The keywords here should be: Names (as per Grice's "Vacuous NAMES"), Descriptions (as per Grice, "Definite Descriptions in Russell and the Vernacular") and Quantifiers (as per Grice's "System Q", relabeled System G by Myro).
We can have thoughts, it seems, when there is no object to be a constituent of the proposition:
the universal quantifier: "all" or "every" (represented by (x))
We cannot, as it were, think about the set directly, i.e., it doesn’t enter into the proposition.
The denoting concept is there in the proposition, it is an independent matter whether the denoting concept has a value or not.
For the denoting concept takes the place of the missing king, if you will.
Surface form need not be a guide to logical form (the form of the proposition, that which determines truth conditions).
But there isn’t a constituent here which corresponds to ‘every number’. Consider:
The meaning of the subject is, as it were, smeared across the quantifier and the antecedent of the conditional.
Some expressions contain no subject at all.
In other words, there is no propositional constituent corresponding to ‘every number’ (cfr. "The average family has 2.1 children").
Whitehead's and Russell’s proposal, therefore, is simply that definite descriptions fall together with quantifier binding rather than singular terms.
Any context in which a phrase of the form occurs can be translated into one in which only quantifiers occur.
The definition of all logical constants in terms of ‘¬’ and ‘and is another example of contextual definition.
We thus want to make a decision about
The king of
But since there is no such person it might seem that he is neither bald nor not bald (excluding synthetic wigs alla Hegel that Russell quotes in "On Denoting" -- "Hegelians love a synthesis").
This comes down to an issue of scope of negation -- what Grice symbolizes by ~n, or by the use of the square-bracket device: whatever falls WITHIN the square brackets is IMMUNE to negation, since it is not controversial and won't be challenged by your addressee.
"Do not multiply senses of "not" beyond necessity."
"Do not multiply senses of "the" beyond necessity".
"Do not multiply senses of "a/an" beyond necessity."
(He is most clear regarding 'a/an': we would hardly be sympathetic to a philosopher that 'a' has three different senses: "I broke a finger yesterday", "I saw a tortoise in my garden", "Smith is meeting a woman this evening").
a is ¬F
mean the same thing.
Another reason why definite descriptions are not singular terms.
the king of
But there is an independent reason for thinking that definite descriptions do not contribute an object to the propositions in which they occur.
What object does ‘the author of Waverly’ contribute to the proposition?
George IV wanted to know if the author of Waverly was Scott, not if Scott was Scott.
Thus: definite descriptions are not singular terms.
There are two responses.
If one accepts the distinction between surface and logical form, then the former does not impose a tight constraint on the latter.
We do not, though, need to effect such a reduction, we can treat ‘the’ as a quantifier in its own right:
Grice almost adopted it, but Hans Sluga said, "No!".
Think of the ‘(the x)’ as expressing a function defined over two sets, the set of kings and the set of bald things.
The value of the function is true just if there is no member of the king set that is not a member of the bald set and there is only one member of the king set, i.e.,
This gives us the same truth conditions as the Whiteheadian-Russellian analysis without beating surface form to a pulp.
Whitehead's and Russell’s theory of descriptions only pertains to ‘the so and so’-type phrases.
What Whitehead and Russell do propose is that apparent names (singular terms), such as 'Louis XIV', are in fact truncated or telescoped descriptions --to an associated 'dossier' as Grice would have it in "Vacuous Names".
This claim is a separate thesis from the one which says that definite descriptions are not singular terms.
Prima facie, one can accept the theory of descriptions without thinking that ‘Louis XIV’ is, logically speaking, really a description.
It simply doesn’t follow from any semantic thesis Whitehead and Russell accepted.
a is F
is meaningless, where ‘a’ is empty (lacks a referent) or is 'vacuous' (in Grice's terminology), cfr. "Empty names" (Stanford University Press).
---- Russell, Knowledge by Acquaintance and Knowledge by Description.
For the moment, consider that there is a set of options available.
One may, for instance, say that, contra intuition, ‘a is F’ does not express a thought when ‘a’ is empty, but ‘a’ is still a singular term!
Whitehead and Russell did not consider this option because of an epistemological principle: to understand a proposition, one must be acquainted with its constituents.
It thus appears that we are led to view a as complex, as made up out of constituents with which we may be acquainted.
If we reject such a picture, then we have removed the motivation for thinking of names as complexes, descriptions.
But am I acquainted with Russell,
--- Russell, KAD, p. 208).
For Whitehead and Russell, names are truncated or telescoped descriptions; e.g.,
When we use definite descriptions and names we are having general thoughts, not about objects.
The only genuinely referring expressions (“logically proper names”), by Whitehead's and Russell’s principles, are ‘this’, ‘that’ and ‘I’.
Here are some problems for Russell’s view, based on Kripke’s notion that names are rigid -- Grice speaks of inexorable tying.
For example, one can say:
If Bismarck weren’t
But if ‘
If I pick up the name ‘Bill’ in a conversation, it seems that I can use ‘Bill’ in the conversation to refer to Bill.
In what sense would I fail to refer to him?
Whitehead's and Russell's account of names as definite descriptions is equally widely rejected.
There have been, however, a number of criticisms of the theory of definite descriptions. here we’ll just look at two standard complaints.
Firstly, there is the claim that truth attaches to statements, not sentences.
Call this the truth bearer objection.
This is of little consequence, for Russell was clearly concerned with propositions, not sentences.
Strawson’s second objection is more interesting.
The F is G
presupposes (or implies, or implicates) the existence of something which is F.
Russell’s analysis has it that ‘The F is G’ entails the existence of something which is F.
Because the proposition expressed is conjunctive, and a conjunction is true just if each of its conjuncts are true, and the first conjunct in Russell’s analysis is that there is a king of
It is not possible for B to be false and A to be true)
Thus, for Whitehead, Russell, and Grice, if there is no king of
For Strawson, ‘The king of
Strawson takes this reading to be intuitively correct.
It is easy to find instances where Strawson’s intuition is simply wrong:
"The king of
That is, if A putatively presupposes B, then we can always jointly assert the falsity of A and B.
This shows that presupposition simply does not hold, for if it did, the falsity of B would be enough to show that A lacked a truth value (true or false).
A is false because B is false, e.g.,
In Grice's famous cancellation:
The king of
Again, this seems to be just false:
Mary doesn’t know she is pregnant, because she is not pregnant, it was a phantom pregnancy.
(The particular object may be France's President).
Donnellan’s claim, then, is that, at best, Whitehead's and Russell’s account is partial (never mind Strawson's): it completely ignores referential or identifcatory uses, which were the only uses that interested Strawson ironically!
The murderer of Smith is insane.
On the other hand, Donnellan suggests that, as said by a trial spectator as the accused of Smith’s murder is frothing at the mouth, is true just if the accused is insane, regardless of whether he murdered Smith or not.
Similar examples by Grice in "Vacuous Names" regarding 'the butler that Smith relies on so much' "will be looking for a new position", "was in fact his gardener".
Referential or identificatory uses are where we communicate an object dependent proposition by using a sentence that expresses an object independent proposition.
Grice says to Warnock at Collections:
‘He has beautiful handwriting’.
The utterance of the above simply means that the candidate has beautiful cellent handwriting, what else on earth can it mean?
But Grice knows that Warnock will understand something more, namely, the candidate is no hopeless at philosophy (The example occurs in the segment of "The causal theory of perception" that Grice excluded from Way of Words).
Grice, by uttering "He has beautiful handwriting", has thus, by exploiting the context, communicated a proposition to Warnock that does not JUST have the truth conditions of the sentence he wrote on the reference.
Just so with Donnellan’s example:
expresses an attributive proposition true of whoever is the unique satisfier of
x murdered Smith.
But it can be used referentially to have an utterer-meaning (reference): its utterer-meaning is an object-dependent proposition about, say Nowell, frothing at the mouth in the dock.
The object-dependent proposition is communicated because the addressee can work out such a proposition because he realises that the spectator thinks that the man in the dock is the murderer of Smith, even though he did not say that he was.
If we admit the ambiguity of
on the basis of referential or identificatory use, we must say that all quantifiers are ambiguous:
One's addressee would thus get an object-dependent proposition about A and B.
But one have not said anything ambiguous.
They can infer the object dependent proposition from one's general proposition and their knowledge about the people in the room and what one knows.
We do not have to think of ‘most’ as ambiguous.
The utterer is trying to get A to admit his crime.
Again, an object dependent proposition is inferred by the utterer's addressee, but the sentence doesn’t express one.
‘Some’ is not ambiguous. (Cfr. "That was some party"), or as murderous Robespierre would say, with a slight wicked relief, "That was SOME bald king (of France)".