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Thursday, February 26, 2015

Grice on 'the'

What would Grice have to say about Russell’s ‘On

We suppose he was mainly triggered to consider these issues after two events:

-- Strawson's publication of "On referring"
-- Russell's reaction in "Mr. Strawson on referring".

(All three items in "Mind", to which Grice had contributed with "Personal identity" in 1941).

The problems Whitehead and Russell in "Principia Mathematica" -- which Grice calls the source of Modernism -- provides
solutions problems which are still the subject of controversy -- as it should. If philosophy generated no problems it would be dead!
The problems involved utterances like
1. The king of France is bald.

and its negation:

1b. The king of France is not bald.
Russell KNEW there was no King of France when he wrote "On Denoting", although it is more debatable to think that neither Whitehead nor Russell DESIRED that to be the case.

(1a) and (1b) still differs from Grice's example in "Vacuous Names
(2) Pegasus, the flying horse Bellerophon rode, does not exist.

The lack of denotation for "Pegasus" makes (2) true but also seems to rob (2) of a meaningful constituent. But Grice wants to Meinongian jungle!
 Once a definite description (as philosophers call them) like "the king of France" (never mind 'bald') is unpacked in a tripartite way according to Russell’s analysis, (1b) is revealed to be, shall we say,


But surely our adage is:
"Do not multiply senses of 'the' beyond necessity."

It’s logical forms are given in (3).

(3) Ex[Kx and (y)[Ky ) y=x] and ~Bx]
 ---  ~Ex[Kx and (y)[Ky ) y=x] and Bx]

(3a) states that there is a unique king of France who is not bald. This is obviously false.

(3b), the negation of (1a) says that it is NOT the case that there is a unique king of France who is bald

-- which is true. No need for a truth-value gap, as Quine calls them, or a truth value other than those accept by bivalent calculi such as those that Whitehad and Russell and Grice endorsed.
We can apply the same analysis to (2) "Pegasus does not exist" once we correlate "Pegasus" to a 'dossier' as Grice calls it, or
definite description, e.g. :the winged horse (that Bellerophon rode)", here symbolized by "W", a predicate.
(2) can then be unpacked as (4)

(4) ~Ex[Wx and (y)[Wy ) y=x]]
-- which is false, seeing that horses don't fly (on their own -- polo horses 'fly' but when brought by millonaires to play this or that polo match -- and Bellerophon never played polo, anyways).
So (4) seems both meaningful and true, as required. Problems solved.

In "On referring", Sir Peter Strawson who says in the "Acknowledgment" section to "Introduction to Logical Theory" he learned all the logic he knew from "Mr. H. P. Grice", challenged the first solution above, arguing that neither
(1a) nor (1b) could be used to state the existence of a king of France.
The emphasis on 'assertion', or 'stating' is not necessary: "Off with his head!" "Off with the head of the bald king of France!" poses the same problems.
Rather, for Strawson the USE of such
sentences "presupposes" (or implicates, as Grice prefers) the existence of a king of France, and failing that existence, neither of
(1a) or (1b) could be used to make either a true or a false statement.
In Strawson’s words, “the
question of whether it’s true or false simply doesn’t arise”.
He forgot to say: "for me". It did arise for his teacher, Grice -- and for most members of the Grice Club!

Atlas (who studied at Grice's uni, Wholfson) for one takes issue with the work of both Russell and Strawson.
Donnellan also.
Grice only took issue with the work of his student, naturally!
To summarize his views, a sentence

Strawson’s views here are highly reminiscent of those of Frege, though Strawson did not mention that
earlier work by Frege, even if Frege was translated to English by J. L. Austin -- not to mention Geach and Black.  For a long time some assumed that Strawson’s neglect of Frege’s work was the consequence of Oxonian parochialis, but apparently almost everybody ignored Frege. Dummett won't. When Michael Wrigley went to UC/Berkeley to study under Grice to write his dissertation on Frege the following conversation took place:

WRIGLEY: I intend to base my dissertation on Dummett's "Frege". I hope you read it.
GRICE (offended). Hope? No. I have NOT read it, and I hope I won't.

But this tells more about Grice's prejudice against Dummett than Frege. Grice will refer to something like a "Fregean sense" in some of his unpublications and publications. Or "Fregeian", as he preferred to spell this.
Like (1b) (The king of France is not bald) can be used to express (at least) two thoughts – one of
which predicates "non-baldness" of an assumed-to-exist king of France.

The other thought is a blanket denial that the actual world (at present) is one which contains a unique male monarch of France with no hair on his head.
These correspond to (3a) and (3b) respectively.
contrary to Russell’s analysis, the sentence is hardly ambiguous.
 Atlas uses the confessedly confusing term “sense general” to describe the sentence semantically, but does not mean that term to imply a proposition – something with truth conditions.
The latter sort of thing only arises in particular contexts, associated with "tokenings" of (1b) -- particular conversational moves in the conversational game, as Grice preferred to say. Since the early 1960s, Grice was lecturing his students (not Strawson, by then) on helpfulness in conversational exchanges, and how we have to be cooperative when speaking. And what would the POINT be of "The King of France is bald" or "not bald" for the matter, out of the blue as they are uttered by BOTH Lord Russell and Sir Peter (as he then wasn't?).
It's quite different from Whitehead's and Russell's (or is it just Russell's?) example
"Scott is the author of Waverley".
meaning: Sir Walter Scott is the writer who wrote the series of novels that have Waverley as main character. But Waverley does not exist.
In those tokenings, either  "the king of France" can serve as a sentence topic, or it can serve as part of the sentence focus.
In the former case, but not the latter, the existence of a king of France will be implicated.
Strawson's example:
(i) A: What a lovely exhibition!
--- B: Indeed. The exhibition was visited by the king of France, too.
--- A: I thought France was a republic.
--- B: Well, president. Whatever. The man in office, top exhibition, it shows.
Finally, in
the statement made in the utterance of a sentence like (2) (Pegasus does not exist)
"Pegasus" does not serve as sentence topic. Hence such a statement will not implicate the
existence of Pegasus -- even if we can create a context when we are being generous about 'exist': "Pegasus exists in the pages of Apollodorus's Bibliotheca" -- now reprinted in a lovely two-volume set by the Loeb Classical Library -- LOEB IS ALL YOU NEED.
Atlas’s work has done a great deal to clarify our thinking about these troublesome issues, but then it would, since he studied at Wolfson -- at the same university that also gave us Grice.
Atlas (who studied under A. J. P. Kenny) deserves praise for the methodical care he has taken with them. However there remain
some aspects of Atlas's approach which may deserve further examination. How do we understand
negative sentences involving definite or indefinite descriptions? Why should there be a problem about that?
Why should we care about addressees, anyway? Isn't Grice's work supposed to be based on what an UTTERER means.
“Understanding”, though, is the general term from Zwicky and Sadock, which we can take to include instances of ambiguity as well as generality, vagueness, pragmatic conversational implicature, and whatever else could conceivably be included.
Two different kinds of ambiguity of NEGATION ("not") rather than the definite descriptor ("the")  have been proposed historically, and it makes
a difference to Atlas’s claims which one he is concerned with.
 What is the ‘sense general’ theory of negative sentences like (1b),
containing a definite description?
The Griceian alternative is of course to bring in implicature
At least two different kinds of ambiguity of negation, or two
different views of what such an ambiguity consists of, have been proposed for the combo of 'the' and 'not'.
Whitehead and Russell, like Grice, postulate a simple scope ambiguity.
But it has also been suggested that this ambiguity is of a different type, which might be viewed as an ambiguity
in the word not, -- see Grice on notn if not 'the' (cfr. Donnellan, "Speaking of nothing").

In the formal languages of logic, negation is a sentence operator –
something which combines with a sentence to make a new sentence.

Grice goes on to speak of the root (or radix), where we have the phrastic and the neustic (which can be assertoric). Negation applies to neustic-cum-phrastic.

As such it has a semantic scope which is determined by its syntactic scope – the sentence with which it combines.

sentence operators are the other sentence connectives (conjunction, disjunction, etc.); the
existential and universal quantifiers;  operators expressing necessity and possibility, in a
modal logic;  sentence-taking predicates like believe' and try' in an intensional logic like

Montague’s and both the 'iota' and the 'epsilon' operators used for definite and indefinite descriptors ('the', 'a'). Each of these operators has a semantic scope, determined by its syntactic scope.
In these formal languages, the scopes of any operators in a sentence are fixed by the
syntactic structure and the result is the desirable property of univocality.
i. Do not multiply senses of 'the' beyond necessity.
ii. Do not multiply sense of 'not' beyond necessity.
iii. Do not multiply sense of 'a' beyond necessity (indefinite description).

It has been traditional to view natural languages, like Latin, that lacked 'the', as being different from formal languages in this regard.

That is, a natural language sentence with more than one sentence operator may be ambiguous as a result of having different ways to construe the semantic scope of the syntactically fixed operators.

e.g. Latin for "The emperor died" would lack 'the' -- and still be undertood in a definite way, rather than as "An emperor died". It's different for "Consul died", since there hundreds of them!
Typical examples, with paraphrases intended to suggest the commonly attributed understandings,
are given in (5)-(10).
(5) Mary will win or Bill will win and Sue will discover an anomaly.
a. Mary or Bill will win, and Sue will discover an anomaly.
b. Mary will win, or alternatively Bill will win and Sue will discover an anomaly.
(6) Many of the arrows did not hit the target.
meaning either
a. The arrows hitting the target were few in number.
b. Lots of arrows missed the target.
(7) The current president might not have been a Democrat
meaning either
a. Obama might not have been a Republican.
b. It might have been the case that a Democrat was elected when Obama was elected.

(Grice's examples, he being British, concern Harold Wilson and Macmillan, and on occasion a third candidate).

(8) Ralph believes that someone is a spy (or a witch, on an honest man)
a. Ralph believes that there are spies (or witches or honest man)
Or Ralph believes that Pegasus flies.
b. Someone is suspected by Ralph of being a spy.
(9) John would like to marry a girl his parents don’t approve of.
a. John wants to irritate his parents by marrying somebody they don’t approve of.
b. The girl who John wants to marry isn’t approved of by his parents.
(10) Oedipus wants to marry his mother -- after Sophocles's tragedy.
meaning, de se, or de dicto
a. Oedipus wants to commit incest.
or, de re
b. Oedipus wants to marry a woman who, unbeknownst to him, was his mother.
Thus it is not uncommon for natural language sentences with two (or more) sentence operators t
show these scope ambiguities.
Natural language sentences with more than one sentence operator are not necessarily ambiguous.
It can happen that potentially different understandings turn out to be equivalent, a in the case of (11):
(11) Someone likes someone.
Or for other reasons an operator can be prevented from taking a bigger scope than another
operator within whose syntactic scope it lies, as in example (12):
(12) Not many arrows hit the target.
where many cannot escape from the clutches of not.
But in general we have been led traditionally to expect scope ambiguities in sentences containing more than one sentence operator, and usually we have not been disappointed.
The phenomenon just scouted should be distinguished from another possibility.
Aristotle (and Grice loved Kantotle) proposes that a sentence like (13):
(13) Socrates is seriously ill: he has just drunk some hemlock.
has two negative counterparts.
The contradictory (or EXCLUSION) negation of (13) results in a
proposition that is true if (13) is not true, regardless of whether there is anybody named Socrates.
This might be roughly paraphrased as in (14a):
(14) a. It is not the case that Socrates is ill.
However negation can also function to deny a term, in this case the predicate, giving the
understanding in (14b) (also called the “choice” negation):
(14) b. Socrates has the property of not being ill – i.e. Socrates is well, or alive and kicking as we should say.
This distinction was apparently expressed in Greek (not alive and kicking) with two distinct word orders (and Greek was almost Grice's first language -- at Clifton and later Corpus Christi) but it has been claimed that both interpretations are expressible with the one negative sentence given in (14c)
(14) c. Socrates is not ill.
Viewed in this way, the distinction would constitute a kind of ambiguity of negation for

Possibly the difference could be represented as one of sentence scope, were Socrates taken to be a sentence operator.
Of course that is what Whitehead and Russell propose, by analyzing proper names (like "Socrates", "Scott", apparently Russell's favourite novelist -- odd Russell being such a highbrow -- or "Pegasus") as standing for definite descriptions, which Whitehead and Russell in turn had analyzed as
quantificational expressions.

Nevertheless it seems useful in principle to distinguish the two sorts of potential ambiguity.
Atlas is aware of the difference between the two sorts of potential ambiguity.
Nevertheless it seems that he views the difference as of no significance for his project, since he is arguing against either version.
So sometimes he seems to blur the two together, as in the following quote:
It was Russell’s, and is presently the standard, view that the sentence:
(15) The king of France is not wise.
as ambiguous, having two SENSES and two logical forms, one the narrow-scope predicate-negation, usually represented by:
(16) The king of France is “non-wise”.
and the other the wide-scope sentence-negation usually represented by:
(17) It is not {true/the case} that the king of France is wise.
In this passage we seem to have an identification between narrow scope negation and predicate
negation, on the one hand, and wide scope negation and sentence negation, on the other.
However, in general scope ambiguities involve sentence operators, and not a
variation in an operator taking a sentence vs. a predicate as its argument.
The difference between the two types of alleged ambiguity becomes
relevant when we inquire as to the intended extent of the claims about "sense generality" (Atlas's invention).  

If Atlas’s arguments are aimed at negation ("not") qua predicate or sentence level operator, they would
seem to have no implications for other sentence operators and the scope ambiguities they seem to
be involved in.
However if Atlas's arguments are aimed at negation simply as a sentence operator,

then they can be expected to have much wider repercussions.

And Atlas himself is

uncharacteristically indecisive on this point.

In an early introduction of

his thoughts about the ambiguity of negation, example (15) above was contrasted with an

example involving an explicit quantifier.


(18) Everyone didn’t show up.

a. No one showed up.

b. Not everyone showed up.

Concerning these sentences he remarks in the earlier work: “This is a genuine ambiguity

accountable for by a difference in scope”.

However, by the time of Atlas thinks

the distinction is between sentence negation and predicate negation. However, Aristotle held that neither was a case of sentence

Instead, the contradictory reading is a general type of predicate negation which has been called “predicate

denial”, while “predicate negation” is a term negation of the predicate.
Atlas's opinions shifted, and why shouldn't they? (18) is used as an apparent example of his sense generality view. Thus, in the later work.

the text preceding (18) begins: “The paradigm cases of scope ambiguity involving negation have

led to a mistaken semantic description of negative sentences standardly thought to possess

presuppositions. These mistaken descriptions assign to a single surface structure two distinct

underlying forms” Example (18) is then introduced as an

illustration of this mistake.

Atlas intends his remarks to hold for all

scope ambiguities, and not just the traditional interaction between negation and definite

descriptions, were it not for the fact that he does not return to example (18), or others like it, until

the very end of his essay, and there he seems to have retreated to a less confident position. The

example in question at that point is a sentence from one of Abraham Lincoln’s classic remarks –

example (19) below:

(19) You can fool all of the people some of the time.

Concerning this example Atlas writes:

if the quantifiers were scope-non-specific in the semantic

representation of the sentence [my claim ] would be…that there are no distinct ‘readings’….”

His discussion continues briefly in this

hypothetical mode before the final summary of his essay.

Thus it remains unclear how

broadly the concept of sense generality is intended to apply.

This makes a difference, because it is much easier to argue against an ambiguity of the

negative morpheme (sentence vs. predicate operator) that it would be to argue against negation

participating in scope ambiguities.

That is because the latter sort of phenomenon is quite

common, as noted above in connection with examples (5) – (10).

Now enter Donnellan.
We turn now to the arguments that sentences like (1b), repeated here as (20),

(20) The king of France is not bald.

are not ambiguous – do not get assigned two (or more) different logical forms by the grammar of


Instead, the claim is, (20) is sense general, and can be used to express different

propositions and make different statements in different contexts, only some of which will

presuppose that there is a king of France.

Atlas puts forward a number of arguments toward this


Most of them are based on the seminal discussion of ambiguity in Zwicky and Sadock

1975. However the first one we consider below is new.

The first kind of argument we’ll consider rests on the fact that the

very same sequence of words can be associated with different intonational contours, with

different results for what is taken to be the sentence topic, and what is taken to be the new

information being conveyed.

Compare the following (we follow Atlas in using italics for

what are to be taken as statements rather than sentences):

(21) a. The king of France isn’t bald.

b. The king of France isn’t bald.

c. THE KING OF FRANCE isn’t bald.

Atlas holds that (21a) actually has two “unmarked” uses, both of which we have represented as


These are the two understandings corresponding to (15) and (16), repeated here as (22a,

b), respectively.

(22) a. The king of France is “non-wise”.

b. It is not {true/the case} that the king of France is wise.

These are the ones that we are primarily concerned with.

The first of these is described as failing

“to be a semantically referential, singular assertion”, due to the absence of a king of France,

while the other is the “true, non-singular assertion that is the external negation of the proposition

that the king of France is bald”.

On the other hand (21c) is a “true [assertion]

about the bald” (90).

“All of these statements employ the same sentence, whose meaning is

unspecified for, rather than ambiguous between, predicate and sentence negation or between

object-language negation and meta-language denial” (90).

He continues (p. 91): “Our

interpretations depend not on the syntactic and semantic but on the possible phonetic

representations of the sentence uttered."

"The range of interpretation includes statements that are

choice [i.e. predicate term] negations, exclusion [i.e. sentence] negations, and metalinguistic


The strange part about this claim is the apparent assumption that phonetic form is not part

of sentence form.

For a linguist this assumption goes against the grain.

Spoken language, as we

are taught early on, is the primary form of language -- except you learn Greek, as Grice did, at Clifton -- vide "Greek Grice". But Grice did care about STRESS: "I don't KNOW". "Peter does not like her, he LOVES her".

Furthermore it has become standard in

linguistic analyses these days to include some indication of topic-focus structure in

representations of sentences, and to assume that such structure is semantically relevant.


Gundel and Fretheim  note: “It is not surprising…that most accounts of topic and focus

have built these concepts into the grammar, as part of the syntax and/or semantics…or as a

separate information structural component.

Thus for most linguists nowadays sentences

(21b) and (21c) are different, because their prosodic structures, which reflects their informational

structures, are different.
That being the case, it would seem that we don’t really have an

argument for the sense generality view yet.

The remaining arguments have rather a different

character. For these we assume the association of distinct statements with a given sentence, and

apply tests found in Zwicky and Sadock to determine whether these

statements count as different readings, or whether they are encompassed within a single, general


Even if the evidence points to the latter conclusion (as Atlas believes), it would seem that

it does not point specifically to a conclusion that this general sense is not one that could be

grammatically encoded in the sentence. We will turn to that issue below, in §4.

As Atlas notes, there is a potential complication in the application of

Zwicky's and Sadock’s tests.

If we consider just the two “unmarked” understandings of (21a) – the

one that presupposes the existence of a king and says he isn’t bald, and the one that is the blanket

denial – we can see that the former understanding entails the latter. Thus we have the kind of

situation Zwicky and Sadock call “privative”.

Zwicky and Sadock’s example of an expression with a privative ambiguity is the word dog,

which they take to be ambiguous on whether it’s specified for the sex of the animal.

For some,

this word is not ambiguous. – Some don’t have the +male reading. Ignoring that,

the test for privative ambiguity, as opposed to generality, is whether the same expression can be

both asserted and denied of the same object or situation. Were dog ambiguous in the way

Zwicky and Sadock assume, (23) should be o.k.

(23) It’s a dog, but it isn’t a dog. [I.e. it’s a bitch.]

 find (23) completely impossible, but, then some don’t have the reading in question.

(Cfr. "My ball itches" in "Elements of Discourse Understanding". Is uniqueness implicated? Apparently, only MALE native speakers should be able to decide).

The only

potential example some have been able to think of that might work for me is the word drink, which I

think people agree is ambiguous depending on whether the drink is taken to be alcoholic or not. Literally, 'drink' is not alcoholic; via conversational implicature, it _might_ ("The dog went to the pond, and had a drink -- or two").

Still, (24) is far from being completely natural:

(24) I’d like a drink, but not a drink, please.

The reason is not far to seek – any speaker of (24) would be being unnecessarily obscure -- i.e. violating Grice's maxim, "be perspicuous!" (Grice is being ironic in that it's not perspicuous what perspicuous means. In earlier lectures he just spoke of the Principle of Clarity vs. the Principle of Candour).


some obnoxiously coy person might say is (25):

(25) I’d like a drink, but not a drink drink [wink wink].

using what some describe as a “value added” type of lexical clone, to specify the R-narrowed,

+alcoholic reading.

In any case, Atlas accepts the test, and applies it to (26):

(26) The king of France is not wise.

The two commonly assumed, following Whitehead and Russell, understandings of (26) are paraphrased

unambiguously in (27a) and (27b):

(27) a. It’s not the case both that there is a unique king of France and that he is wise.

b. There is a unique king of France, but he is not wise.

(27a) is of the form not (p and q), while the more specific (27b) is of the form (p and not q).

These are shown in (27a') and (2b') respectively.

(27) a'. not (p and q)

b'. (p and not q)

If (26) is ambiguous in this way, it should be possible to assert it on the (27a) reading, but deny it

on the (27b) reading.

Given the equivalence in (28):

(28) not (p and q) and not (p and not q) not p

this should yield a net assertion that there is no king of France.

Atlas’s applications of this test are given in (29)

(29) {?The king of France is not wise/?It’s not {true/the case} that the king of France is

wise}, but {he/the king of France} is (not non-) wise.

None of the variants in (29) is very good.

Atlas remarks that they are “semantically out of


However, in addition to the already expected obscurity problem for this test,

noted with respect to example (24) above, the applications in (29) have another difficulty.


difficulty comes from Atlas’s assumption that the denial of (26) on the (27b) reading must be a

predicate denial rather than a sentence denial.

Observe the parentheses around “not non-“ in


If we conjoin an assertion of (27a) with a predicate denial of (27b), we are left with a

contradictory statement – something of the form (30a), or equivalently, (30b):

(30) a. not (p and q) and (p and not not q)

b. not (p and q) and (p and q)

Definitely out of bounds for those who like logical consistency, but not the right structure for

what we want to test.

A better example to use for the application of Zwicky and Sadock’s test for privative

ambiguity would be (31):

(31) The king of France isn’t bald but the king of France isn’t not bald.

(Strawson for some reason prefers wisdom. Grice sticks with Whitehead and Russell and focus on baldness -- to allow Russell to joke about the Hegelian who suspects "he still may wear a wig" (a synthesis -- but royalty was due in the debate to Bradley, "The King of Utopia died last Tuesday").

Now admittedly (31) isn’t great, but (23) and (24) weren’t that great either.

Furthermore I have

been assured by a number of informants that there are circumstances in which (31) could be

felicitously used to deny the existence of a king of France (though see below, §4). Compare also

the discussion by Strawson of the example in (32):

(32) A: Does he care about it?

B: He neither cares nor doesn’t care; he’s dead.

The next test is one which involves “employing a

transformation whose application to underlying structure requires identity of sense of

constituents”. This test uses examples like (33)

(33) The king of France is not bald, and the same goes for the Queen of the United Kingdom.

-- the "Queen of England" is, now, a misnomer.

The crucial understanding for (33) would be the one on which the first clause is understood with

sentence negation (i.e. not presupposing the existence of a king of France), while the second

clause does presuppose the existence of a Queen of the Great Britain and Northern Ireland. This is the so-called “crossed”

understanding. If we can understand (33) in this way, it is supposed to be evidence against an

ambiguity for (26) (The king of France is not bald) and in favor of its generality.

However, it’s

not clear to me that the results of the identity of sense test will be any more conclusive than one’s

intuitions concerning (26) itself. That is, I don’t know why people who find (26) ambiguous

won’t find it difficult to get the crossed reading for (33), and vice versa.

The identity of sense test is a subcase of Zwicky and Sadock’s tests of “transformational

potential”. The idea behind them is that if the semantic representations for certain sentences

lack specification of some piece of meaning, then the applicability of transformations to them

cannot possibly depend on whether or not this piece of meaning is present. Atlas leaves other applications of this test as an exercise for the reader, but assures us

that the results will confirm that the sentences in question are not ambiguous. However a couple

of constructions that were assumed to be derived by transformational rule at the time Zwicky and

Sadock were writing – the cleft and pseudocleft constructions – do seem to “disambiguate” e.g.

(26) in favor of a non-presuppositional interpretation. Compare the examples in (34):

(34) a. It isn’t the king of France who is bald.

b. The one who is bald isn’t the king of France.

Both of these sentences move the definite description the king of France into predicate position, where it tends to

lose its presuppositionality or implicaturality, if you must use the word. We are not sure what the response would be to this – perhaps that these

constructions should not be considered transformationally related to the canonical sentence form


Of course the whole basis for this kind of test lies in a model of syntax-cum-semantics which is

no longer assumed as the default.

The last test we’ll consider is what Atlas, following Zwicky and

Sadock, calls semantic differentia. When a sentence has relatively similar understandings” as is true in

this case, “but these differ only by one’s being sense-specified and the other sense-unspecified

for some particular semantic feature, e.g. [+/- FACT], the feature must be such that the lexicons of

natural languages can plausibly fail to use it.

Note the suggestion here that we are

not dealing with a scope ambiguity, but instead with a lexical ambiguity.

This may relate to Grice,

"He was caught in the grip of a vice" -- but the two vices Grice has in mind are two different words, not an ambiguous one!

The discussion

continues to talk about the degree of difference between the putative readings of an ambiguous


If the difference in understanding were very great it would point to ambiguity rather

than sense-generality. The implication is that small differences in understanding are

more likely to be a reflection of generality rather than ambiguity.


There seems to be a small disagreement between Atlas and Zwicky and Sadock over the declension of differentia

which is a plural for Atlas, but a singular for Zwicky and Sadock. The plural for them is, correctly, differentiae.

The idea is one for which

Zwicky and Sadock cite Richman).

However this criterion is certainly not absolute. Indeed,

we have Jerry Morgan’s example (35):

(35) Someone is renting the house.

where it is clear that there is an ambiguity, but

where the two readings are mutually entailing. As Zwicky and Sadock note,
from the facts that a particular semantic differentia is simple and that it is formally
marked in some language we can conclude nothing about the status of this distinction

for any particular example in any language; both lack of specification and systematic

ambiguity are consistent with these facts.

Against this background, the systematic scope ambiguities illustrated in (5)-(10) above provide

evidence in favor of ambiguity for the sentences we have been considering.

Let us for the moment ignore the evidence reviewed so far, which is not that conclusive anyway,

and assume that Atlas’s arguments go through. It still seems possible to hold the view that

sentences like (1b), (21a), and (26), repeated here as (36a-c):

(36) a. The king of France is not bald.

b. The king of France isn’t bald.

c. The king of France is not shaggy.

do have a logical form, which is that of the more general, sentence level negation, and that an

understanding which presupposes or entails the existence of a king of France is the result of a

conversational implicature.

The idea would be that, if the UTTERER *knew* that there

was no king of France, it would be more informative for him to have said JUST that.

Grice's question: "Are we rational, or not?"

Given that the

king of France does not exist, the issue of his baldness should not ordinarily arise as what Americans call 'a conversational topic'.

It would be being

unnecessarily obscure in almost any context to assert any of (36) knowing that there is no king of France.


The only exception might seem to be when someone else, ignorant of the king of France’s nonexistence,

has for some reason made the corresponding positive assertion, although even then the simple

denial of existence would be more informative.

Given the generality of this line of reasoning,

the conversational implicature in question would be a generalized one (not a particularized one like Grice's "He has beautiful handwriting" (+> but his philosophy sucks), uttered at Collections), neutralized only in very special contexts,

or with an explicit cancellation, as in (37):

(37) The king of France isn’t bald  – there isn’t any! The last one was decapitated by the Jacobins.

Some, but not Grice, find (37) somewhat strained.

Something like this is the view of Kempson, whom Atlas frequently cites

approvingly, and it seems to have been Atlas’s original thought as well.

However he argues

against this view in Atlas, and toward the end of his essay.

The arguments

given there against the Gricean view are highly theoretical.

Indeed, they verge on the aesthetic -- which is a GOOD thing.

The situation is summarized as in (38)

(38) a. PRAG (K*, L- ) = L+

There is a pernicious typo in Zwicky and Sadock’s reproduction of Richman’s conclusion.

They quote him

(unfortunately under the name “Richmond” rather than “Richman” -- but Donnellan would say that by uttering "Richmond", Zwicky and Sadock are using Richman attributively -- thus (where φ and ψ represent two properties

expressed by some term T): “The question is this, are φ and ψ sufficiently alike (in some unspecifiable way)? If they

are, T is ambiguous; if not, not.  What’s missing is the

“un-”prefix for “ambiguous”.
This alternative is “Griceian” rather than “Grice’s” because Grice’s own views on this particular issue were

somewhat more complicated, and he kept changing!

His most specific proposal is in "Definite descriptions in Russell and in the vernacular". He conversed with Donnellan on this and goes on to credit Donnellan's seminal "Reference and Definite Descriptions" (the locus classicus for the critique of Strawson's On Referrring) when Grice was visiting Cornell. Grice goes on to say, in his tribute to Quine (cfr. Quine, "Reply to Grice") that he acknowledges the identificatory/non-identificatory uses of definite descriptions, but is not sure he is wholly sympathetic towards the rather polysemous conclusions Donnellan draws from the existence of the distinction. Perhaps Kripke's conclusions are less polysemous.

Grice's examples include the gardener that Smith has wear the clothes of a butler to impress the guests to one of his parties. Another is the Merseyside native who climbed Mount Everest on hands and knees.

Grice's account involves the ESSENTIAL idea of a 'dossier' -- and J. Evans, in "Varieties of Reference" noted the basicness of this notion, and agreed with it.

See Grice 1981.

b. PRAG (K**, L- ) = L where

“PRAG” represents “the Gricean inference”, the Ks are different kinds of contexts, “L+

represents the understanding which assumes the existence of the king and “L -” the understanding

which doesn’t.

For Atlas, the problem with (38) seems to be its asymmetry between the affirmative and the negative utterances.

In the second case the

pragmatics adds nothing to the semantic interpretation. In the first case it obviously does.

But this claim can be questioned, since the contextual features which give rise to the

neutralization or cancellation of a generalized implicature are certainly affecting the

interpretation, and therefore in that sense adding something to it.

Atlas schematizes his own view of the situation as in (39):

(39) a. PRAG (K*, L ) = L+

b. PRAG (K**, L ) = L


L stands for “the sense-general semantic representation of

The F is not G.

Cfr. Neale's book, and Ostertag's reader (which includes Grice's segment) and Elbourne's "Definite descriptions" (Oxford University Press).

The idea is that we have a single semantic representation (or logical form, as Grice prefers -- "Some like Witters, but Moore's MY man" -- and those who like Witters like him because he knew what logical form was all about), and pragmatic factors determine which

of the two propositions associated with sentences of the type we’ve been discussing is actually

expressed on any occasion of utterance.

Thus, the pragmatic theory does theoretical work in

BOTH cases.

The problem of asymmetry is removed.

An important assumption throughout the discussion here is that the two understandings

represented with L+ and L- are equally natural.

This is reflected in Atlas’s assertion that, in

effect, both are ‘unmarked’ uses of sentences like those in (36).

And it is made explicit when he

says the following:

Taking a negative sentence in isolation competent utterers (and their addressees, of course) know that it has (at

least) two uses or understandings.

Independently of context, the understandings are

phenomenologically of equal status, neither judged less a function of the meaning

of the sentence than the other.

And he describes the advantage of his (39) over the Griceian competitor in (38) as follows:

Understandings that phenomenologically are of equal status are now represented by the theory
of being as equal status, produced in the same way by the same mechanism.

However, we do not believe that the two understandings represented with L+ and L- are

We want to claim instead that these understandings are not phenomenologically

equivalent; rather, it is the L+ understanding of sentences like those in (36) that is

overwhelmingly the favourite, or if you prefer, preferred, or MARKED, or even, as Grice would go on to say, 'rational'!

That is why the examples in (36) seem so strange.

In fact it is very

difficult for me to get the L- understanding of these sentences at all.

Some find it very hard to make

(37) sound anything but contradictory.

It might be thought that one factor promoting the prominence of the presuppositional

understanding is the fact that syntactically, negation occurs with the verb of the sentence, as

though not became glued onto the verb making it more difficult to become semantically unstuck

and go flying to the front of the sentence.

On the other hand modals don’t seem to have this


Examples like (7) above, repeated here as (40):

(40) The current president might not have been a Democrat.

a. Obama might not have been a Democrat.

b. It might have been the case that a Democrat was elected when Obama was elected.

(Grice's examples are somewhat dated: he speaks of Harold Wilson, and Macmillan, and he kept crossing out surnames, as he rewrote versions of his essays on this. In "Indicative Conditionals" he goes on to quote THREE possible candidates for the office of Prime Minister -- and he uses "Harold Wilson" in "Logic and Conversation" to fit with Frege's paradigm of sense and reference -- but not implicature).


These things are common in the literature.

And indefinite descriptions can vary their scope with respect to

negation pretty easily.

It seems pretty easy to get examples like those in (41)

Some argues that (37) is an example of metalinguistic negation. We regret that space has prevented

inclusion of discussion of this phenomenon with the other varieties of negation being considered here. But most (including Grice?) regard 'metalinguistic negation' as somewhat 'illogical' and there are cases he discusses in the William James lectures that make it obvious he knew what it was all about -- but he was no English Ducrot!

(41) a. Someone didn’t call me up today.

b. A book isn’t on the table.

with the indefinite subject possibly understood as being inside the scope of the negation.

Compare also example (18), repeated here as (42),

(42) Everyone didn’t show up.

a. No one showed up.

b. Not everyone showed up.

where the interpretation in (42b), with wide scope negation, is perhaps easier to get than (42a).

That being the case, it is something of a mystery as to why the non-presuppositional

understanding of sentences like those in (36) is not more robust.

In any case, leaving this puzzle aside, the Griceian account seems to match the data better

than Atlas’s alternative.

Grice was obsessed with "a" and "one", which he must have seen as falling under "Ex" which he paraphrases as "some (at least one)".

His examples include:

I broke a finger yesterday.

I saw a tortoise yesterday.

In the first case, the specific finger need not be mentioned. But a nurse can break different fingers, by mistake.

It is odd to utter "I saw a tortoise yesterday" if the utterer means that he saw HIS TORTOISE as he walked into his house, and saw his pet in the front garden.

Given that the implicature (if that’s what it is) of the existence of a

referent for a definite description occurring in a negated sentence is a generalized conversational implicature,

we expect that interpretation to predominate.

Note, though, that we could have a similarly

Griceian account were these sentences actually ambiguous.

The same line of reasoning would tell

us why one interpretation was more plausible and prominent than the other.

We turn now to the last group of issues, those concerning negative existence statements like (2),

repeated here as (43), that Grice loved (He learned about Pegasus while at Clifton).

(43) Pegasus does not exist.

Let’s quickly review the traditional problem such sentences present.

Given his assumptions of

compositionality of both sense and reference, Frege would potentially have problems at

both levels.

Martin too, but he solved the problem by naming his cat Pegasus.

If proper names do not have a sense (as suggested by intuition and argued by Mill -- cfr. Grice, "Grice to the Mill"),
the sense of the whole sentence should be defective or nonexistent.

But Grice wants no Meinongian jungle.

At the level of

reference, the truth of a sentence like (43) would mean that the subject term, Pegasus, lacks a

referent, and so the whole sentence should lack a referent, which in Frege’s view (if not Apollodorus's) is its truth

value; in brief, the truth of (43) implies its being neither true nor false.

These are the problems.

Frege solved the problem at the level of sense by postulating senses for proper names,

senses equivalent to those expressed by definite descriptions.

Russell completed the solution by

analyzing definite descriptions into referential parts (plus quantifiers and so forth).

(Cfr. Quine, "Pegasus pegasises").

However, as

noted at the outset, Strawson raised objections for Russell’s quantificational analysis of

definite descriptions, and Kripke has argued very convincingly for a return to Mill’s

position, that proper names are not equivalent to definite descriptions anyway. What to do?

Burton-Roberts makes a number of important points.

His first approach was Aristotelian: "What is necessary, is possible."

This led him to being a neo-Strawsonian!

However he does not approve of the
Griceian approach -- and that's why he calls himself a neo-Strawsonian. He called himself a neo-Strawsonian even when Strawson was alive.

Similarly, some Griceians called themselves neo-Griceians when Grice was still alive. Grice retorted by calling himself palæo-Griceian.

Rather, his own view is something which he schematizes as in (i):

(i) a. PRAG (K*, L+ ) = L+

b. PRAG (K**, L+) = L where

the more specific, presupposing understanding is the semantically assigned reading, and the other is derived


There's a careful critique of Atlas’s views in Burton-Roberts.

Curiously, Atlas remarks that the truth of (43) will imply its falsity rather than its truth-valuelessness on the

traditional view.

A statement like
Pegasus doesn’t exist will be predicted to be false if true.

Possibly this is a typo. Or one is missing something -- not the flying horse necessarily.

Atlas’s idea is that the problem stems from an improper informational analysis of sentences

like (43).

More specifically, he argues that (43), or a statement made with (43), does not have

Pegasus as a topic NP, and thus that the NP Pegasus is not presuppositional. Instead, the topic

of (43) is existence.

Atlas gives three main criteria for a definite description ("the flying horse that Bellophoron rode") to be considered a topic.

Each of these is given

as a necessary, but not a sufficient condition.)

They are

(a) ability of the containing statement to

be an answer to the question What about NP?

(b) the acceptability and equivalence of a

statement with an as-for-NP prefix; and

(c) lack of primary stress on the definite description in question.

fourth, but somewhat more contentious criterion is given as a sufficient condition for topichood:

that the existence of a referent of the definite description is presupposed. Cfr. Grice on IDENTIFICATORY uses of definite description.

A non-identificatory use is weaker,

"The butler that Smith uses is rather inept."

"The butler that Smith uses, whoever he is, is rather inept."

"Smith is bankrupt. His butler, whoever he is -- let's call him Bill -- will be looking for a new position. If he HAD a butler in the first place!"

-- All examples from Grice.


A: The Merseyside native who climbed Mount Everest on hands and knees won't be attending the party on his honour organized by the Merseyside Geographical Society.
B: Why?
A: He doesn't exist. He was yet another sensationalist invention by the journalists. The sad thing is that they gave him a proper name too: Marmaduke Bloggs.

Atlas first considers criteria (a) and (c).

With normal intonation and stress, to what

question is the statement of John exists a felicitous answer?

I think it is Who/What exists? (and

more generally, What about what exists?).

The topic is: what exists….”


notice that the unmarked pronunciation of John exists is with main sentence stress on John rather

than exists.

Subsequently the reader is given the following pairs

(44) a. John exists.

b. As for what exists, John does.

(45) a. John exists.

b. As for John, he exists.

The pairing in (44) is asserted to be correct – i.e. they are paraphrases.

However the pairing in

(45) is not correct. Instead, (46) is given as an appropriate paraphrase for (45b).

(46) John EXISTS. (e.g. John doesn’t LIVE, John EXISTS.) [= Atlas 1989, 113, ex. 53a']

Again the conclusion is that the subject proper name or corresponding definite description is not a topic NP in the unmarked case of an

existence statement.

Instead, “the topic is: what exists”.

And if the subject NP is not

the topic, then, according to his fourth criterion, the existence of a referent is not presupposed,

but is instead asserted.

It is significant that these criteria are examined primarily with respect to positive, rather

than negative, existence statements.

When Atlas comes to consider the case of negative

existence statements he says that parallel arguments support the same conclusion for explicit

negative existence statements.

A quick argument to this effect is easily formulated:

presuppositions are invariant under main-verb negation.

This claim might be seen to conflict with the assumption that negative sentences like those in

(36) above have, as one of their uses, a “true, non-singular assertion that is the external negation

of the proposition that the king of France is bald”.

On this use, the

presupposition of existence of a king of France is not maintained.

Unless the positive sentence

also has a nonpresuppositional use, we can’t be certain that negative sentences maintain the

presuppositions of their positive counterparts.

But possibly by “main-verb negation” Atlas

means to exclude the sentence level negation interpretation.

In any case there is a more pressing reason not to assume that positive and negative

existence statements have the same topic-comment structure, and that is that typically the

nonexistence of something is more interesting and newsworthy than its existence.

Almost all the

time in our ordinary daily lives, the things we are talking about are things of whose existence we

are confident, and that being the case, the fact that these things exist is almost always not worth


So Atlas may be right about positive existence statements typically being about what

exists instead of about the referents of their subject NPs.

It may also be true that 99.99% of the

tokenings of such sentences occur in discussions at the Grice Club.

However this is not true of


Thus, given the general correlation between topichood and old information, we

might expect existence to be topical in the case of positive existence statements without holding

the same expectation for nonexistence in negative existence statements.

Atlas, however, insists

that both positive and negative existence statements are about existence.

Thus he suggests that


(47) As for what exists, Pegasus doesn’t.

is a natural paraphrase of (43).

However some find this suggestion hard to accept. To some ears (47) has something of the

jarring sensation felt with (48):

(48) As for Bill, Jane smokes.

On the other hand some find (49)

(49) As for Pegasus, he doesn’t exist.

to be perfectly natural.

Of course another factor playing a role in the determination of sentence topics is what the

surrounding discourse concerns.

And it would seem that, outside the philosophical discussions

of existence alluded to above, the question of something’s not existing would typically most

naturally arise in the case that one had assumed that that thing did exist, and when that thing was

the subject of discussion.

Consider a typical child’s disabusements concerning Santa Claus and

other nonexistent notables.
These seem much more likely to occur during a conversation about

the putative entity in question, rather than one about existence.

The scenario in (50) strikes some

as more likely than the one in (51).

(50) A: Mommy, is Santa Claus a real person?
----- B: No dear, Santa Claus doesn’t exist.
---- A: What about the tooth fairy?
---- B: Sorry dear, the tooth fairy doesn’t exist either.
(51) A: Mommy, what exists?
----- B: Well, as for what exists, Santa Claus doesn’t. And while we’re on the topic of
existence, the tooth fairy doesn’t either. And Pegasus, and of course the bald King of France, poor soul.

Of course (51) may be a little unfair to Atlas, but on the other hand, he has to admit that (50) is a
perfectly natural discourse.

This raises the question of the extent to which the problem of

negative existence statements has been solved.

Even assuming he were right that the unmarked

case of a negative existence statement has existence for its topic, Atlas cannot deny that there are

natural conversations like (50), where it would seem that a nonexistent entity is topic.

It would

seem that he would have to say that such conversations are ill-formed, that Mother B in (50) can’t

be making the statements she seems to be making because of the lack of a referent for the

topical, hence presupposed, NPs.

But that is hard to accept.

We think Atlas has made an interesting and correct point about the intonational structure of

existence statements.

It does seem that the subject typically receives the main sentence stress,

and this seems to be true equally for both negative and positive existence statements.

However it

is clear that, at least in the case of negative existence statements (which are the troublesome

ones, after all) this criterion for topichood can come apart from the others, as in example (50).

Even if Atlas’s claims were right about all negative existence statements, would that solve

the problem?

We don’t think it’s clear that it does.

It seems that we would still have the

fundamental problem associated with any statements involving proper names of nonexistent

entities (cfr. the Stanford book on "Empty Names") and that is the question of what such proper names contribute semantically to the

sentences (or statements) in which they occur.

If we accept Russellian direct reference, then we

have only one level of meaning (in a medium sized sense of the word “meaning”, i.e. one not

including pragmatics) to worry about, but if we also accept Kripke’s arguments for the

nondescriptionality of proper names then we still seem to have a problem on that one level –

namely, that proper names of nonexistent entities have nothing to contribute semantically.


seems that that problem remains, and that it continues to be particularly pressing with the

negative existence statements that we want to say are true, and outside of any fiction.
We have  tried, while geing Griceian, to counter arguments for the “sense generality” of negative sentences, and
to provide some support for the alternative Gricean view that negative sentences literally express

a simple sentence negation and only conversationally implicate the existence of referents for any

singular terms involved. We should make it clear that I’m not ready to adopt the many Gricean views -- some are better than others. Some prefer his square-bracket device, some his subscript device, some his identifcatory/non-identificatory distinction. We

have to confess that we really don’t know what to think about definite descriptions in negative

sentences, and perhaps Grice thought that was a good thing and a proof that he was a good philosopher. After all he taught Strawson logic and he (Strawson) came up with truth-value gaps!

We've pointed out what seem to me to be clear examples of negative existence

statements where existence itself is not the topic of the statement, and also tried to suggest that

serious problems remain for these kinds of statements no matter how the issues of topicality are

ultimately resolved. We should note that I have not questioned the assumption that changing the

topic-focus structure of a statement affects the presuppositions of its singular terms, but see von

Fintel 2004 for arguments that this is not the case.

This paper was originally written as a tribute to Grice's university, and especially Wolfson, that hosted Atlas, and it may not seem

like a very nice one, but we've tried to call into question a number of Atlas's important contributions

to the philosophy of language.

Still, someone has said that there’s no such thing as bad publicity,

so perhaps ultimately we've only added to Atlas's and Wolfson's’s well-derserved renown.

And possibly he’ll find some amusement

in pointing out where we've gone wrong in all this.

And finally I should emphasize how much

I’ve enjoyed puzzling through this work – it has given us a lot to think about, and not just about Pegasus -- how high could he fly?


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