difficulty. Russell wasn’t blind to the distinction

between assertion and what is asserted, but his discussion of ‘propositions’ and ‘propositional

concepts’ shows that he had difficulties in fitting it into his metaphysical framework.

Russell’s way of drawing the distinction is not so far from how Frege conceived of it in

Begriffsschrift. Frege explained there that judgment consists in two elements: assertion plus

judgeable content. This distinction is made explicit in Frege’s logical language, where a

judgment is written as ‘ ’; this consists of a vertical stroke or ‘content stroke’, which

9 Russell needs the conception of assertion primarily to make sense of inference. Inference is grounded in the

relation of implication, as q can be inferred from p only when p implies q. This is not yet sufficient though. What more is needed is assertion; if p is not merely true in fact but is flagged as such (‘ p’ to use the symbol that Russell would later adopt from Frege), and if similarly for ‘p implies q’ (‘ p implies q’), we can then flag q true as well (‘ q’), i.e., we can infer q from ‘p’ and ‘p implies q’.)

17

indicates that what comes after it is a ‘combination of ideas’ (that is, a unity) and thus capable

of being judged, and a horizontal stroke or ‘judgment stroke’, which indicates that the

combination of ideas (the symbol for) which comes after it is, or is asserted to be true or to be

a fact. Frege explains that in his logical language there is only one predicate, ‘…is a fact’,

whose function is thus to turn a mere content into a judgment (see the explanations in sections

2 and 3 of Begriffsschrift). Translated into Russellian vocabulary, the symbol

is to be understood as an external relation between a propositional concept–like “the death of

Caesar”–and truth; an appropriate Russellian reading of the symbol would thus be ‘the death

of Caesar is a truth’ (letting ‘ ’ stand for the death of Caesar).

Frege would later discard this explanation of the symbolism (though not the symbolism

itself, or the basic point it’s meant to underline); this was partly on the grounds that assertoric

force doesn’t reside in a special predicate but in the form of assertoric sentences, a point that

we have already. From Russell's point of view, on the other hand, the difficulty is this: he is in

a position to account for the problematic notion of asserted proposition by distinguishing, in

an asserted proposition, the two elements of assertion and propositional content. But then he

will have difficulties in understanding ‘ p’ except as indicating an external relation in which

p stands to some entity when p is asserted. And yet he doesn't want to have this. The question

is: what element of assertion–asserted proposition–does this construction miss that Russell

thinks should be accounted for?

To be sure, some of the uses to which Russell wants to put ‘assertion’ can be understood

in the usual ‘Fregean’ way, including, crucially, the point that assertion is needed to escape

Lewis Carroll’s puzzle about inference (cf. PoM, §38). And the point he makes in §52 that

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where a propositional concept has an external relation to truth, assertion proper somehow

contains its own truth or falsehood could be taken as an acknowledgement, similar to Frege’s,

of the sui generis nature of truth ascriptions.

Russell’s discussion of truth, however, assumes an altogether new direction when he

explains that assertion in his sense is not a psychological but logical notion and that in the

logical sense only true propositions are asserted (in §478 he criticizes Frege for allowing

psychological elements to intrude in his description of judgement as the recognition of truth).

What Russell has ultimately in mind in his discussion of assertion, I suggest, is the idea that

true propositions are ontological grounds for external relations; it is this that explains why he

forges a connection between assertion and truth, and why he thinks that propositional

concepts and external relations won’t do the trick here:

[A]ssertion is not a term to which p, when asserted, has an external relation; for any

such relation would need to be itself asserted in order to yield what we want. (PoM,

§478)

Russell’s point here, I take it, is that the holding of an external relation calls for an

explanation or identification of an ontological ground; and only an asserted proposition–in the

sense of an assertion that involves ‘verb’ as opposed to a verbal noun–will do here, a point

that he spells out elsewhere by means of the regress argument.

To be sure, once the model of external relations is ruled out, there’s precious little that

Russell can do by way of explaining what is involved in the truth of a proposition: the

analogy with the colours of roses suggested in Meinong’s Theory turns out to be seriously

misleading as to the form of truth-ascriptions, and the notion of assertion, as it is used in PoM,

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cannot offer much help either, once it has been lifted out of its original context and purged of

‘psychological elements’.

6. One role, then, that propositions play in Russell’s philosophy around 1903–6 is that of

ontological ground for external relations. But Russell needed propositions for another purpose

as well, a much more familiar one, namely that of objects of propositional attitudes.

The early Russell follows a well-established tradition when he argues that a

‘propositional attitude’ is a binary relation between a subject and a single entity, which is a

proposition. There is a further feature of propositions thus understood that tallies with their

role as an ontological ground. Clearly, being an ontological ground, a proposition must

somehow be directly concerned with worldly entities. The ontological ground of Aristotle’s

wisdom must somehow directly involve Aristotle himself as well as a certain property. And

Russell’s way of securing this was to hold that Aristotle himself and the property are

constituents of the relevant proposition/ontological ground. This same picture–the idea of a

‘Russellian proposition’–is also reached through a very different line of thought, but this was

no less germane to Russell’s thinking at the time than ontological ground (and was certainly

much more prominent).

Frege held that thoughts in his technical sense are a kind of representational entities:

they consist of senses, which are ways things are given us in thought.10 Russell, on the other

hand, was insistent that thought is in no way representational in character. You may be

familiar with the exchange between Russell and Frege on the nature of propositions/thoughts.

Frege pointed out to his younger colleague that the thought that Mont Blanc is over 4000

10 Given Frege’s understanding of the sense/reference -distinction, it seems to follow that a thought is a way a

truth value (the reference of a complete thought) is given to a thinker of that thought. This sounds obscure, but the impression is somewhat alleviated by Frege’s distinction between grasping a thought (which involves only the sense of the thought) and asserting it (which is involves acknowledgement of the truth of the thought). Recall also that truth and falsehood are not properties of thoughts, according to Frege. So, whatever may be involved in assertion, it certainly doesn’t involve the recognition that a thought has a certain property.

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metres high does not contain the mountain among its constituents; to which Russell replied

that the view Frege had discarded as preposterous was exactly what he, Russell, held: that

Mont Blanc, despite all its snowfields, is a constituent part of what is asserted in ‘Mont Blanc

is over 4000 metres high’. He continued by arguing out that we do not assert the thought,

which is a psychological matter. What we assert is an object of thought, and this is a certain

complex: ‘If we do not admit this, we get the conclusion that we know nothing at all about

Mont Blanc’ (Russell’s letter to Frege, 12 December, 1904; PW, p. 169.)

It is this somewhat brusque anti-representationalism that underlies Russell’s rejection,

around 1903–6, of the correspondence theory of truth; the idea that propositions should owe

their truth-value to something that is external to them supposedly depends on the erroneous

notion that a proposition is a psychological entity existing in the head of thinking and judging

subjects. The only way to avoid the pitfalls of psychologism, Russell thought, was to

emphasize the independent character of the objects of thought, i.e., propositions. And

independence here must be construed in strong ontological terms. When one asserts that Mont

Blanc is over 4000 meters high, what one asserts does not in any way represent a certain

mountain as being one way rather than another; what one asserts is a certain object, which is a

complex entity containing the mountain itself as a constituent or ‘component part’.

7. Putting the roles of ontological ground and object of propositional attitudes together, we

arrive at the following list of key features of Russellian propositions:

1) Propositions are bearers of truth-value: every proposition is true or false.

2) No proposition is both true and false.

3) The constituents of propositions are ‘worldly’ entities (rather than representations).

4) Propositions don’t owe their truth-value to anything; they simply are true or false.

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5) Propositions are complex entities, that is, they have constituents.

6) Propositions are unities, that is, their complexity is of the sort that makes them capable

of possessing a truth-value.

7) Propositions are objects of thought; a proposition is what is believed, judged, etc.

8) The ontological status of propositions, however, is not dependent upon their being

thought of; a proposition is out there or has being, whether or not it is thought of.

This was Russell’s conception of proposition around 1903–6, one that we find in such works

as The Principles of Mathematics (1903), ‘Meinong’s Theory of Complexes and

Assumptions’ (1904) and ‘On the Nature of Truth’ (1905), for example. It’s is likely to strike

us as somewhat exotic, but Russell himself took the view with utmost seriousness. Ultimately,

this was probably because the notion of proposition promised for a while to give him a theory

of logic (but I won’t go into this here). On the other hand, it became increasingly clear to

Russell that the position riddles with difficulties, both philosophical and technical.

8. From the beginning, Russell saw quite clearly that he was committed to truth-primitivism;

propositions are not made true by anything, but simply are true or false, just as some roses are

red and some white. This feature of propositions, I argued above, has ultimately to do with

their role as ontological ground: the obtaining of a fact consists in a certain proposition's

being true, and hence the notion of true proposition is not amenable to a similar treatment;

ontologically speaking, the truth of a true proposition is not grounded in anything more

fundamental. Russell seems to have felt uneasiness about the general character of truth

primitivism; as he observed in MTCA, ‘this theory seems to leave our preference for truth a

mere unaccountable prejudice, and in no way to answer the feeling of truth and falsehood’ (p.

473). This, though, is by no means the only worry about propositions.

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Propositions are complex entities: they have parts or ‘constituents’. But, for a number of

reasons, there must be more to a proposition than its constituents. What, then, is the

difference between a proposition and a mere list of entities:

Consider, for example, the proposition “A differs from B.” The constituents of this

proposition, if we analyse it, appear to be only A, difference, B. Yet these constituents,

thus placed side by side, do not reconstitute the proposition. The difference which

occurs in the proposition actually relates A and B, whereas the difference after analysis

is a notion which has no connection with A and B. It may be said that we ought, in the

analysis, to mention the relations which difference has to A and B, relations which are

expressed by is and from when we say “A is different from B.” These relations consist

in the fact that A is referent and B relatum with respect to difference. But “A, referent,

difference, relatum, B” is still a mere list of terms, not a proposition. A proposition, in

fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of

constituents will restore the proposition. (PoM, § 54)

In PoM Russell argues, although the point is made very tentatively, that the difference

between a proposition and a list has to do with one of the proposition’s constituents occurring

in it in a special way, as a relating relation, and not simply as an entity (or logical subject; in

such a way that the proposition can be said to be about that entity). In short, a proposition, as

opposed to a list, is an actual unity of its constituents.

Unfortunately for Russell, the notion of relating relation, as it is used in PoM, is just

confusion. Even if one identifies facts with true propositions, as Russell did at the time, one

must still observe that not all propositions are true and hence not facts. One must observe, that

is, that there are two kinds of unity: one gives rise to propositions, entities that are true or

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false (we may call this propositional unity), while the other underlies truth (facts or

something’s being the case; fact unity). ‘Relating relation’ could at best be mobilized to

explain how there can be fact unities: if A and B are actually related by the relation of

difference, then they are different. In the metaphysics of propositions, however, there can be

no factual unity independently of propositional unity.

The point generalizes: if the problem of unity is to explain how a proposition–any

proposition–can be an actual unity, then, as long as Russell thinks of its constituents as

worldly entities–Rose and Redness, say, rather than entities representing or standing for Rose

and its colour–anything that he could invoke to provide such an explanation is bound to yield

the other sort of unity. Russell was thus committed not only to primitivism about truth but to

primitivism about propositional unity as well.

We shouldn’t make too much of the PoM notion of relating relation. Russell supplied it,

I’m inclined to think, to throw some light on an otherwise puzzling phenomenon, the ‘unity of

the proposition’ , which had so exercised the idealists and which, he felt, couldn’t easily be

left unaccounted; and he was himself the first to admit that the light wasn’t particularly bright:

The verb, when used as a verb, embodies the unity of the proposition, and is thus

distinguishable from the verb considered as a term, though I do not know how to give a

clear account of the precise nature of the distinction. (PoM, §54)11

11 And, we should add, although the notion of relating relation doesn’t really fit the rest of his metaphysical

framework, he did manage to make sound points in his discussion of the phenomenon, as when pointed out, against Bradley, that there’s nothing contradictory or paradoxical about an actual infinity of implied entities; a relational proposition does imply an infinity array of further relations between a relation and its terms, between these further relations and their terms, and so on, but that's entirely harmless, because the implied relations don't ground the unity of the proposition (PoM, §99).

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Later, Russell achieved much more clarity on the relevant issues. Here I want to mention two

things. First, there’s the distinction between the two kinds of unities, conspicuously absent in

PoM, but duly observed in later works.

To begin with, let’s consider a particularly straightforward attempt to refute Russell's

first theory of propositions (by ‘Russell’s first theory of propositions’ I mean the theory which

accepts the theses 1) – 7) stated above in section 7).12 Consider a false belief, such as

Othello's belief that Desdemona loves Cassio. What is involved here? Suppose first that there

is such an entity as Desdemona's love for Cassio. (Othello, Desdemona and Cassio are

fictional characters, but here they are to be treated as if they were real life.) This looks like a

natural assumption to make. As Moore observed in SMPP:

Suppose a man believes that God exists […]. It seems […] quite natural to say that what

he believes is that God exists. And it is quite certain that when he believes this he is

believing something. It seems, therefore, quite certain that there is such a thing as what

he believes, when he believes this. But what is this something which is what he

believes? It is that God exists, or turning it another way, we may say it is ‘God’s

existence’; since to say that a man believes in God’s existence is plainly merely another

way of saying that he believes that God exists. This way of putting it is indeed not open

to us in the case of all beliefs: in a great many cases we can only express the object

believed or what is believed by a sentence beginning with ‘that’ because what is

believed is so complex that we cannot easily make a verbal noun of it. But this is, I

think, plainly, a question of words: in every case what is believed is equivalent to what

could be expressed by some verbal noun. (p. 250).

12 Moore main have had this sort of argument in mind in SMPP: see Cartwright (1987, pp. 80–1)

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Clearly, Moore’s first point–the inference from ‘a man believes something’ to ‘there’s such a

thing as what he believes’–is in line with Russell’s first theory of propositions. But if we

follow him further, we must admit the following two points, formulated in terms of our

example: (a) Othello believes that Desdemona loves Cassio; (b) there is such an entity as

Desdemona’s love for Cassio. Now, from these two premises it should surely follow that

Othello's belief is true; the conclusion, we might say, accords with the correspondence

intuition that we have about truth. Othello’s belief, however, is not true, as Desdemona didn’t

in fact love Cassio. Should we conclude from this, then, that there is no such entity as

Desdemona’s love for Cassio? This would be equally unpalatable, for then (i) Othello

believes that Desdemona loves Cassio, but (ii) there is no such entity as Desdemona's love for

Cassio. And (i) and (ii) are incompatible, if we follow up Moore: if (ii) holds, there's nothing

such that Othello believes it when he believes that Desdemona loves Cassio; that is, it follows

that Othello believes nothing. But that isn't correct, for Othello did believe something, namely

that Desdemona loves Cassio.

Russell himself used reasoning similar to the first part of the above argument. But he

used it to show that what he calls an ‘Objective of a judgment’ – this is Meinong’s

terminology–cannot be an event or a particularized relation as distinct from a proposition, as

these would be entities for which the correspondence intuition is valid: if a judgment is true,

then the event or particularized relation is there, whereas if the event or particularized relation

is not there, then the judgment is false. Russell makes the point in the following passage from

ONTF:

But what is the Objective of the judgment “Charles I died in his bed”? There was no

event such as “Charles I died in his bed”. To say that there ever was such a thing as

“Charles I's death in his bed” is merely another way of saying that Charles I died in his

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bed. Thus if there is an Objective, it must be something other than “Charles I's death in

his bed”. We may take it to be “that Charles I died in his bed”. We shall then have to

say the same of true judgments: the Objective of “Charles I died on the scaffold” will be

“that Charles I died on the scaffold”. (p. 151)

Russell discusses particularized relations in (MTCA, pp. 453), where he argues, against

Meinong, that the being of a particularized relation cannot be what is ‘actually mean by a

relational proposition’. Armed with Russell’s distinction, we can ward off the straightforward

argument by pointing out that the premise from which it begins–that there is such an entity as

Desdemona’s love for Cassio–is ambiguous. It is ambiguous because it fails to observe the

distinction between propositional unity and fact unity. What indicates that we are concerned

with a propositional unity is that the entity will be there whether or not the judgment is true,

while this doesn't hold for fact unities (the sort of unity that makes for facts: events,

particularized relations, etc.). Contrary to Moore’s suggestion, the entity to which Othello is

related in the example is not (best expressed by) ‘Desdemona’s love for Cassio’, which

suggests an entity which, no matter how you choose to categorise it, complies with the

correspondence intuition; rather, the entity is (indicated by) ‘that Desdemona loves Cassio’,

which is there independently of truth or falsehood.

Russell’s point here is of course precisely what an advocate of the first theory of

propositions should say (although in the quoted passage, which was written in 1909, Russell

is no longer defending the old theory, but spelling out its commitments for criticism).

What Russell says in ONTF and MTCA show that after certain initial confusions that are

evident in PoM he managed to clear up the distinction between the two kinds of unity. Now,

drawing the distinction is not exactly the same thing as observing that it must be construed as

a primitive one–observing that there is no explaining, given premises integral to the old

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theory of propositions, what constitutes propositional unity and truth. But I find it difficult to

believe that he could have formulated, as he did, a sharp distinction between propositions, on

the one hand, and such entities as events and particularized relations, on the other, without

seeing that ‘relating relation’ won’t be available to him to make sense of propositional unity.

Furthermore–and this is the second point I want to mention–there’s reason to think that

Russell did come to see that he was committed to ‘double primitivism’. Consider the

following quotation from MTCA:

The unity of a complex [sc. proposition–AK] raises a logical problem, of which

Meinong seems not to be fully aware. What is added, we are told, is the relation, rightly

related; but when we consider the relation as well as the terms, we do not obtain the

complex. And if we add the relations of the relations to the terms, and all the relations

generated in the endless process, we still do not obtain again our original unity, but only

an aggregate. Thus what distinguishes our complex is not any constituent at all, but

simply and solely the fact of relatedness in a certain way. Out of given constituents,

even when account is taken of all the infinitude of relating relations, different

complexes can be constructed: thus e.g., “a is greater than b” and “b is greater than a”

differ in no respect which analysis can preserve. It is this special and apparently

indefinable kind of unity that I should propose to employ in characterizing the notion of

a complex. This kind of unity belongs, as is evident, to all propositions [...]. (MTCA, p.

437; emphasis added)

To be sure, this passage is not straightforward to interpret. We could read it along the lines

familiar from PoM. After all, how could there be a ‘fact of relatedness’, containing a relation

plus other entities, even when it is not the case that the entities are related by the relation?

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Talk of a ‘fact of relatedness’, that is, could be taken to indicate the same confusion that was

present in PoM. Another reading is available here, however, which links the passage with

primitivism about propositional unity. Notice first, though, that what Russell says here about

unity and indefinability doesn’t decide the interpretative issue, because holding unity to be

indefinable is compatible with the PoM position. There, as here, definability amounts to

analysability (cf. PoM, §108), and he's explicit that analysis–a process that identifies the

constituents of a proposition–will inevitably destroy the unity of the proposition (PoM, §54).

Hence, whatever elucidation there might be for the phenomenon of unity, it will inevitably

fall short of analysis/definition.

Talk of ‘fact of relatedness’ may be taken in a more charitable way, however, as a

recognition that unity will have to be accepted as a primitive feature of a proposition. At the

very least we can say that by the time he was writing MTCA Russell had formulated all the

premises from which this follows as a simple corollary. Given that what distinguishes a

proposition from an aggregate is not any constituent of the proposition but the ‘fact of

relatedness in a certain way’, it’s easy to draw the further conclusion that the fact of

relatedness can only be identified with the proposition itself: after all, a fact is in general a

true proposition, but the unity of a proposition p cannot be grounded in any further

proposition about p–a proposition to the effect that the constituents of p are related in a certain

way–for if there’s a general problem of the unity of the proposition, it arises for the new

proposition just as much as much as it does for p. This final step was easy for Russell take,

given what he had argued in PoM, namely that although a relational proposition aRb does

imply further relations between a and R and between b and R, between these further relations

and the original constituents, and so on, these fresh relations don't contribute to the unity of

aRb, which is grounded, somehow, in R alone; just substitute 'fact of relatedness' for 'relation'

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in the argument of PoM and you arrive at the primitivist position that is at least implicit in

MTCA.

To recapitulate, I’ve argued, first, that the distinction between propositional unity and

fact unity was duly observed by Russell after PoM; and second, that there's at least some

textual evidence for attributing an explicit recognition of double primitivism to Russell (this

issue merits further exegesis, perhaps).

So, what were Russell’s reasons for abandoning propositions in the sense of his first

theory of propositions? There’s a theme that recurs in his later comments on the theory, the

problem of false belief. Consider the following quotations from PLA:

It is obvious from the fact of false belief that you cannot cut off one part: you cannot

have I believe/Socrates is mortal. (PLA, p. 192)

Time was when I thought there were propositions, but it does not seem to me very

plausible to say that in addition to facts there are also these curious shadowy things

going about such as ‘That to-day is Wednesday’ when in fact it is Tuesday. I cannot

believe they go about the real world. It is more than one can manage to believe, and I do

think no person with a vivid sense of reality can imagine it. (PLA, p. 196)

So, Russell argues, it’s the fact or existence of false beliefs that shows the first theory of

propositions to be mistaken. Why? Because it entails commitment to false propositions.13

13 Let’s spell this out once again, although the point was made above with reference to Moore. The existence

of false propositions follow from the 'binary analysis' of propositional attitudes, which is an integral part of the first theory of propositions:

Belief is a binary relation between a mind (or act) and a proposition There are false beliefs There are false propositions

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Facts are quite OK as an ontological category, as there's no doubt that there are such entities;

the existence of facts, Russell argues in PLA, is a truism so obvious that it's almost laughable

to mention it (p. 182). But false propositions, if there were such entities, would be objective

falsehoods and ontologically exactly on a par with facts; and this would be just too much to

fathom. So the trouble with the first theory of propositions appears to be that its commitment

to false propositions infringes our ‘vivid sense of reality’.

Yet, this sort of argument doesn’t give an accurate picture of Russell’s original

philosophical concerns about the first theory of propositions. The latter passage from PLA

presents a stark contrast between facts and false propositions. Hence there ought to be some

difference between the two that accounts for and justifies Russell's adopting such different

attitudes towards the respective entities: the existence of facts is a truism, whereas to suppose

that there are false propositions is an insult to vivid sense of reality. However, assuming the

first theory of propositions, what could the relevant difference consist in? A false proposition

is a complex entity having being and having its own falsehood somehow contained in itself. A

fact is just a true proposition, which is a complex entity having being and having its own truth

somehow contained in itself. So the only difference is whether it’s truth or falsehood that is

'somehow contained' in the proposition. And disregarding questions about truth-ascriptions,

that does look like a difference between a rose that is red and a rose that is white. So, if there

One might want to add an extra premise to this argument to make it strictly deductive. Russell does so in the

following passage: ‘It might be thought that we could say simply that true judgments have Objectives while false ones do not. With a new definition of objectives this view might become tenable, but it is not tenable as long as we hold to the view that judgment actually is a relation of the mind to an objective. For this view compels us, since there certainly are false judgments, and a relation cannot be a relation to nothing, to admit that false judgments as well as true ones have objectives’ (ONTF: 167–7).

But Russell also had compelling logical reasons for assuming the existence (or subsistence or being) of false propositions. For instance, in ‘p implies q’, both p and q may be true, but in that case, since ‘p implies q’ implies ‘not-p implies q’, in the latter proposition both ‘not-p’ and ‘not-q’ will be false. But if only true propositions exist (subsist, have being), there will be a gulf between ‘p implies q’ and ‘not-q implies not-p’, ‘but of such a gulf to trace is to be seen’ (MTCA, p. 462). Again, ‘p implies q’ may be true, although p is false; but then p– supposing it doesn’t subsist or have being, as true propositions do–will be at best a mental entity. This would make the entire proposition mental in the sense that its being would depend upon the existence of a mind. But this would be clearly incorrect, according to Russell (ibid.)

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is something suspect about false propositions, this ought to hold in equal measure for facts–

true propositions–as well.

Observing Russell’s careful distinction, in some of his post-PoM writings, between

propositional unity and fact unity, it’s plausible to speculate that he felt uneasiness about the

former notion; and that feeling extends to facts as well, given that they are just a species of

propositional unities. In PLA Russell was working with a radically different conception of

facts, one that enabled him to say, among other things, that ‘obviously propositions are

nothing’ (PLA, p. 196). By the time of PLA, he’d probably forgotten about his old notion of

fact, and hence the objection against the old theory is formulated as a sort of ‘incredulous

stare’, as in the quotation above.

The reason why he originally put the focus on false belief was rather different, however:

the existence of false propositions makes absolutely clear the necessity of distinguishing

propositional unity from fact unity, thus helping us to put the finger on the weak spot in the

old theory of propositions, namely its treatment of propositional unity. And it’s really not

difficult to see what the trouble is here. It’s readily formulated in terms of ‘fact of

relatedness’, the notion that we’ve already met. For false propositions, the difficulty is one

that was indicated above: how could there be a ‘fact of relatedness’, containing a relation plus

other entities, even when it is not the case that the entities are related by the relation? As

Bernard Linsky observes (1999: p. 48) observes, with true propositions the problem is equally

serious and indeed even clearer: in a true proposition its constituents are brought together to

yield a unity, but this unity is not 'yet', as it were, a fact; for that, the proposition must possess

a different sort of unity, one that brings together a propositional unity and its truth.

Linsky (1999, pp. 47–9) argues, further, that Russell abandoned propositions in the

sense of the first theory because of difficulties for ‘propositions, as distinct from facts’, where

the difficulty is essentially that of explaining how there could be propositional unities. In a

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way, I concur with Linsky’s conclusion, but would add one more round to the argument he

attributes to Russell, thus giving Russell a little more leeway here. This extra leeway comes

from double primitivism. Since it’s absolutely impossible to see what’s involved in the

supposed unity of a proposition, the only way to maintain that there are propositional unities

and to prevent the theory from falling into absurdity is to accept such propositional unities

and their key features as primitives.

But this is philosophically unsatisfactory. The dichotomy of true and false propositions

false very little room for explanation or even elucidation of any of the key concepts. Once he

has ruled out analytical understanding of truth and falsehood, Russell is left with ‘direct

perception’ as the only source of understanding regarding these concepts; hence the analogy

with the colours of roses. Unfortunately, however, even this turns out to be seriously

misleading. First, the analogy assumes that truth and falsehood are properties of propositions,

when in fact they are not. Second, nothing informative can be said about the nature of the

entities that bear truth-values. They must be complex, for it’s on account of their complexity

that they are true or false. But since complexity is tied to unity, the only sort of explanation

that is possible here will be in terms of a contrast with what other sort of entities there are.14

Given the metaphysics of propositions, then, there really isn’t much of a grasp of what truth

and falsehood are, how they differ from one another, what kind of entities they are ascribed to

and what is involved in this ascription.

In ONTF, Russell raises two objections to his old theory of propositions:

14 This this was one of the reasons why Russell welcomed the results reported in ‘On Denoting’ as such a

huge step forward. For what he found there was a way of eliminating non-propositional complexity. Semantically speaking, this meant that there were no referring complex expressions, as Russell’s new theory of denoting now decreed that all apparently referring complex expressions have an implicit propositional structure. And metaphysically, this meant that there are only objects–entities that are simple, at least relatively speaking, and propositions, which are complexes with objects as their constituents.

33

The first is that it is difficult to believe that there are such objects as ‘that Charles I died

in his bed’, or even ‘that Charles I died on the scaffold’. It seems evident that the phrase

‘that so and so’ has no complete meaning by itself, which would enable it to denote a

definite object s (e.g.) the word ‘Socrates’ does. (p. 151)15

The second objection is that the old theory

[…] leaves the difference between truth and falsehood quite inexplicable. We feel that

when we judge truly some entity 'corresponding' in some way to our judgment is to be

found outside our judgment, while when we judge falsely there is no such

'corresponding' entity. (p. 152)

We can think of these objections as directed against the primitivist account, or non-account,

of propositional unity and truth respectively. The first passage suggests that the problem lies

in the notion of propositional unity; for the felt difficulty concerns not only propositions that

are false but also those that are true. Why does it seem “evident that the phrase ‘that so and

so’ has no complete meaning”?

I don't think this is meant as an intuitive judgment or report of what we feel on instinct.

Russell’s point here is rather that thinking through the consequences of the old theory, we can

come to see that the phrase ‘that so and so’ has no complete meaning: we see, first, that

propositional unity is a phenomenon that permits no explication. We are thus left with double

primitivism. But this is problematic on its both aspects: primitivism about propositional unity

denies insight into what sort of entities these unities could be (this is problematic at least

philosophically, if not ‘logically’ or ‘technically’). And it denies insight into the distinction

15 Russell is here treating ‘Socrates’ as a genuine proper name, that is, the sort of expression that acquires meaning solely through the fact that it stands for an object of acquaintance. His official view was, of course, that ‘Socrates’, being an ordinary proper name, is really a definite description in disguise.

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between truth and falsehood, this being the second objection; the old theory treats the

distinction as something ‘ultimate and not further explicable’ (p. 153), and although this isn’t

‘logically impossible’, it is nevertheless unsatisfactory.

I add one complication regarding Russell's argument in ONTF against the old theory of

proposition. Its structure is apparently more complicated than I’ve presented it. I don't think

that this is really so, however. Let me spell this out. In the text I’ve only given a part of

Russell's second objection (cf. ONTF, pp. 152–3). He actually begins the objection by

pointing out that the old theory is committed to there being objective falsehoods. He then

raises the familiar complaint that the existence of such objective falsehoods is ‘almost

incredible’. It's only after making this point that he adds the further one about truth and

falsehood which I quoted above, namely that the theory treats their difference as primitive.

Now, why is the existence of objective falsehoods almost incredible? The reason

Russell gives here is that ‘we feel that there could be no falsehood if there were no minds to

make mistakes’ (p. 153). This point deserves an extended comment.

Richard Cartwright (1987, p. 80) raises the following sort of objection to Russell's claim

about falsehood. Using ‘there are no subways in Boston’ as an example of a falsehood,

Cartwright formulates the supposed dependence of falsehoods on minds as the claim that ‘it

could be false that there are no subways in Boston only if there were someone who could

mistakenly believe that there are no subways in Boston’. Given this, the argument against

Russell runs as follows. First we observe that

(1) There are subways in Boston

entails

35

(2) It’s false that there are no subways in Boston.

Suppose now with Russell that (2) entails

(3) There is someone who can think that there are no subways in Boston.

Since (1) entails (2) and (2) is supposed to entail (3), it follows, by transitivity of entailment,

that (1) entails (3). But surely this is incorrect, Cartwright argues: it doesn’t follow from there

being subways in Boston that there’s someone who can think that there are no subways in

Boston.

Here we should note, however, that on the new theory of truth that Russell advocates in

ONTF, it’s not just falsehoods that are dependent on the existence of minds: truths are thus

dependent, too. And this is because the entities that are true or false are beliefs or judgments,

and there couldn’t be beliefs and judgments if there were no minds. Thus there is a general

dependence of truths and falsehoods (true and false propositions) on the existence of minds:

this is a key element in Russell’s new theory of truth (as we shall see below in more detail).

Keeping this in mind, we next point out that ‘entailment’ holds between propositions. We

must therefore take (1) to refer to something that involves a belief or judgment. And if we

take it this way, there is nothing counterintuitive about the conclusion: the conclusion would

be counterintuitive only if (1) referred to a certain fact. But here we are talking about

propositions, and propositions are ‘mental entities’, Russell now thinks. So, if the existence of

the proposition that there are subways in Boston depends on the existence of someone who

could believe that there are subways in Boston, then, presumably, it follows that that someone

could think that there are no subways in Boston (I take it that Russell would regard it as a sort

of 'logical' fact that a mind capable of judging that p is also capable of judging that not-p).

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I wouldn’t want to deny that Russell's new theory, which makes truth-bearers mental

entities, is indeed implausible in many ways. The point here, however, concerns only the

structure of the argument in ONTF. And the point is that Russell's view that falsehood

depends on the existence of minds is plausible only to the extent that the theory of truth is

plausible which renders truth similarly dependent. And in Russell's argumentative context this

theory contrasts with the old one according to which there are objective truths and falsehoods

(propositions in the old sense). Thus, on a charitable reading of what he's up to in the relevant

passage, Russell's claim in ONTF about falsehood doesn’t introduce an independent argument

against the old theory of propositions but is dependent on the previous argument about

propositional unities.

9. Russell’s case against the old theory of propositions has the following structure:

1) We cannot explain what propositional unity is.

2) But it’s unsatisfactory to construe propositional unity as a primitive feature, either.

This is because (I) this denies (almost all) insight into what propositions are; and (II)

because this denies insight into what the difference is between truth and falsehood.

3) Therefore, it’s evident that a propositional unity is not a single entity at all.

The conclusion is the key element in the so-called multiple relation theory of judgment, which

replaced the old theory of propositions and which is the only theory that is consistent with all

the requirements that he wanted to impose on the phenomenon of propositional thought at the

time. These requirements are listed in Chapter XII of The Problems of Philosophy:

First, a theory of truth must admit of its opposite, falsehood. According to Russell, ‘[a]

good many philosophers have failed adequately to satisfy this condition: they have

37

constructed theories according to which all our thinking ought to have been true, and have

then had the greatest difficulty in finding a place for falsehood’. Russell may have his own

former theory in mind as well: as we have seen, the notion of relating relation, which he used

to explain what propositions are, rules out false propositions, and then the only way to make

room for falsehoods is in fact just to assume that every proposition has one or other of these

features.

Second, it now seemed ‘fairly evident’ to Russell that if there were no beliefs there

could be neither falsehood nor truth, ‘in the sense in which truth is correlative to falsehood’, a

comment that fits nicely with what was said above about Russell's objections to his old theory

of propositions in ONTF.

Third, ‘the truth and falsehood of a belief always depends on something which lies

outside the belief’. This is the correspondence intuition, and together with the second point it

shows how far Russell had gotten from his old theory. There he had chalked the

correspondence idea up to a mistaken conception of judgment as consisting of ideas which

could then ‘correspond’ or fail to ‘correspond’ with reality. But now he thought he could

resolve this difficulty by ceasing to treat propositions as single entities and treating the phrase

‘that so and so’ as incomplete, one that ‘only acquires full significance when words are added

so as to express a judgment’ (ONTF, p. 151)

Thus judgment is no longer construed as a binary relation between a subject and a

proposition–J(s, p)–but as a ‘multiple relation’, i.e. as a relation which has more than two

places. Its terms are the ‘subject’ (the judging mind or act) and its ‘objects’, one of which is a

relation–J(s, Fn, o1,…,on). Judgments are now taken to be facts, not in the old sense of true

propositions but in a new one which is more familiar: facts are complex entities consisting of

particulars and property universals.16 Thanks to the new sense of ‘fact’, the correspondence

16 Indeed, Russell usually calls them ‘complexes’ rather than ‘facts’; the latter term becomes prominent only

later, under Wittgenstein’s influence.

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theory becomes available to Russell: a judgment or belief is true when there is a complex or

fact appropriately related to it, and is false if there's no such complex or fact.

With the new conception of facts, Russell also re-introduces relating relations. Some

initial confusions notwithstanding, their role is now unequivocally that of explaining the unity

of facts:

[I]n every complex there are two kinds of constituents: there are terms and the relation

which related them: or there might be (perhaps) a term qualified by a predicate […] But

there are some terms which appear only as terms and can never appear as predicates or

relations. These terms are what I call particulars. The other terms found in a complex,

those which appear as predicates or relations, I call universals. (AR: 135)

A fact, then, is a complex and is a genuine, actual unity, and this is so because one of its

constituents occurs in a special way in it. Clearly, Russell owes an explanation of what the

distinction between universals and particulars, thus conceived, consists in. Whether or not

such an explanation is forthcoming, the new use of ‘relating relation’, unlike the one in PoM,

will not fall at the first hurdle. Accordingly, the clear differentiation between propositional

unity and fact unity, on the one hand, and the use of ‘relating relations’ (and, perhaps,

‘predicating predicates’) to make sense of the latter, on the other, contribute to resolving the

analytical task that confronts advocates of the correspondence theory of truth.

10. How, then, is propositional unity to be treated on the new theory? This is a major

difficulty for Russell because there’s a constant danger of relapsing into the old conception of

propositions as single entities. In every judgment, he explains in chapter XII of The Problems

of Philosophy, there is the judging mind, which is the subject of the judgment, and there are

39

the terms concerning which the mind judges, which are the ‘objects’ of the judgment: for

instance, Othello would be the subject, and Desdemona, Cassio and the relation of loving the

objects in Othello’s judgment that Desdemona loves Cassio. Now, clearly, there’s more to

propositional attitudes than mere acquaintance with the relevant objects: a propositional

attitude, he would explain in a later work, involves the further aspect of ‘what is supposed to

be done with’ the relevant objects (ThK: 116). And it is precisely this that the multiple

relation theory has to capture somehow without invoking propositional unities as actually

existing entities.

In the first version of the multiple-relation theory, Russell sought to resolve this

problem by drawing on a key feature of relations, namely their having an inherent sense or

direction. Thus, he explained in ONTF that what distinguishes the judgment that A loves B

from the judgment that B loves A is that in these judgments the relation of loving is not

‘abstractly before the mind’ but must before the mind as proceeding either from A to B or else

in the opposite ‘direction’, from B to A (ONTF: 158).

This explanation won’t do, however. To say that the relation is before the mind as

proceeding from one term to another is simply to put forth the requirement that the object-

relation must be before the mind as a constituent of a propositional or factual unity. For how

else, except as a constituent of an actual complex, could a relation run or proceed from A to B

rather than vice versa? But making the relation a constituent of a propositional unity just

presupposes the old theory of propositions, while factual unity would rule out false judgment.

Russell tried to improve on this account in The Problems of Philosophy, arguing that it

is the relation of judgment that supplies the requisite unity-of-sorts:

It will be observed that the relation of judging has what is called a ‘sense’ or ‘direction’.

We may say, metaphorically, that it puts its objects in a certain order, which we may

40

indicate by means of the order of the words in the sentence. […] Othello’s judgement

that Cassio loves Desdemona differs from his judgement that Desdemona loves Cassio,

in spite of the fact that it consists of the same constituents, because the relation of

judging places the constituents in a different order in the two cases. Similarly, if Cassio

judges that Desdemona loves Othello, the constituents of the judgement are still the

same, but their order is different. This property of having a ‘sense’ or ‘direction’ is one

which the relation of judging shares with all other relations. (PP, p. 73)

But this won’t help either. Unless the judging mind is dealing with fictional entities of its own

creation, it cannot really put the objects of the judgment in any order. On the other hand, to

hold that talk of a judgment ‘putting its objects in a certain order’ is just metaphorical is to

admit that while the mind cannot really accomplish the ordering, judgment still involves the

suggestion, as it were, that the relevant entities are united in a particular way. But this is just

to highlight the explanatory task that Russell has so far refused to undertake, of explaining

how the multiple relation theory is deal with the ‘what is supposed to be done with the

objects’ part of the story.

Russell came to see this quite clearly, and in the Theory of Knowledge -manuscript he

introduced logical forms to replace earlier metaphorical talk with a genuine philosophical

theory. As he now put it:

It is essential that our thought should, as is said, “unite” or “synthesize” the two terms

and the relation [sc. A and B and similarity]; but we cannot actually “unite” them, since

either A and B are similar, in which case they are already united, or they are dissimilar,

in which case no amount of thinking can force them to become united. The process of

“uniting” which we can effect in thought is the process of bringing them into relation

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with the general form of dual complexes. […] In an actual complex, the general form is

not presupposed; but when we are concerned with a proposition which may be false,

and where, therefore, the actual complex is not given, we have only, as it were, the

“idea” or “suggestion” of the terms being united in such a complex; and this, evidently,

requires that the general form of the merely supposed complex should be given. (ThK:

116)17

To understand ‘A and B are similar’, one must be acquainted with A and B and similarity plus

the ‘general form of dual complexes’, namely, ‘something has some relation to something’

(TK: 116; Russell is here discussing understanding, which he now regards as the fundamental

propositional attitude presupposed in all others). In symbols:

U(S, A, B, similarity, xRy);

Here S is subject, and ‘xRy’ symbolizes the relevant logical form. In this fact–i.e., the fact that

the subject, S, understands that A and B are similar–the logical form is brought to bear on A

and B and similarity, with the intended effect of merely representing and not actually

generating the supposed complex which, if it is there, acts as the truth maker for attitudinal

facts involving the propositional content ‘A and B are similar’.

Russell emphasizes that this is just an example and a first approximation, the point of

which is to show that and how logical form is relevant to the analysis of propositional

attitudes. Here there are a number of complications, including the following ones.

First, the structure of understanding-complexes varies depending on the content

understood. In particular, Russell’s example applies to atomic propositional contents, while

17 Russell’s use of similarity here isn’t accidental. He chooses an example that is neutral with respect to the ‘direction’ of the relation, thus drawing a clear distinction between his treatment of the problem of unity and the problem of the direction or sense of relations.

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nothing has been said about ‘molecular complexes’; this he meant to do in Part Three of the

manuscript, but that was never written, for well-known reasons.

Second, the symbolization U(S, A, B, similarity, xRy) does not show how understanding

relates the different relata, while it is clear that there must be such differences (ThK: 117): the

subject enters the complex in a way that is different from how the other constituents enter it;

the form enters it differently from the rest of the content; and the relation that similarity bears

to the form is different from how A and B are related to it. It is questionable, to say the least,

whether all these differences can be accounted for without reintroducing actual propositional

unities as constituents of attitudinal facts; this issue may have played a major role in

Wittgenstein’s subsequent criticism of the multiple-relation theory, but I won’t consider here

this intriguing chapter in the history of early analytic philosophy.18

Third, Russell’s example–the judgment that A and B are similar–is intentionally simple

in that only one complex can be formed from A, B and similarity. This simplicity carries over

to the definition of truth. A, B, similarity and the form xRy determine a unique complex, and

hence we can give a simple definition for this sort of case:

The belief that A and B are similar is true only if there is a complex consisting of its

objects and is false otherwise (ThK: 144–5).19

Not all cases are so simple, however. Often the objects of a belief complex do not determine a

unique corresponding complex. As Russell himself notes, for such cases one must find

additional constituents in attitudinal facts so as to retain the principle that for every truth-

18 See MacBride (2013) for a recent account of the Russell-Wittgenstein exchange. 19 According to Russell, A, B, similarity and the form of dual complexes, xRy, determine a unique complex.

For this to be the case, such impossible complexes as ‘A B’s similarity’ will have to be excluded. How he thought this result would be secured isn’t very clear.

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maker there is a unique set of constituents (including relations and logical forms) in an

attitudinal fact which pick out that truth maker (ThK: chapter 5).

11. The problem of actual propositional unity was Russell’s speciality, rooted in his insistence

that cognition is a direct, unmediated relation to objects. Having rejected the first theory of

propositions, on which belief and other propositional attitudes are to be understood as binary

relations between a subject and a ‘Russellian’ proposition, he then tried out different versions

of the multiple relation theory of judgment, in order to find a way of accounting for the

phenomenon of propositional unity without assuming that there actually are any such unities

as single entities. Eventually, however, he drew the conclusion that this cannot be done.

The ultimate reason for this, it seems, was the ‘puzzle about the nature of belief’ that

Russell formulated in PLA. Essentially, this has to do with requirement, deriving from

Wittgenstein and stated, though not defended in Russell’s lectures, that the ‘subordinate verb’

in the judgment complex has to occur as a verb and not as a term in any complex in which it

occurs, because ‘if a thing is a verb it cannot occur otherwise than as a verb’ (PLA, p. 198).

Thus, Russell acknowledges, on the one hand, that in “Othello believes that Desdemona loves

Cassio”, the verb “loves” occurs in the proposition and seems to–indeed, has to, if the

Wittgensteinian stricture is to be followed–occur as relating Desdemona to Cassio, whereas in

fact it doesn’t do so; and on the other hand, that nevertheless the verb does occur in the

proposition in the way that a verb should. This is the puzzle about the nature of belief, and it’s

clear that it can be resolved only if one discards the old assumption of real propositional

constituents.

By 1918, then, Russell was forced to adopt an altogether different view of the matter,

one according to which the entities with which one is directly concerned in propositional

attitudes are representational in nature. This development took place around 1918–19, and it

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owes something to Wittgenstein’s influence, something to William James, other American

realists and their ‘neutral monism’, and something to Watson’s behaviourist psychology.

Russell now held, very roughly, that there are two kinds of propositions, ‘word-propositions’

and ‘image propositions’, of which the latter are more fundamental in that while a word-

proposition means an image-proposition, an image-proposition stands in a relation of

‘objective reference’ to a fact which makes it either true or false (OP: 308–9).

This is a psychological (or ‘psychologistic’) account of propositional attitudes and of

meaning. The central element in it, in the present context at least, is its ‘rehabilitation of

content’. What I believe when I believe that Caesar crossed the Rubicon is not the actual

event, which took place in 49 BC; it is a present occurrence, something that is now in my

mind’ (AM, p. 233); ’[w]hat a man is believing at a given moment is wholly determinate if we

know the contents of his mind at that moment” (AM, p. 234). It’s this present event, an

occurrence in the mind of the believer, that Russell calls the “content” of the belief (ibid.).

According to Russell, the introduction of content has two advantages to it:

The advantages are those derived from the rehabilitation of content, making it possible

to admit propositions as actual complex occurrences, and doing away with the difficulty

of answering the question: what do we believe when we believe falsely? (1919: 307)

Now, one might think that the first point leads directly to the second; that is, that admitting

propositions as actual complex occurrences is itself enough to resolve the difficulty of the

false belief. After all, on Russell’s new theory, to believe truly or falsely is to stand in an

appropriate relation to what we may call an image-content. So, the content will be there,

whether or not it is true. And since the content is just a representation, its existence won’t give

rise to the old problem of objective falsehood; this was the problem of actual propositional

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unity. Nevertheless, it would be rash to conclude that there’s such an easy connection between

the two points; and Russell himself certainly didn’t think so. For now there arises a fresh

problem, acute for any form of representationalism, including Russell’s imagist account. The

difficulty can be brought out by considering a key aspect in Moore’s account of truth in

SMPP.

In SMPP, Moore is quite clear about the general form of a definition of truth:

To say that a belief is true is to say that the fact to which it refers is or has being; while

to say that a belief is false is to say that the fact to which it refers is not—that there is no

such fact. (SMPP: 267; emphasis in the original)

But Moore is uncertain about how to define or analyse the relevant notion of reference. He

concludes in the end that carrying through this analytical task is not absolutely necessary for

understanding what truth is; we do understand, he argues, what truth is, even if we might not

be able to give a complete and correct analysis of the event that is happening in someone’s

mind when she believes that something is the case. For, Moore argues, first, that we do

possess common sense understanding of what it is to believe that p; and, second, that we can

be said to be acquainted with the relevant notion of referring to, in that we know what it is to

believe that p for a wide range of instances of ‘p’ and we can readily tell which fact it is

whose presence in or absence from the Universe decides the truth value of a given belief.

Accepting the correspondence intuition, Moore holds that a belief is true only if what it

refers to is there; and accordingly, that a false belief is false precisely because something isn’t

there, something that would be there if the belief were true. But he then raises the crucial

question: ‘How can we believe in something which simply has no being?’ (SMPP: 263); that

is, what do we believe when we believe falsely? This, then, is the question that Russell, too,

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faces with his new theory of propositions, and it’s not resolved simply by referring to contents

as actual occurrences.

This is why Moore is uneasy about the proposed definition of truth. Shunning the

analytical task and accepting ‘referring to’ as a primitive commits him to non-existents as the

correlates of false beliefs. This uneasiness is reflected in Moore’s rather infelicitous

terminology. As we saw, he holds that a belief refers to a fact, whether or not the belief is

true, and hence he is committed to there being not only existing facts but also non-existing

facts or facts which are not (SMPP: 255). Now, ‘non-existent fact’ and ‘fact which is not’ are

illegitimate phrases, but at least we can appreciate the reasons behind the terminology. In

Russell’s case, on the other hand, this was a compelling reason not to make use of an

unanalysed notion of reference, or any other notion with the same consequence; commitment

to non-existents is yet another case that offends our vivid sense of reality. The point is made

emphatically in The Philosophy of Logical Atomism:

You will notice that wherever one gets to really close quarters with the theory of error

one has the puzzle of how to deal with error without assuming the existence of the non-

existent. I mean that every theory of error sooner or later wrecks itself by assuming the

existence of the non-existent. As when I say “Desdemona loves Cassio”, it seems as if

you have a non-existent love between Desdemona and Cassio, but that is just as wrong

as non-existent unicorn. (1918, p. 198)

‘[T]hat every theory of error sooner or later wrecks itself by assuming the existence of the

non-existent’ is an unduly pessimistic statement, of course, written at a time when Russell had

little positive to say about the topic of belief and judgment. But the puzzle will be there, and

one of the key points to see about Russell’s new theory is how it is meant to solve it. As was

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mentioned above, Russell now holds that an image-proposition–and this is the fundamental

case–has an ‘objective reference’ to a fact which makes it true or false. It is this notion of

objective reference that has to be unpacked in a way that incurs no commitment to non-

existents.

There is another option that is available in principle to the likes of Moore and Russell,

although they make no explicit mention of it: false propositions, understood as

representations, might be taken to involve reference to merely possible entities (possible facts,

states of affairs), which are of course entities that are or ‘have being’.20 Indeed, this might be

regarded as a more promising option than the Meinongian one: the notion of a merely

possible entity is perhaps less in conflict with our vivid sense of reality than non-existents.

Many philosophers, though, would resist the division, arguing that both inferences–inference

to non-existents and inference to entities that are merely possible–are instances of the same

fallacy. It would be a fallacy to infer from the denying that Homeric gods, golden mountains

or winged horses exist to speaking of non-existent Homeric gods, golden mountains and

winged horses. Just so it would be a fallacy to rephrase ‘it is possible that there is a state of

affairs…’ with ‘there is a possible state of affairs…’ In both cases we end up inflating our

ontology, by adding non-existent or merely possible entities (or both) to our ontology (I

borrow this formulation from Read 2005: 331–2). To be sure, one would like to see reasons

here, and not just a charge of having committed a fallacy. Russell gave one reason when he

objected to both non-existents and possibilia, chiefly on the grounds that analysis is the

20 An example of a philosopher who is explicit in making this commitment is Gustav Bergmann, although his

considerations relate not to truth as such but to intentionality in general. According to Bergmann, mental facts (“knowing situations” in a broad sense of “knowing”) involve the relation of intentionality, which relates a subject to an actual or possible fact (1964, p. 308; 1967, pp. 214–5). This presupposes that both actual and possible facts are genuine unities, and then one must give some ontological ground for the difference between the two–the question of ontological ground is one that Bergmann always stresses. An actual fact is an actual unity, where actual unity is a matter of what Bergmann calls a ‘nexus of exemplification’ actually relating the other constituents of the fact. A possible fact, on the other hand, is as much a unity as an actual one, but here unity is grounded in possibility as a mode of existence (1967, pp. 248; 250). To be sure, this calls for further elaboration, as it’s not clear what the unity of a merely possible fact could amount to. This question arises for ‘non-existent facts’ as well. I’ll return to this latter issue below, in section 13.

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correct method in philosophy and that the end points of analysis should entities ones with

which one can be acquainted.21 From Russell’s point of view, there’s little difference between

the two cases, the non-existent and the merely possible.

12. So, how did Russell’s new theory avoid commitment to non-existents (and mere

possibilia)? Here the influence of Wittgenstein and his picture theory becomes conspicuous.

As early as 1914 we find Russell informing Bradley: “Chiefly through the work of an

Austrian pupil of mine, I now seem to see answers about unities; but the subject is so difficult

and fundamental that I still hesitate.” (Russell to Bradley, 30 January, 1914, as cited by

Griffin 1993, p. 159). Russell’s lectures on logical atomism, delivered 1918, are, as their

author explains, “very largely concerned with explaining certain ideas which I learnt from my

friend and former pupil Ludwig Wittgenstein (PLA, p. 160). And in the transitional period

1918–9–transitional, that is, when it comes to the theory of judgment–we find Russell

explaining that “[o]ne vital point in the theory [of propositions] is that a proposition is a fact.

This is why it can express a fact (1918, p. 268; emphases in the original).

That propositions themselves must be construed as facts because it’s only in this way

that we can make sense of how they can have sense or express something is a point that we’ve

learned to associate with Wittgenstein.22 And it’s not difficult to see why Russell should have

been attracted to it. He believed he possessed an explanation of fact unity in the notion of a

relating relation: a fact is a unity because one of its constituent actually relates the other

constituents. If, now, propositions, too, are facts, the explanation can be extended to cover

propositional unity as well. Thus, propositional unity is to be treated as a special case of fact

unity:

21 See (ThK, p. 111). 22 See NB, p. 105; Tractatus. 3.142.

49

The simplest possible schema of correspondence between proposition and objective is

afforded by such cases as visual memory-images. I call up a picture of a room that I

know, and in my picture the window is to the left of the fire. I give to this picture that

sort of belief which we call “memory”. When the room was present to sense, the

window was, in fact, to the left of the fire. In this case, I have a complex image, which

we may analyze, for our purposes, into (a) the image of the window, (b) the image of

the fire, (c) the relation that (a) is to the left of (b). The objective consists of the window

and the fire with the very same relation between them. In such a case, the objective of a

proposition consists of the meanings of its constituent images related (or not related, as

the case may be) by the same relation as that which holds between the constituent

images in the proposition. When the objective is that the same relation holds, the

proposition is true; when the objective is that the same relation does not hold, the

proposition is false. (OP, pp. 302–3; emphasis added)

A proposition, according to Russell, is a fact and hence an actual unity because it is, quite

literally, a picture which shares a common relation with what it pictures. Saying just this

much, however, wouldn’t solve all of Russell’s problems, because nothing has so far been

said about the problem of non-existence.

Consider some of the very first things that Wittgenstein wrote concerning the idea of

propositions as pictures:

The general concept of the proposition carries with it a quite general concept of the co-

ordination of proposition with situation [...]. In the proposition a world is as it were put

together experimentally (as when in the law-court in Paris a motor-car accident is

represented by means of dolls, etc.) (NB: 7)

50

In the proposition we–so to speak–arrange things experimentally, as they do not have to

be in reality’ (NB: 13; emphasis in the original).

The ‘situation’ with which a proposition is ‘coordinated’ is an ‘experimental arrangement of

things’, and it looks very much like a possible state of affairs. Using this as a clue, one might

unpack the import of Wittgenstein’s idea as follows:

Wittgenstein’s claim is that propositions represent by virtue of providing (or, indeed,

being) a picture of a fact. The elements of a picture stand for elements of the fact to be

pictured and it is then the arrangement of the elements of the proposition in a

determinate way that represents the elements they stand for being so arranged in reality.

If the fact pictured obtains, then the proposition is true, otherwise it is false. To

understand the proposition, therefore, is simply to know what would be the case if it

were true; in other words, to understand what is being pictured. (Stevens 2005: 113)

This reading uses ‘fact’ in the same inappropriate way as Moore did in SMPP. There cannot

be question of whether a fact obtains; its’ only states of affairs (possible facts) of which we

may ask this question. Once this detail is set straight, Stevens’ gloss on the picture theory

comes down to just this. A proposition is a logical picture of a state of affairs. If the

proposition is true, what it pictures is a fact; and if the proposition is false, what it pictures is

not a fact but a merely possible fact.

Thus understood, the picture theory incurs a forthright commitment to merely possible

states of affairs. This may or may not have been to Wittgenstein’s liking; but it certainly

wasn’t congenial to Russell. Hence, in determining what was Russell’s conception of

51

propositions as pictures, we should take care to avoid the above reading of the idea of

picturing.

A key element that Russell took over from Wittgenstein’s account of propositions and

how they can have sense or express facts was the notion of bipolarity of propositions. It

occupies a central role in Wittgenstein pre-war Notes on Logic, and is summarized by its

author–or by Russell23–as follows:

What corresponds in reality to a proposition depends upon whether it is true or false.

But we must be able to understand a proposition without knowing if it is true or false.

What we know when we understand a proposition is this: we know what is the case if it

is true and what is the case if it is false. But we do not necessarily know whether it is

actually true or false.

Every proposition is essentially true-false. Thus a proposition has two poles

(corresponding to case of its truth and case of its falsity). We call this the sense of a

proposition. The meaning of a proposition is the fact which actually corresponds to it.

The chief characteristic of my theory is: p has the same meaning as not-p [...]. (NB, p.

94; emphases in the original)

Russell’s own account of the matter is found, for example in Chapter 13 of The Analysis of

Mind. The meaning of a proposition consists in the fact that it has an ‘objective reference’, a

relationship that differs from the meaning of names because of the duality of true and false

propositions. As before, Russell claims that there are true and false propositions but not true

and false facts (and, we may add, there’s no duality of existent and non-existent facts or of

actual and merely possible facts). It is for this reason, Russell continues, that the meaning of a

23 The quotation is from the so-called ‘Costello Version’ of ‘Notes on Logic’, which was probably edited by

Russell, in early 1914, from a text dictated by Wittgenstein. See McGuinness (2002) for details.

52

proposition cannot just be the entity that it refers to. Rather, given a proposition, there’s just

one fact which is the objective reference of both that proposition and its contradictory

opposite. We may say, metaphorically, that a true proposition points towards the fact while a

false one points away from the fact. Thus–and this is clearly meant to be more than just a

metaphor–the meaning of a proposition “today is Tuesday” consists in pointing to the fact that

today is Tuesday, if that is a fact, or away from the fact that today is not Tuesday, if that is a

fact; and the meaning of “today is not Tuesday” is the exact opposite of this. In this way we

can speak of the ‘meaning’ of a proposition without knowing whether the proposition is true

or false. Thus, according to Russell, ”we know the meaning of a proposition when we know

what would make it true and what would make it false, even if we do not know whether it is

in fact true or false”(AM, p. 273).

13. So, the psychological account of belief, propositions and meaning promises solutions to

two problems which had confounded Russell for so long; the problem of propositional unity

and the problem of the false proposition. The new theory has its own difficulties, however. To

close this paper, I will discuss one problem–or, rather, a set of problems–that connects the

new theory with an old theme, the definability of truth.

As we have seen, Russell’s new theory is calculated to avoid the postulation of non-

existent and merely possible facts. This comes at a price, however, for as we’ve also seen, the

theory is committed to there being negative facts. Given a pair of contradictory propositions,

p and not-p, there’s just one fact that is the objective reference of both; if p is true, then it’s a

fact that p; if not-p is true, then it’s a fact that not-p; thus, given the bipolarity of propositions,

it follows that there are negative facts. As Wittgenstein observed in the Notes on Logic, ‘if the

proposition “This rose is not red” is true, then what it signifies is negative’ (NB, p. 94).

But these negative facts turn out to be problematic entities; and not just because there is

the “almost unquenchable desire to find some way of avoiding the admission that negative

53

facts are as ultimate as those that are positive” which Russell once diagnosed in the human

breast (OP, p. 280). To see the difficulties, let’s retrace the steps that brought Russell here.

Accepting a correspondence account of truth, Russell began from the intuitive view that

the truth or falsehood of a proposition depends upon the existence or non-existence,

respectively, of a suitable entity. As he observed in ONTF, ‘it is difficult to abandon the view

that, in some way, the truth or falsehood of a judgment depends upon the presence or absence

of a “corresponding” entity of some sort’. Understood one way, the introduction of ‘absences’

leads to the problem of non-existents, as is shown by Moore’s theory of truth in SMPP, which

grounds the asymmetry of truth and falsehood on the distinction between existence and non-

existence.24 Since Russell wouldn’t have this, he was forced to ground the asymmetry in

something actually existent,; hence the notion of ‘objective reference’. Given this, he could

continue to agree–with the Moore of SMPP and with his own former self, for example– that

‘the truth or falsehood of a judgment depends upon the presence or absence of a

corresponding entity’. Now, though, the role of absences is taken over by negative facts,

which are actual unities, rather than simply absences. Russell himself is clear on this:

There might be an attempt to substitute for a negative fact a mere absence of fact. If A

loves B, it may be said, that is a good substantial fact; while if A does not love B, that

merely expresses the absence of a fact composed of A, and loving and B, and by no

means involves the actual existence of a negative fact. But the absence of a fact is itself

a negative fact: it is the fact that there is not such a fact as A loving B. (OP, p. 280)

Focusing on ‘atomic facts’, we may ask at once: What kind of entities are negative facts, and

how do they differ from positive facts? What makes for the unity of negative facts? The fact

24 “To say of [a] belief that it is true would be to say of it that the fact to which it refers is–that there is such a fact in the Universe as the fact to which it refers; while to say of it that it is false is to say of it that the fact to which it refers simply is not–that there is no such fact in the Universe” (SMPP, p. 255; emphases in the original).

54

that Desdemona loves Othello is a unity because the relation of loving actually relates

Desdemona and Othello: universals only ever occur in facts in this distinctive way, and that’s

why a (positive) fact is a unity. What, then, of negative facts, like the fact that Desdemona

does not love Cassio?

Linsky (1999, p. 48) argues that there is no special problem here: “Negative facts would

only require a distinctive mode of combination of objects and universals, a new variety of

predication, which would tie objects together in a negative way”. Now, I’m not sure that I can

see how this could be. How can things’ not being tied together be a way for them to be tied

together? After all, that’s what a unity is, a way for given things to be ‘tied together’.

Despite the felt difficulty, Linsky’s suggestion, or something similar to it, is the sort of

thing that Russell was committed to. His own remarks on the subject are sparse, and what

little he says is given in the course of a discussion of what are the constituents of negative

facts, this being one way of getting at the question of what in general grounds the distinction

between positive and negative facts.

Russell is quite clear that negative facts don’t differ from such as are positive by having

a further constituent corresponding to the sign of negation that occurs in a negative

proposition (OP, pp. 279–80): a negative fact ‘Plato does not precede Socrates’ has just as

many constituents as the positive fact ‘Socrates precedes Plato’. Russell doesn’t give any

reasons for this here, but there’s the familiar consideration, pointed out for instance by

Stevens (2005, p. 132), that if the difference between the fact verifying ‘A’ and the fact

verifying ‘ A’ consisted in the latter’s having a constituent corresponding to the negation

operator, then we ought to apply this to ‘A’ and ‘ A’ as well, which, presumably, we

wouldn’t want to say. I won’t pause to consider whether this is plausibly attributed to Russell.

Whatever his reasons, Russell does maintain that the difference between positive and negative

facts (and between their forms) is not one of constituents.

55

Given this, it would be natural to revert to an account similar to Linsky’s, saying that

the negativity of a negative fact resides in the relation of the fact. Potter (2009, p. 144)

considers this idea, too, saying that it’s we should ‘roll up the negation into the verb of the

fact’, rather than see the structure of a negative fact as consisting of a positive fact plus an

‘element called negation’. He attributes this view to the Russell of OP. But what Russell

himself says about this in OP is just that the difference between the two forms–forms for

which he uses the symbols ‘xRy’ and ‘not-xRy’–is one of opposing qualities. According to

Russell’s own account, then, atomic facts (and their forms) ‘have two opposite qualities,

positive and negative’ (OP, p. 280).25

Of course, none of this answers the original worry about negative facts and their unity.

Russell has nothing to contribute to this issue, and the introduction of qualities of facts is

meant not so much to resolve the problem of unity as to address the more general question of

how to distinguish negative facts from such as are positive. But here, too, he has nothing more

to offer than to declare that the difference between the two qualities is ‘ultimate and

irreducible’ (ibid.).

These rather meagre results extend to truth and falsehood as well. Russell’s new theory

does deliver an account of truth and falsehood for atomic propositions:

An atomic proposition <p> is true if and only if there is a fact [p] which is of like

polarity to <p>;

an atomic proposition <p> is false if and only if there is a fact [p] which is of opposite

polarity to <p>.

25 This wasn’t Russell’s last word on the subject of negative facts; see Stevens (2005, pp. 138–44) for his

later views, formulated in An Inquiry into Meaning and Truth (1940) and, in greater detail, in Human Knowledge: Its Scope and Limits (1948).

56

(Or we may say, if we wish to make explicit the semantic-cum-logical relationship between

<p> and [p]: ‘an atomic proposition <p> is true if and only if the fact [p] which is the

objective reference of <p> is of like polarity to <p>’; similarly for falsehood.) Clearly, the

schematic account cannot stand alone. And they it won’t gain much in this respect if we

expand on it along the following lines:

An atomic proposition, <p>, is true if and only there is a fact [p] which possesses

positive quality;

the negation of an atomic proposition, <not-p>, is true if and only if there is a fact [p]

which possesses negative quality.

‘Technically’, this account of truth doesn’t belong with truth-primitivism. According to truth-

primitivism, we are ‘compelled to regard it as an ultimate and not further explicable fact that

[propositions] are of two sorts, the true and the false’, whereas here the difference is

explicable by the sort of conditions given above: an atomic proposition is true if its objective

reference is of like polarity, and false if it is of opposite polarity.

But Russell himself was dissatisfied with the definition of truth that emerges from

bipolarity and negative facts. He argues that what he calls the ‘formal correspondence which

makes truth’ isn’t untrue but it is inadequate (AM, p. 278), and the reason he singles out

echoes what he once felt about truth-primitivism. Recall how he defended, in MTCA, the view

that ‘there is no problem at all in truth and falsehood; that some propositions are true and

some false, just as some roses are red and some white’. This was then accompanied by the

qualm that the ‘theory seems to leave our preference for truth a mere unaccountable prejudice,

and in no way to answer to the feeling of truth and falsehood’. He now levels similar

complaint at the new account of truth:

57

I do not believe that the above formal theory is untrue, but I do believe that it is

inadequate. It does not, for example, throw any light upon our preference for true beliefs

rather than false ones. This preference is only explicable by taking account of the causal

efficacy of beliefs, and of the greater appropriateness of the responses resulting from

true beliefs. (AM, p. 278)

The target here is the explanatory basis of the account, the distinction between positive and

negative facts. To say merely that “Socrates precedes Plato” is true while “Plato precedes

Socrates” is false because the fact corresponding to the former possesses a certain primitive

quality whereas the fact corresponding to the latter possesses a certain other primitive quality

is inadequate in much the same way as the primitivist account. Clearly, primitivism fails to

account for the asymmetry between truth and falsehood. Arguably, this applies to the new

theory as well: why should we label this quality ‘positive’, i.e. one whose presence in a fact

renders a certain proposition true while calling that quality ‘negative’, i.e. one whose presence

in a fact renders a certain proposition false?

Perhaps this is the reason why Russell calls correspondence a ‘formal’ relation. His

theory of truth is a sort of structuralist account; truth and falsehood are properties which are

structurally identical–and hence you might imagine them swapped one for the other without

making any difference to the definitions of truth and falsehood (Moore’s theory of truth is

quite different in this respect as it aligns truth with existence and falsehood with non-

existence). So, when Russell says the ‘formal theory’ of truth is inadequate what he means is

that it is incomplete.

But as the quotation also indicates, he also believes that the asymmetry–our preference

for true beliefs over false ones–can be made sense of by resorting to what we might call extra-

58

formal considerations, namely by deriving this asymmetry from the different causal efficacy

of true vs. false beliefs.

14. In this paper, I’ve outlined some of the developments that took place in Russell’s theories

of truth between, roughly, 1903 and 1923. My focus has been, first, on the so-called problem

of the unity of the proposition, with a view to showing how Russell gradually came to

appreciate it’s full complexity; and second, on the problem of the ‘existence of the non-

existent’. Together, these are the two major determinants on Russell’s attempts at working out

a theory of truth.

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