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February 2004 Contents

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Russell on Nuclear Deterrence

Generality and Disimilarity

The Russell Cambridge Companion

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Traveler’s Diary


ambiguity, dissimilarity and conjunction failure


Rui Zhu

When a general term is used to describe very different things, may we still treat it as the same general term? This question has survived centuries of debate in ontology. Plato's problem of the being of non-being is a product of his positive answer to it. Russell thinks that Plato's problem can be avoided by treating some key general terms as ambiguous. Although the ontological context is no longer relevant today, the issue remains interesting, for it still challenges our intuition concerning what counts as a legitimate sentence. In this paper, I will discuss a group of sentences such as “The chair and question are hard” that use a general term to describe (or subsume) drastically different objects. While there is an obvious quaintness with such a sentence, what shall we do with it? Shall we disallow it for the reason that its general term is ambiguous (Bertrand Russell thinks so), or shall we deem it permissible, only with its quaintness attributed to the dissimilarity of the objects (Quine thinks so)? I will argue that such a conjunction is not permissible, but Quine might be right that there is no ambiguity involved in the general term itself. Instead of attributing the conjunction failure to the ambiguity of the term, I will construct a rule (based on the rule of contraction in transformational grammar) to bar such conjunctions.

1. PLATO'S PUZZLE

In The Sophist, Plato compares

(1) The not-great is not-great,
(2) The not-beautiful is not-beautiful,
(3) The not-being is not-being. [1]
The trifling innocence of (1) and (2) is contrasted with the horror felt by the Eleatic stranger over (3), for it contradicts Parmenides' teaching, ‘Non-being never is.’ The indisputable truth of (1) and (2) forces both the stranger and his interlocutor, Theaetetus, to agree that
In the same manner [ la (1) and (2)] not-being has been
found to be and is not being. (Italics added) [2]
Besides his reluctant discovery that non-being has being, the stranger verges on saying that non-being is assured of the same kind of being as being itself, as the not-great and the not-beautiful are assured of the same kind of being as their opposites. It is apparent that Plato sees no difference in the tokens of ‘is’ in (1) - (3). ‘Is’ has the same meaning in all three occurrences and ascribes being to the subject of the sentence in which it is embedded.

2. A RUSSELLIAN AMBIGUITY

When Russell of 1912 considers the issue of being, he is not addressing the puzzle over non-being. Instead, the existence of universals in contrast with the existence of particulars occupies his attention. Compare
(4) Chairs and rocks exist,
(5) Numbers exist.
According to Russell, the word ‘exist’ has different meanings in (4) and (5). Numbers as universals do not exist in the same way as particulars such as chairs and rocks do. The existence of universals is timeless and belongs to a realm of subsistence, while the existence of chairs and rocks is fleeting and constitutes the ordinary meaning of existence. [3]

Supposing that Plato's non-being belongs to Russell's class of universals, the being of non-being would be taken as the subsistence of non-being - the original air of absurdity would go by the board. This is the benefit of Russell's ambiguity verdict.

3. NOT ABOUT ONTOLOGY

With the introduction of quantification, the ontological quirkiness of the occurrences of ‘is’ or ‘exist’ in a sentence ceases to be fascinating. But trouble is often a possessive spirit - it chooses to appear in a different body if the original fails it. Forget ontology, but one can still ask whether the word ‘existent’ means the same in the following equivalent renditions of (4) and (5):

(6) Chairs and rocks are existent,
(7) Numbers are existent.
At this moment, insistence on the fact that ‘existent’ is not a predicate (therefore, it does not have any meaning) only delays the problem. For it shows up again in this example of Quine's
(8) The chair is hard,
(9) The question is hard.
Is the word ‘hard’ ambiguous in (8) and (9)? Could one claim, in the way Russell does with ‘existent’ in (6) and (7), that ‘hard’ has different meanings in (8) and (9)? The apparent awkwardness of
(10) The chair and question are hard
seems to support the ambiguity verdict.

4. QUINE'S OBJECTIVAL DISSIMILARITY

Quine dismisses the Russellian diagnosis as baseless. In his own words, Quine says that he is baffled by philosophers' maintenance that ‘true’ said of logical laws and ‘true’ said of confessions (or ‘hard’ said of the chair and ‘hard’ said of the question, or ‘existent’ said of chairs and rocks and ‘existent’ said of numbers) are two usages of an ambiguous term instead of the same very general term. [4] He demands evidence for the ambiguity verdict. With regard to the air of peculiarity of (10), Quine attributes it to the drastic dissimilarity between chairs and questions. ‘Hard’ is the same general term in (8) and (9), and there is nothing wrong with (10) itself. What causes discomfort is not the feared illegitimacy of (10), but the dissimilarity in objects - which is not a concern for logicians.

5. FAILURE OF CONJUNCTION

Indeed, Russell's ambiguity explanation of such odd sentences does not apply here. But Quine's attitude is all too cavalier. Although I would like to agree that there is no foundation for one to claim that the meaning of ‘hard’ is different in (8) and (9), their conjunction (10) offends us just a little more than we can bear. Compare (10) - (12) (call them ‘Group A’)

(10) The chair and question are hard,
(11) John's arthritis and punch are deadly,
(12) The ball and landing are soft
with
(13) Her eyes and the fountain are pure,
(14) The boy and monument are tall,
(15) His personality and the mud are soft.
While (13) - (15) (Group B) are also awkward and involve drastically different things, they do not abuse our linguistic taste to the same extent as do (10) - (12). The difference between the two groups lies not just in the familiarity of existing similes evidenced by Group B, but also in the absolute incomparability of the pairs of things in Group A. Most languages allow a comparison between a pair of eyes and a fountain, and some languages (e.g. Chinese) allow comparing an individual's character to mud. [5] But it is no accident that no language allows comparing a hard question to a hard chair, a punch to arthritis, or a landing to a ball. An English speaker may be amused by some unexpected exotic comparisons (like Mencius' comparing an indolent mind to a weedy road), but a comparison between a question and chair is far from amusing.

In my opinion, Quine's analysis applies to sentences of Group B, but not to those of Group A. Conjunctions of Group A affront us not just in the dissimilarity of their conjuncts, but also in their semantic propriety. When an English speaker decides against a sentence like (10), what motivates her is not so much the pragmatics of English as a sense of semantic propriety that underlies all languages. As a matter of principle, conjunction should be barred with respect to a hard chair and a hard question, or a punch and arthritis.

How could Group A be disallowed, if we agree that ‘hard’ means the same in (8) and (9), or ‘deadly’ means the same (the very general term, ‘deadly’, meaning ‘capable of causing death’) in ‘John's arthritis is deadly’ and ‘John's punch is deadly’?

6. SEMANTIC FRAMES

Conjunction failure under the same predicate presents such a dilemma: there are two things such that we can use the same general term to describe them, but they are absolutely incomparable with regard to this term, and conjunction fails as a result. Before one can conjoin the two terms, one has to see if one sentence's “semantic frame” clashes with that of the other. If the semantic frames of two sentences clash, such conjunction shall be barred.

Unfortunately, given the paucity of our knowledge of semantic frames, it is impossible to formalize the constraints over conjunction. The best we can do is examine the concrete examples we have seen above in order to illustrate the way the subject and predicate of a sentence interact with each other which leads to a formation of a semantic frame. Intuitively speaking, the semantic frame of a sentence functions like a box. When the semantic contents inside the boxes of two sentences have nothing in common, conjunction is barred. Before we get bogged down in a swamp of speculation, let us turn to the examples again:

(i) The subject imposes a referential frame on the
predicate. For instance, compare, ‘His punch is deadly’
and ‘His arthritis is deadly’. Because ‘deadly’ said of the
punch refers to other people than the boxer himself,
whereas ‘deadly’ said of the arthritis refers the patient
himself but never to others, the conjunction ‘His punch
and arthritis are deadly’ would cause violent semantic
spasm.
(ii) The subject imposes a dynamic frame on the predicate.
Compare: ‘The ball is soft’ and ‘The landing is soft’.
(iii) The subject imposes a strict mental or physical frame
on the predicate. Compare: ‘The chair is hard’ and ‘The
question is hard’.
Note that the whole matter is largely intuitive and frustratingly vague because we do not have a working concept of semantic frames. Not all conjunctions are ruled out because of the clash of the frames. Sentences of Group B are examples of permissible conjunctions. It seems that a term can still be used to describe drastically different things as long as there is no clash of semantic frames. Although this “whistle in the dark” approach helps nothing, we may not take flight and refuse to acknowledge possible conjunction failure under the same predicate. Healthy greed for clarity should not blind us to real problems.

7. CONTRACTION

Since we do not really know what a semantic frame is, and whether it belongs to the pragmatics or semantics or syntax of a language, we end up with many questions and no clear solutions in hand. What I will propose in the following is to treat conjunction after the model of contraction in transformational grammar and form a constraint on conjunction which our intuition about semantic frames captures but fails to deliver. It should not come as a surprise that we treat conjunction after the model of contraction because of the similarity in the two operations. But I must add the disclaimer that I am not treating conjunction as a particular case of contraction.

In transformational grammar, a rule of deletion concerning contraction says:

(Contraction-Rule) Contraction is blocked if there is a
missing constituent after the item concerned.[6]
For examples of contraction, we have in the following, where the ‘is’ of (16) is contracted into the ‘'s’ of (17):
(16) It is a jolly good day,
(17) It's a jolly good day.
Or where ‘had’ is contracted into ‘'d’:
(18) He had a jolly good day,
(19) He'd a jolly good day.
But a similar contraction would fail between (20) and (21):
(20) A jolly good day (that) it is,
(21) A jolly good day (that) it's.
Or between (22) and (23):
(22) A jolly good day (that) he had,
(23) A jolly good day (that) he'd.
While (17) and (19) are grammatical, (21) and (23) are not. The explanation from transformational grammar points out the fact that there is a trace of a wh-pronoun that is left behind after the wh-movement of the constituent following ‘is/had’ in (21) and (23). The D-structure of (20) is
(24) A jolly good day (that) it is which
Now move the wh-phrase and get the S-structure:
(25) A jolly good day which (that) it is
Delete the wh-phrase and get the surface structure, which is (20):
(20) A jolly good day (that) it is
Because ‘which’ is the missing constituent after ‘it is’ in (20) but still exists in the D-structure, (24), contracting ‘is’ to ‘'s’ is blocked according to the contraction rule. The same account applies to the ungrammaticality of (23).

Out of the same account, Chomsky explains the ‘wanna’ contraction failure of contracting

(26) Who do you want to die
into
(27) Who do you wanna die (ungrammatical)
in virtue of the fact that there is a missing constituent of ‘who’ in between ‘want’ and ‘to’ in the D-structure of (26)
(28) (That) you want who to die.
That is to say, the trace of ‘who’ in between ‘want’ and ‘to’ blocks the contraction of ‘want to’ into ‘wanna’.[7]

8. CONJUNCTION RULE

I suggest that we treat conjunction failure along the similar line of contraction failure. Perhaps we might want to say something like this

(Conjunction-Rule) Conjunction is blocked if there is a
missing constituent after the general term concerned.
If so, we must look for the missing constituents in sentences such as
(8) The chair is hard,
(9) The question is hard,
so that we can block
(10) The chair and question are hard.
In fact, we might have what we want here. But first let us compare
(29) John's arthritis is deadly
and
(30) John's punch is deadly.
We see that arthritis is deadly only to John himself while his punch is deadly to someone other than John. When an English speaker hears (29) and (30), she understands them in the manner of (31) and (32), respectively,
(31) John's arthritis is deadly [to John himself],
(32) John's punch is deadly [to someone other than John].
Because of this tacit knowledge, she would not accept (33), the conjunction of (29) and (30)
(33) John's arthritis and punch are deadly.
The parallel between the failure of contraction and that of conjunction in (33) is striking. In both cases, a competent speaker sees something still functioning in her linguistic understanding (or the D-structure) but missing in the surface structure of the sentences concerned. The missing constituents are often unconsciously filled up by the competent speaker whenever she comes upon those sentences. In fact, if we spell everything out, it is very easy to see why conjunction in (33) fails. Compare (31), (32) and (33) to (31'), (32') and (33'):
(31') John's arthritis is deadly to him,
(32') John's punch is deadly to him,
(33') John's arthritis and punch are deadly to him.
We can see that the pronominal ‘him’ in (31') and (32') refers to different persons (to John himself in (31'), to someone other than John, say, Fred in (32')). And (33') is blocked because the two occurrences of ‘Deadly to him’ are not the same type of general term, for one is ‘Deadly to John’ while the other is ‘Deadly to Fred’.

Conjunction can fail as long as one of the sentences has a missing constituent. (10), ‘The chair and question are hard’, is illegitimate because there is also a missing constituent in (9). When one reads (9), ‘The question is hard’, she must tacitly understand it as an abbreviation of

(34) The question is hard [to solve].
Otherwise, suppose (9) is complete as it is, it must allow a nominal transformation such as
(35) The question's hardness
or
(35') The hardness of the question
just as (8) allows
(36) The chair's hardness
or
(36') The hardness of the chair,
so that a question like ‘Does the chair have hardness?’ or ‘What about the hardness of the chair?’ can be posed. But (35) and (35') are unacceptable. In no circumstance can one make sense of the question ‘Does the question have hardness?’ or ‘What about the hardness of the question?’ This shows the incompleteness of the term ‘hard’ in (9). If we complete it as (to repeat (34))
(34) The question is hard [to solve],
its nominal transformation (37) and (37') would be acceptable, awkward as it is,
(37) The question's hard-to-solveness,
(37') The hard-to-solveness of the question.
Sometimes the incompleteness of the term stems from the inseparable bond between the adjectival and nominal phrases because of the existence of an idiom-like phrase. Let us examine (38) and (39)
(38) The landing is soft,
(39) The moon is new.
The particularity of the two sentences lies in the fact that each predicate is somehow attached to the nominal phrase in the subject position. The propriety of using ‘soft’ to describe ‘landing’ depends on the presence of the idiom ‘soft landing’, while the acceptability of ‘The moon is new’ presumes the idiom or quasi-idiom or ‘complex noun-phrase’ ‘new moon’. The evidence of this tight predicate-subject bond is the insubstitutability of the general terms in question by their exact synonyms. (38') and (39') are unacceptable,
(38') The landing is impressionable (or easily yielding to
         pressure),
(39') The moon is novel.
In contrast, (40) and (41) allow such substitutions:
(40) The ball is soft,
(40') The ball is impressionable (or easily yielding to
         pressure),
(41) The garage is new,
(41') The garage is novel.
As such, (38) cannot be conjoined with (40), forming ‘The landing and ball are soft’; nor can (39) with (41), forming ‘The moon and garage are new’. A native speaker always understands (38) and (39) under the influence (often subliminal) of complex noun phrases like ‘a soft landing’ and ‘a new moon’. And it is this tacit registration of the fact that terms like ‘soft’ and ‘new’ in such contexts cannot stand by themselves the prevents substitutions of the kind shown in (38') and (39').

The Conjunction Rule needs to be modified because of the obvious counterexamples such as ‘The first and second landings are soft’, ‘January 15th's and February 15th's moons are new’, or even ‘John's punch and hepatitis are deadly’. In the last case, when John's punch and hepatitis are both deadly to Fred, nothing can prevent such a conjunction. So, the modified Conjunction Rule should be

(Conjunction-Rule)* Conjunction is blocked if there is a
missing constituent after the general term concerned and
the general terms of the two sentences are not identical
after all the missing components are added on.

9. CONCLUSION

Our position stands between Russell and Quine. Russell bars conjunctions like ‘The chair and question are hard’ on the ground that ‘hard’ is ambiguous, whereas Quine acknowledges the identity of ‘hard’ in its two occurrences and therefore sanctions the conjunction. We agree with Quine that ‘hard’ is indeed the same general term meaning a certain degree of impenetrability, but with Russell's conclusion that the conjunction should somehow be prohibited. In fact, it is not difficult at all to find a footing in the middle ground. One could say that, although the different occurrences of predicates like ‘hard’ are of the same type of a general term, they have different implications in different contexts such that the conjunctions would be barred because of the divergence in implicature. This pragmatic approach should work, but misses the important general feature shared by the sentences that thwart such conjunctions. We have tried to capture this general feature by offering a syntactic explanation for an intuitively semantic impropriety.

We do not fancy that our explanation, which is produced after the model of contraction failure in transformational grammar, must be correct or even has great explanatory power. If it has any success at all, it must be limited. For instance, we still have to let such an odd conjunction, ‘The night and wooden beam are long’ (from ‘The night is long’ and ‘The wooden beam is long’) pass as legitimate.[8] There is no ground for us to object to this sentence, for we cannot possibly say something like “The predicate ‘long’ in ‘The night is long’ is somehow incomplete.” This might be a great discomfort for us, for the sentence ‘The night and wooden beam are long’ is just as weird as ‘The chair and question are hard’. It is up to the reader's judgment whether or not to deem the sentence ‘The night and wooden beam are long’ as a decisive counterexample to our Conjunction Rule*.

Our best case is the example of (33) ‘John's arthritis and punch are deadly’ out of (29) ‘John's arthritis is deadly’ and (30) ‘John's punch is deadly’. It is very clear that the two tokens of ‘deadly’ are of the same general term, meaning ‘capable of causing death’. But it is equally clear that (33) ‘John's arthritis and punch are deadly’ is unacceptable. We must come up with a theory, which should be different from either Quine's or Russell's, to explain this conjunction failure. Our Conjunction Rule* is the first attempt toward offering an explanation. Like every other initial experiment, its significance is fortunately largely independent of its explanatory success.

NOTES

[1] Sophist, 258

[2] Ibid.

[3] The Problems of Philosophy, Dover Publications, 1999, p. 71.

[4] Word and Object, MIT Press, 1960, p. 131.

[5] Jia Bao-yu, the playboy from The Dream of the Red Chamber, famously compares men to mud and women to water.

[6] See Transformational Syntax, by Andrew Radford, Cambridge University Press, 1981, p. 263.

[7] See Chomsky, Rules and Representations, Columbia University Press, 1980, pp. 158-160.

[8] This example is discussed in the ancient Chinese Mohist writings dated between the 4th and 3rd centuries BC. Similar examples discussed by Mohists include: ‘His wisdom and grains are plentiful’, and ‘His official position and the price are high’. According to Mohists, one should not compare wisdom and grains (or title and price) in this way because they do not belong to the same type. Applying our Conjunction-Rule* to these sentences, we would legitimize ‘His wisdom and grains are plentiful’ but not ‘His official position and the price are high’ due to the fact that ‘high’ is idiomatically attached to ‘position’ in the sentence ‘His position is high’.


Department of Philosophy
Lake Forest College
555 N. Sheridan Road
Lake Forest, IL 60045
zhu@lfc.edu

© 2004 Rui Zhu.