RUSSELL, CHOMSKY
and NOMINALIZATION
Steven R. Bayne
Bertrand Russell held, at one time, that all propositions of pure
mathematics are of the form "p implies q" (1903:3). But, when he set
out to state the meaning of this, he encountered a problem he would
describe as "inevitable," a problem he professed to be unable to
solve. What I propose to do is show how, working within the framework
of Russell's early platonism, a solution to this problem based on
Chomsky's (1970) views on nominalization can be made available. Others
have commented on the significance of Russell's use of nominalization
(Cocchiarella 1980; Landini 1998), but here the larger objective is to
demonstrate how tools supplied by theoretical linguistics may be
applied in resolving subtle philosophical problems of consequence.
Russell's Problem
What bothered Russell was a semantic contrast between (1) and (2).
1. Socrates is a man therefore Socrates is mortal
2. Socrates is a man implies 2+2=4
(1) states a relation which obtains only between asserted
propositions, whereas (2) asserts a relation that may hold between any
two propositions such that the first is false or the second is true;
although neither proposition is itself asserted by (2). Problematic is
the fact that if assertion modifies a proposition then "no proposition
which can possibly in any context be unasserted could be true, since
when asserted it would become a different proposition" (Russell
1903:35). Russell observes that the distinction between asserted and
unasserted propositions is expressed grammatically in terms of
sentential and nominal constructions: the difference, he says, between
(3) and (4) is that (3) is asserted, whereas the proposition
represented by (4) is merely considered, insofar as it is a "complex
concept."
3. A is greater than B
4. A's being greater than B
Russell argued that we must be able to make propositions logical
subjects. Although he formulated his argument in terms of adjectives
(1903:46), his reasoning can be clearly stated in the case of
sentences: suppose we were unable to nominalize some proposition, p,
then we could not say "P is F," since we must make a subject
(argument) of the proposition; but neither could we say "P is not F."
Conjoining these two facts, double negation, applying in the second
instance, leads to a violation of the principle of
non-contradiction. Russell was acutely aware, however, that
nominalization was a grammatical move that might have logical
consequences. In one important passage he remarks:
The question is: What logical difference is expressed by the
difference of grammatical form?... By transforming the verb, as it
occurs in a proposition, into a verbal noun, the whole proposition can
be turned into a single logical subject, no longer asserted, and no
longer containing in itself truth or falsehood. But here too, there
seems to be no possibility of maintaining that the logical subject
which results is a different entity from the proposition... Yet it is
quite plain that the latter ["the truth of Caesar's death" - SRB] at
any rate is never equivalent to "Caesar died"...thus the contradiction
of an entity which cannot be made a logical subject appears to here
become inevitable. (1903: 48)
Central to Russell's problem is that nominalization may result in an
expression indicating some entity other than the entity expressed by
the associated sentence. If assertion is an essential feature of
sentences, then since nominalization dispenses with the feature of
assertion, there arises a reasonable doubt whether the nominalization
can be used to indicate the same entity expressed by the sentence. If
it cannot, then not only is it doubtful that propositions can be
represented as logical subjects; it also becomes a matter of
controversy whether the truth conditions for material implication can
even be stated. Material implication could become as ineffable as
logical form in Wittgenstein's Tractatus. In his remarks on
Meinong (1904:339), Russell sides with Meinong, and against Frege, in
maintaining that sentences and associated derived nominals refer to
the same things.
Russell's Problem and Chomsky's (1970) Views on
Nominalization
It will prove significant that the nominals Russell employs for the
purpose of indicating "complex concepts" are frequently gerundive
nominals and not, following Chomsky's typology, "derived nominals"
(Chomsky 1970). Aside from relations of material implication (and
recall that for Russell material implication is fundamental to
understanding formal implication) , there are other constructions
besides material implication where the problem posed by Russell
arises. Here I have in mind sentences involving propositional
attitudes such as (5) - (6).
5. John believes that Ortcutt is a spy
6. Mary fears that Olatunji may play Howard's drums
The attitude verbs, "believes" and "fears," appear to take a
proposition indicated by the expression following the complementizer
"that" as relatum. Such examples have been pursued with considerable
persistence by philosophers. What I will attempt here is to examine
sentences, such as (6) and (7), incorporating verbs of propositional
attitude that take nominal objects which themselves are related to
verbs of propositional attitude.
6. John believes Bill's assertion that Mary left
7. Mary doubts Bill's denial that John left
We will discover that Russell thought that he could speak consistently
of complex propositional concepts instead of asserted propositions
possessing a truth value by nominalizing the verb and thereby
cancelling the assertion. Nevertheless, he oversimplified, treating
all nominalizations as essentially the same.
Russell typically located the assertion element of a proposition in
the v erb (1903:44); more specifically, he relied on the notion that
the assertion element of the verb is always tied to a predicate, so
that in the proposition "John left home" the assertion "left home"
would combine with the subject in forming that proposition. What
Russell paid little attention to were differences among the various
sorts of nominals. He would move freely from gerundive nominals such
as "Socrates' being dead" to derived nominals such as "the death of
Socrates" (1903:43). No doubt his only concern was to detach the
assertion element using any stylistically acceptable nominal that
suited him.
Russell's effort to clarify material implication by using nominals to
refer to propositions minus the assertion feature opens the door to
consideration of other forms of entailment and of the role of
assertion. Hopefully, this will be made evident once we have laid out
some linguistic data, but for now a general point needs to be made,
and that is that Russell in moving back and forth between gerundive
and derived nominals failed to appreciate the fact that what sentences
are asserted by an utterance in at least one sense of "assert" depends
on the syntax of the particular nominal being used. Perhaps Russell's
neglect of the details of nominalization in his treatment of
propositional attitudes can be attributed to confining his concept of
implication to relations of the propositional calculus.
Chomsky and the Variety of Nominals
Chomsky (1970) identifies three sorts of nominals: gerundive (8),
derived (9), and "mixed" (10).
8. John's refusing the offer
9. John's refusal of the offer
10. John's refusing of the offer
His primary focus is on gerundive and derived nominals. For our
purposes what distinguishes them are two facts: first, in the case of
gerundives there is a uniformity of meaning between them and
corresponding subject-predicate sentences; and second, our inability
to substitute determiners for the "subject" of the nominal suggests
that it lacks the internal structure of an NP and is in fact arrived
at by transformation from a sentence. There is a third difference
between gerundive and derived nominals (Chomsky 1970: 264-265),
productivity, but for the time being I will concentrate on these two
features alone.
Chomsky (1970): The Transformationalist and Lexicalist
Positions
With respect to gerundive and derived nominals there are at least two
positions to take: the lexicalist position and the transformationalist
position. The lexicalist position (Chomsky 1970: 265) is that in order
to accommodate such nominals we must extend the base, consisting now
of both lexical and phrase structure rules (Chomsky 1965: 84). It's
competitor, the transformationalist position, would require additions
to the transformational component of the grammar. In the case of
derived nominals, for example, where internal structure "mirrors"
(Chomksy 1970:282) that of the corresponding sentence, we may take
advantage of the fact - on the lexicalist position - that the lexical
entry for the head is free to take the categorial feature of noun or
verb. No transformation is involved in accounting for the difference,
just a difference in the categorial feature. Much later Chomsky is
quite explicit in maintaining that this "correspondence" involves
possessing "essentially the same internal properties" (Chomsky
1986:63), a position also strongly encouraged by Abney (1987:110).
Chomsky ultimately concludes that gerundive nominals are best treated
by the transformationalist theory while derived nominals belong in the
lexicalist camp. He is less certain about the mixed cases, which will
not concern us. Now that we have some of the elements of Chomsky's
theory, let us return to Russell and see what philosophical ground can
be gained by Chomsky's analysis.
Russell's "indifference" Re-examined
Because Russell locates both assertion and having a truth value in the
verb, he tends to treat them as one and the same. This may not always
be obvious, as when he maintains that there is a sense of logical
assertion tantamount to truth itself (1903:49), and which is to be
distinguished from "psychological assertion." We will benefit at this
point by entertaining the possibility that assertion and truth are to
be distinguished. Doing so will allow us to state a proposal that
avoids violating the principle of non-contradiction, which Russell
felt was unavoidable. Before making explicit how this proposal is to
be implemented an emendation of Chomsky's 1970 views on nominalization
will provide a suitable opportunity to consider linguistic data that
would have considerably benefitted Russell's position.
Selectional Properties and Chomsky's
Nominalizations
Chomsky concludes that some complex nominals, gerundives, are best
treated transformationally, while other nominals require a lexicalist
approach. Besides this there is at least the implicit suggestion that
there are two kinds of syntactic nominals: those which are transforms
and those which follow from the freedom of lexical entries to select a
feature, either +verb or +noun. There is another proposal which has
yet to be considered: it may be the case that a derived nominal may be
arrived at in either of these two ways, and that which sort a nominal
must be taken to be depends on certain selectional properties of the
matrix verbs that take such nominals as syntactic complements. Here I
depart, somewhat, from Chomsky's 1970 analysis.
It is quite natural to suppose that if a nominal is reached by
tranformation of the associated sentence that the properties of that
sentence will be retained by, or at least recoverable from, the
transform. In this case the prediction will be that substituting the
sentence for that nominal in context will have no effect on the
relevant semantic properties of the sentence in which it occurs. This
prediction appears to be born out in the case where we substitute
without change in meaning the associated sentence for the derived
nominal in (11), yielding us (12).
11. Mary regrets Bill's belief that p
12. Mary regrets Bill believes that p
There is a further prediction: if we accept Chomsky's view that
gerundives are best accounted for on the transformationalist theory,
then such gerundive nominals will be substitutable for derived
nominals in those cases. The prediction is confirmed by a comparison
of (11) and (13), just as in (12) no change in meaning is apparent.
13. Mary regrets Bill's believing that p
Suppose, however, that the very same nominal, viz. "Bill's belief that
p" in sentences like (14) can also be arrived at assuming lexicalist
principles. In this case, we would have two predictions: first, that
the associated sentence would not be substitutable for the nominal,
and second, that the gerundive would not be substitutable for the
derived nominal. (15) and (16), respectively, confirm these
predictions.
14. Mary doubts Bill's belief that p =
15. Mary doubts Bill believes that p
16. *Mary doubts Bill's believing that p
The substitution resulting in (15) is unacceptable because the meaning
may be that Mary doubts the belief that p; she may not doubt that Bill
believes that p. There is yet another prediction based on the idea
that the derived nominal in (11) is not an NP in its internal
structure, while the one in (14) is: If (11) did possess this internal
structure then, following Chomsky, we would expect a definite article
to be capable of occupying the SPEC position of the purported NP. But
this is not the case, as (17) shows.
17. *Mary regrets the belief that p
The article is, however, capable of occupying this position in
(14). It is fundamental, then, that the matrix verbs have different
selectional properties. The conjecture is that in constructions of the
type under investigation verbs like "regret" select nominals with a
lexicalist explanation, while verbs like "believe" select gerundives
with transformational histories. It is not obvious that gerundives
receive any other treatment than that offered by the lexicalist. With
these linguistic considerations behind us we are now prepared to solve
Russell's dilemma regarding assertion and nominalization.
A Solution to Russell's Problem
Russell takes two seemingly unwarranted positions. First that in some
sense truth and assertion are the same, and second that there is no
significant logical difference between gerundive and derived
nominals. In solving Russell's problem, I will show that the
difficulty arises only in relation to assertion, not truth; next, it
will be shown that taking a "mixed" view with respect to Chomsky's
competing theories of lexicalist and transformational approaches to
nominalization overcomes the challenge presented by assertion.
Since gerundives are actually derived from their associated sentences,
the suggestion that what the gerundive indicates lacks the property of
having a truth value, a property possessed by its associated sentence,
is without sufficient warrant. In the case of derived nominals a
similar point can be made. There is simply no reason to believe that a
nominal expression if it indicates any proposition will fail to
represent a proposition having a truth value. This still the problem
presented under the guise of assertion.
Regarding an attitude verb as taking as its semantic object the
proposition expressed by its syntactic complement is simplistic. While
the syntactic object of (18) is a nominal its semantic object on the
relevant reading is in fact the proposition p.
18. Mary accepts Bill's belief that p
The associated sentence of the derived nominal in (18), "Bill believes
that p," is not asserted, but it is asserted in (19), the verb being
factive in (19) but not in (18). This difference determines what the
sentences can be used to assert. Russell to this extent was quite
right: What is asserted depends on the verb, and the verb can be
treated logically as an operator much like material implication or
entailment.
19. Mary regrets Bill's belief that p
Notice that the speaker in the case of (18) may mean either that Mary
accepts the fact that Bill believes that p or that she accepts p as
true. This attests the possibility that a derived nominal may be
lexically or transformationally accounted for. Although it raises
certain issues related to the degree, if any, to which syntax is
semantically driven it contributes a syntactic solution to a semantic
problem. It is to be observed that there is a certain ambiguity
contra (19) in what is being asserted. If the nominal is
construed transformationally, and, therefore, as capable of
assimilation with gerundives, then what is asserted is the first
interpretation given, otherwise what is asserted is the second
interpretation.
Commonplace examples of opaque verbs, such as "believes" in (5), show
that sentential objects need not be asserted. How, then, does
"believes" differ from "implies"? At least part of the problem is not
limited to nominalization, but by pursuing nominalization, in
particular along Chomsky's lines, we may take some first steps towards
a solution.
The proposal, then, is this: Whether a nominal can be used to indicate
the same entity as that expressed by the associated sentence taken in
isolation depends on whether the nominal is arrived at by
tranformation or is base generated, that is, amenable to explanation
along lexicalist lines. Nominals which are gerundives, following
Chomsky (1970), or derived - albeit substitutable salva
veritate for gerundives - retain the feature of assertion in
Russell's sense of assertion. When the nominal is base generated, the
feature is not retained, and the entity, if any, indicated by the
nominal differs from the proposition expressed by the associated
sentence. Some matrix verbs, as in (19), allow only a reading in which
the complex nominal object is either gerundive or derived but
substitutable for a gerundive; other matrix verbs, as in (18), allow
for the possibility of at least one other reading: the object is base
generated and what is indicated does not retain the feature of
assertion. In the former instance, "Bill's belief that p" indicates
the proposition Bill believes that p and the assertion element
is retained. In the latter case, and on the relevant reading, Mary may
have never heard of Bill. Here what is indicated is the proposition
expressed by "p." The solution to Russell's problem entails saying
that sometimes nominalization preserves the assertional feature and
sometimes not.
It is possible that following Russell's latter approach (Russell 1905)
that a nominalization may not be a referring term at all. If so it may
under no circumstance be used to refer to a proposition. On the
present proposal this would apply only to nominalizations like derived
nominals with true NP internal structure. Nominalizations would then
be definite descriptions, supportable as such by the fact that like
such derived nominals a definite article would be permitted in SPEC
position.
If we flank the operator "therefore" with gerundive nominals, the verb
forces a transformationalist understanding of those nominals: whereas,
"implies" forces a lexicalist interpretation. In the case of "regret,"
the properties are as they are in the case of "therefore," while in
that of "accepts" there is parallelism with "implies." One might ask:
Is it being suggested here that a derived nominal cannot be used to
refer to what is expressed by its associated sentence in "The
mortality of Socrates implies 2+2= 4"? No, only that this sentence is
ill formed, stating a relation between one of Socrates' properties and
a proposition. The intention is fulfilled by using instead "Socrates'
being mortal implies 2+2= 4" or on a transformationalist understanding
"Socrates' mortality implies 2+2= 4."
Russell uses nominalizations in making propositions logical subjects;
but he is faced with a contradiction which he takes to be unavoidable,
a contradiction created by a presumed shift in reference which accrues
to nominalization. It has been argued here that there is equivocation
on the sense of "nominalization." By maintaining distinctions first
drawn by Chomsky and by applying a "mixed" view of nominals derived
from Chomsky's proposals, the contradiction is averted and hopefully
the solution becomes generalized to related problems of propositional
attitude. It is to be admitted that how a nominal is to be arrived at
by transformation has not been given. Limitations of space prevent
this, but a number of possibilities come to mind.
Postscript
On this the occasion of Noam's seventieth year, setting technicalities
aside, we are moved to reflect on how linguistics, as he has come to
have us understand it, has been undertaken in the service of what Kant
regarded as the "dignity" of humankind; in matters of science and
human nature, we consider that by virtue of his intellect he has
inspired both courage and curiosity; and, for those of us who have
benefitted, it is to be recognized that while the intellect may
inspire courage rarely does courage inspire the intellect, amounting
to what philosophers in search of the "cardinal virtues" might
describe along with linguists as a "curious asymmetry."
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Cocchiarella, N. 1980."The Development of the Theory of Logical Types
and the Notion of Logical Subject in Russell's Early Philosophy"
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Davidson, D and G. Harman. The Logic of Grammar
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