sellars on bradley's ‘paradox’

J A M E S J E F F R E Y W I L K I N

S E L L A R S ON B R A D L E Y ' S ' P A R A D O X '

(Received 7 June, 1978)

Some contemporary nominalists hold that predicates are non-referring terms.

Instead, predicates are said to 'characterize', or be 'true of ' , or be 'satisfied by'

objects. Therefore, the use of predicates does not commit one to 'abstract

entities' (classes, properties, relations), a Some realists hold that the use of

predicates does commit one to 'abstract entities' in that they must be taken to

refer to properties and relations. Wilfrid Sellars is such a nominalist, Bertrand

Russell such a realist. Sellars believes that realism can be refuted by making

use of Bradley's puzzle, and argues that Russell's attempt to escape Bradley's

'paradox' lands him in a further 'paradox'. In this paper I will try to show

that Sellars is wrong on both counts. I will argue, furthermore, that Sellars

is mistaken in thinking that Jumblese, his 'perspicuous' notation in which no

predicate words appear, undercuts the issue raised by Bradley. Sellars gives the following 'semantical' version of Bradley's argument

([14], 78). Take the true sentence 'Rab', and assume that 'a' and 'b ' n a m e

objects, and that 'R' names a relation. That 'Rab'is true indicates that a 'fact-

making relation', R ~, obtains between R, a, and b. Therefore, to 'make

explicit' the reference of 'Rab', we must use the sentence 'R~Rab '. But that

'R1Rab ' is true indicates that a further 'fact-making relation' holds among

R 1 , R, a, and b. To 'make explicit' the reference of 'RaRab ' (and 'Rab'), then,

we must use the sentence 'R2R~Rab '. And so on. Sellars construes this pattern as a reductio ad absurdum of the claim that 'R ' names a relation, and

therefore of realism. Russell, on the other hand, believed that Bradley's

regress can be stopped, if a feature of relation words is not confusedly taken

to reflect one o f relations. He claimed that in giving 'verbal expression' to the

fact that Rab, "...the word for a relation does have to be related to the words for its terms" ([9], 264). He held, however, that "this is a linguistic, not a

metaphysical fact..." ([9] , 264), for one may take the relation R to be the

'fact-making relation' in the fact that Rab. One need not recognize the

further relation, R ~ , corresponding to the relation among the words in the

Philosophical Studies 36 (1979) 51-59. 0031-8116/79/0361-0051 $00.90 Copyright �9 1979 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.

52 J A M E S J E F F R E Y W I L K I N

sentence 'Rab' . 2 Since Russell suggests that the relation between the words

'R ' , 'a ' , and 'b ' misled Bradley into thinking that there must be a further relation between R, a, and b, Russell may be interpreted as proposing that in

order perspicuously to represent a relation between a and b, one must fix a

relation between the names 'a ' and 'b ' , and not between 'a ' , 'b ' , and a relation

word. In fact, there are places where Russell discusses this approach, and ap-

parently approves of it ([9] , 275-76 ; [11], 316). This leads to Sellars' main

attack on Russell. Consider the following sentences, the last o f which is in Jumblese:

(1) A, B exemplify preceding.

(2) A precedes B.

(3) A B

Sellars notes that Russell thinks (2) more perspicuous than (1). But Russell's

qualms about the misleading aspect of (2), together with his "surprisingly

lukewarm endorsement" ([14], 82) of (3), are then construed by Sellars as

evidence that Russell came dimly to see that only with (3), and not with (2),

may Bradley's regress be stopped. For Russell, that (2) is more perspicuous

than (1) reflects his view that 'exemplify ' does not refer, or, in other words,

that there is no exemplification nexus between objects and relations. The idea behind Sellars' use of Jumblese is that the move from (2) to (3) implies that

'precedes' does not refer, or, in other words, that precedes is not a relation

in re. So, according to Sellars, where Russell favors (2), he professes realism, but with a vague uneasiness that he has not adequately dealt with Bradley;

and where Russell approves (3), he can rebut Bradley, but only, as Russell did not grasp, at the price of abandoning realism. In Sellars' words, To make the move at the 'exemplify' level, and in the way which Russell makes it, implies that 'precedes' denotes an object in the world. To make the move at the 'precedes' level is to imply that it does not. Thus to make the move at both levels is to imply that 'precedes' does and does not denote an object in the world, and, hence to be trapped in paradox. ([14], 81.)

The mistake responsible for Sellars' 'paradox' is the assumption that, were Russell to make the move from (2) to (3), it would follow that 'precedes',

for Russell, does not denote an object in the world. But the possibility of eliminating a word should not be taken as an argument that cancels any basis for holding that some entity exists. Obviously, writing (2) in place of (1) is a trivial aspect of the reasoning which led Russell to deny that exemplifica-

S E L L A R S ON B R A D L E Y ' S ' P A R A D O X ' 53

tion is needed to 'tie' objects to relations. We have seen a reason why Russell

might favor (3) as compared with (2). But that his endorsement of (3) is

'lukewarm' is not at all 'surprising', for two reasons. First, Russell thought

that one could easily avoid Bradley's mistake once the misleading aspect of (2) is pointed out ([6], 243). So it is not necessary to rewrite (2) in terms of (3) to avoid philosophical perplexity. Second, and more important, to Russell's mind the choice between (2) and (3) would have no ontological im- placations. After all, both (2) and (3) represent the same fact, and Russell's

analysis of that fact recognizes, in addition to A and B, a third constituent,

namely a relation that holds between A and B. Sellars' exaggeration of the force of replacing (2) with (3) reduces his

criticism of Russell to an insinuation that Russell's position on whether

precedes is 'an object in the world' is ambiguous. Sellars does not show that

Russell's reply to Bradley is inadequate or 'paradoxical'. Instead, he focuses

on Russell's apparent and unimportant indecisiveness regarding relation

words, and wrongly infers an inconsistency on Russell's part regarding rela-

tions. Russell claimed that "...there is a sense in which facts can be analyzed"

([10], 193). Bradley may be interpreted as illuminating a sense in which facts

cannot be analyzed. To see this, consider one who holds that facts are analyzable in the sense of being 'reducible' to their 'basic constituents'. Such

a view would be problematic. For suppose that A, B, and the relation pre-

cedes are taken to be the constituents of the fact that A precedes B. Then the

different facts, that A precedes B and that B precedes A, would evidently have the same analysis. Furthermore, we could have ~ e constituents A, B,

and precedes even if the fact that A precedes B did not obtain. The latter point should convince one that facts cannot be construed as 'reducible' to their constituents, or, in other words, that a fact cannot be 'identified' with the set of its constituents. So facts are not analyzable in this sense) I take this to be an implication of Bradley's puzzle, namely that 'complexes' are not

'reducible' to their 'parts'. Understanding this allows us to see how one who 'analyzes' a fact in terms of particulars, a universal, and exemplification car~. still fail to stop Bradley's regress. For even with this proliferation of entities,

one cannot claim that the fact 'reduces' to its constituents. One cannot 'identify' the fact with a set consisting of one or more particulars, a universal, and a nexus or tie. Instead, a fact must be taken to consist of its constituents in a dertain structure, regardless of whether exemplification is included


among those constituents. Grasping this, one sees that Bradley's 'paradox'

cannot be 'resolved', for it is not a paradox, but rather a way of getting at this

basic feature of facts.

Sellars writes: ...the classical problem of universals rests in large part on the fact that in such languages as English and German expressions referring to universals are constructed on an illustrat- ing principle which highlights a design which actually plays a subordinate role, and con- sequently tempts us to cut up such sentences as

Triangular(a)

into two parts, one of which has to do with the universal rather than the particular, the other with the particular rather than the universal, and tempts us therefore to construe the statement as asserting a dyadic relation ('exemplification') to obtain between the particular and the universal. ([121; [15], 266.)

On the other hand, in Sellars' view, Jumblese is perspicuous in the sense of

having a "built-in protection against Bradley's puzzle" ([13]; [16], 243). But

does the use of Jumblese somehow prevent one from attempting to 'analyze'

facts in a way that leads to the regress associated with Bradley? Or, are

linguistic cues present in Jumblese that could mislead an 'incorrigible meta-

physician', as does the emphasis on predicate words and concatenation in

natural languages and PM-ese? The latter, I think, is the case.

In Jumblese the fact that two names are related characterizes two objects

as being related, just as the fact that a 'precedes' occurs between two l~ames

in English represents that one object (or event) precedes another. And just

as one can distinguish in the pattern

A precedes B

the subject signs, the verb, and the order in which the subject signs stand to

the verb, so in the Jumblese pattern

(3) A B

one can distinguish the subject signs, the fact that the subject signs are

diagonally (spatially) related, and the order in which the signs enter the

relation. The point is that (3) and

(4) B A

have an obvious logical complexity, and further, share a specific spatial relation while differing as to the order in which the names enter the relation.


The shared characteristic would lead the incorrigible metaphysician - call him Jones - to analyze the facts represented by (3) and (4) as containing,

in addition to the objects A and B, a third constituent, corresponding to the spatial relation common to (3) and (4). Jones may then be perplexed on two

grounds. First, he may be puzzled as to the relation between the three entities he has recognized. Second, he may decide that his analysis of the distinct

facts represented by (3) and (4), in so far as it indicates just the same three entities in both cases, is inadequate. The Jumblese patterns will 'misguide'

him even at this point, for the different orders in which 'A' and 'B' enter into those patterns provide the cue for his 'discovering', in each of the facts corresponding to (3) and (4), a fourth entity which 'connects' the first three in

a certain order.

At this point, one might claim that Jumblese differs from natural languages and PM-ese in a crucial respect. These latter languages enable Jones to express

his 'discovery' by

(1) A, B exemplify preceding

or some sentence that is equally problematic from Bradley's point of view.

On the other hand, in Jumblese (3) and (4) cannot be reformulated in a way

tl~at suggests there is a further entity involved, which connects and orders

the four of Jones' latest analysis. This difference, then, may be taken to un- pack the sense in which Jumblese has a 'built-in protection against Bradley's puzzle'. For, apparently 'exemplify' cannot be transcribed in Jumblese; nor

therefore, can sentences corresponding to any but the first step in Bradley's

regress be formulated in Jumblese. However, Jones is incorrigible and may insist that the perspicuous render-

ings, in Jumblese, of (3) and (4) are:

(33 A B x

Y (4') B A x

Y

(3') would be construed as indicating that the two objects, A and B, taken in that order, 'stand in' the relation represented by the configuration of variables which follows. Sellars introduces variously spaced pairs of dots -

e.g. ' . . . . . . . . . . . . . - as variables in Jumblese, corresponding to the dyadic predicate variables of PM-ese ([13]; [16], 235). Making use of these


dot-variables, we can coordinate the triadic relational predicate 'exemplify ' in (1) to the Jumblese pattern

(5) X r"

where it is understood that any ' interpreted' configuration of the lower case variables 'x ' and 'y ' - i.e. any such confirguration that has been assigned a

dyadic relation among particulars - may replace the two dots. (5) then indicates a three place relation which takes as relata two particulars and a

dyadic relation. One who uses (Sellars would say abuses) Jumblese in this way runs into Bradley's objection if he 'identifies' the fact expressed by (3')

with the set whose members are

A, B, x , X Y

Y

For, the fact expressed by (4') must evidently be 'identified' with the same

set. Furthermore, we would have the set even if the fact did not obtain. Put

another way, unless Jones breaks out of his futile pattern of analysis, he wi l l

'discover' a further entity 'connecting' the relation indicated by (5) to A, B, and x y . And then a further entity, and so on. One can imagine how such

entities would be represented in Jumblese. Therefore, Sellars is wrong: Jumblese does not have a 'built-in protection against Bradley's puzzle'. Jones'

futile pattern is prompted by syntactical features of Jumblese. Furthermore,

each stage in Jones' analysis (and therefore, in Bradley's regress) can be represented by a sentence in Jumblese. 4

Sellars might respond to this line of thought by claiming that (3 ' ) and (4 ' ) are not well-formed in Jumblese, or cannot be interpreted in the way Jones

interprets them. Such a response would be inadequate for two reasons. First,

if Jumblese is construed syntactically, as a language without predicate words, whose well-formed formulas consist of variously arranged strings of names and variables, then (3 ' ) and (4 ' ) a r e well-formed formulas in Jumblese. But if Sellars makes it a rule of Jumblese that any n-place configuration of individual variables represents an n-place relation between particulars, then

X Y x

Y

and therefore (3 ' ) and (4') , could not be interpreted as Jones tries to interpret them. But then the most that Sellars could claim is that, given his interpreta-


tion rule, well-formed formulas of Jumblese cannot be interpreted in a certain way. In so far as Jumblese is supposed to be syntactically perspicuous, where

natural languages and PM-ese are not, the claim that Jumblese is unproblemat-

ic, given a certain interpretation rule, is irrelevant. Second, one who holds that PM-ese, rather than Jumblese, is perspicuous,

could claim that PM-ese contains a 'built-in protection against Bradley's

puzzle' in the same sense that Sellars' Jumblese does. For, he also could mai(e it a rule that no predicate indicates a relation between particulars and prop-

erties or relations. Furthermore, one whose perspicuous language is confined

to the lower functional calculus could point out that such predicates as would

be needed to express exemplification, e.g. 'Ea' and 'E2' in the following formulas

El (x,j9 E2 (x,y,R)

could not appear among the basic vocabulary of his schema, s All of this

shows, I think, that there would be nothing special about Jumblese with respect to the issue at hand.

Finally, SeUars might claim that, in Jumblese, (3) adequately represents

the fact that A precedes B. That the fact need not be represented by (3 ')

would then be taken by Sellars to show the sense in which Jumblese protects against Bradley's puzzle. However, one could respond that, in English, 'A

precedes B' adequately represents the fact in question: one need not use (1).

This was Russell's view. Why might Sellars think that Russell's elimination of the word 'exemplify' is problematic, but that his own suppression of (3') in

favor of (3) is not? Apparently, Sellars' only reply is that if one takes the relation precedes to be a constituent of the fact, and if one then wants to use a

word to refer to that relation, one must use (1) rather than 'A precedes B ' , since predicates are non-referring terms. But this merely begs the question, for as I indicated at the outset, what is at issue between a nominalist like

Sellars and a realist like Russell is, in the first place, whether predicates refer. One way of arguing for nominalism involves refuting realism. This was tl~e

purported impact of the 'semantical' version of Bradley's 'paradox' consider- ed earlier. However, one does not refute realism by showing only that it is at odds with nominalism. 6

University o f Minnesota

58 JAMES J E F F R E Y WILKIN

NOTES

This nominalistic 'solution' to the problem of universals is criticized by Herbert Hoch- berg in [1], [21, and [3]. 2 Underlying Russell's response to Bradley is his view, stemming from Frege, that relations and attributes are of a radically different nature than particulars. Following Frege, Russell held that the 'proper symbol' for a relation is a propositional function ([7], 338). For example, the proper symbol for the attribute red would be the propositional function 'x is red'. Holding that the proper symbol for an attribute (or relation) must "bring in the form of a proposition" ([10]: 205), Russell views the attribute (or relation) as itself involving the 'form' or predicative aspect indicated by the propositional function. This underlies Russell's attempt to rebut Bradley, for it enables Russell to point to a disanalogy between the fact that Rab and the 'verbal expression' of the fact. The latter involves a relation between 'R', 'a', and 'b' , but the relation R x y is itself 'predicative', and therefore need not be related by a further (predicative) relation to a and b. 3 Russell also makes this point ([8], 28). So it is not clear what the sense is in which Russell holds that facts are analyzable. * Actually, some modification of the syntax of Jumblese would be needed to provide for umambiguous renderings of most of the sentences belonging to Bradley's pattern. The modifications would not, however, involve introducing predicate words. Moreover, corresponding syntactical modifications of PM-ese would be required to allow for sentences like 'R a (R 2 , a, b)', which contain relational predicates that straddle types. s One whose perspicuous schema consists of the lower functional calculus could in- troduce the symbol 'E 1 ' in terms of a definition - eg. 'E 1 (x, .t) = def. fx ' . As noted in the last footnote, the definition would require a modification in the basic syntax of the schema to stipulate the well-formedness of formulas containing such a predicate. 6 I am grateful to Stephanie K. Eller and Professors Herbert Hochberg and William Hanson whose criticisms of earlier drafts and helpful suggestions led to many and in some cases major improvements.

B IBLIOGRAPHY

[1] Hochberg, Herbert: 1977, 'Mapping, meaning, and metaphysics', in: Midwest Studies in Philosophy, Vol. II, P. French et al. (eds.), (The University of Minnesota, Morris), pp. 191-211.

[2] Hochberg, Herbert: 1967, 'Nominalism, Platonism, and "Being true o f" ', Nofis 1, pp. 413-419.

[3] Hochberg, Herbert: 1978, 'Sellars and Goodman on predicates, properties, and truth', in Midwest Studies in Philosophy, Vol. III, O. French et al. (eds.), (The University of Minnesota, Morris), pp. 360-368.

[41 Ramsey, F. P.: 1931, The Foundations of Mathematics (Kegan Paul, London). [5] Rarnsey, F.P.: 1925, 'Universals', Mind 34, pp. 401-417; reprinted in [4] pp.

112-134. [6] Russell, Bertrand: 1954, The Analysis of Matter (Dover Publications, Inc., New

York). [7] Russell, Bertrand: 1968, 'Logical atomism', reprinted in: Logic and Knowledge,

R. C. Marsh (ed.), (G. P. Putnam's Sons, New York), pp. 323-343. [8] Russell, Bertrand: 1973, 'Meinong's theory of complexes and assumptions', reprint-

ed in: Essays in Analysis, D. Lackey (ed.) (George Braziller, New York), pp. 21-76.

SELLARS ON BRADLEY'S 'PARADOX' 59

[9] Russell, Bertrand: 1968, An Outline of Philosophy (The World Publ. Co., New York).

[10] Russell, Bertrand, 'The philosophy of logical atomism', in: Logic and Knowledge, pp. 177-281.

[11] Russell, Bertrand, 'On propositions: What they are and how they mean', reprinted in: Logic and Knowledge, pp. 285-320.

[12] Sellars, Wilfrid: 1963, 'Abstract entities', Review of Metaphysics 16, pp. 627-71; reprinted in [15], 229-69.

[13] Sellars, Wilfrid: 1962, 'Naming and saying', Philosophy of Science 29, pp. 7-26; reprinted in [ 16], 225-46.

[14] Sellars, Wilfrid: 1974, 'Ontology and the philosophy of mind in Russell', in: Ber- trand Russell's Philosophy, G. Nakhnikian (ed.), (Barnes and Noble, New York), pp. 57-100.

[15] Sellars, Wilffid: 1963, Philosophical Perspectives (Charles C. Thomas, Springfield). [t6] Sellars, Wilfrid: 1963, Science, Perception and Reality (Kegan Paul, London).

sellars on bradley's ‘paradox’

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