Week 6 Class Questions
PH221: Sense, Reference and Denoting II
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Grey’s Elegy
Russell is trying to show that the distinction between sense and reference cannot
be maintained. His argument, it seems, is the following.
1. Sense is an intensional concept.
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2. Reference is an extensional concept.
3. But senses can be referents; therefore senses can be extensional.
4. (implicit premise) concepts cannot be both intensional and extensional.
5. Therefore, we have a contradiction.
Much of Russell’s argument about Grey’s elegy is in showing that we cannot, in
fact, substitute the actual first line of Grey’s Elegy (‘The curfew tolls the knell
of parting day’) for the sign, C, which denotes it and still maintain the same
meaning of ‘The meaning of the first line of Grey’s Elegy is. . . ’. This shows that
sense can be intensional. That references are extensional comes from Frege. So
does the claim that senses can be referents (as in indirect reference). Supposing
that concepts cannot be both intensional and extensional—a premise for which
Russell doesn’t argue—we have a contradiction.
There is a major flaw—of equivocation—in this argument. Can you spot it?
Is it a charitable (and, more importantly, correct) reading of Russell? Is the
flaw a flaw of interpretation on my part, or an error in Russell’s argument?
1 From the Stanford Enclyclopedia of Philosophy: A verb is intensional if the verb phrase
(VP) it forms with its complement is anomalous in at least one of three ways: (i) substituting
one expression for another that is coreferential with it in the complement of the verb can change
the truth-value of the sentence in which the VP occurs—for instance, you might admire Mark
Twain but not Samuel Clemens, not realizing that your pesky neighbor Sam is the famous
writer (in this case substitution of the coreferential ‘Samuel Clemens’ for ‘Mark Twain’ in the
VP ‘admire Mark Twain’ will turn a true sentence, ‘you admire Mark Twain’ into a false one,
‘you admire Samuel Clemens’); (ii) the VP admits of a special ‘unspecific’ reading if it contains
a quantifier, or a certain type of quantifier; and (iii) the normal existential commitments of
names and existential quantifiers in the complement are suspended even when the embedding
sentence is negation-free concept.
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Russell’s Three Problems
Russell notes that any theory of denoting must solve three puzzles or problems:
the puzzle of substitution, the puzzle of excluded middle, and the puzzle of
negative existentials.
2.1
What are the three problems?
The puzzle of substitution is the problem that we should be able to replace coreferential terms in sentences while maintaining their truth-values. But we also
need to explain what it is that George IV wanted to know when he wished to
know that Scott was the author of Waverly. For he did want to know whether
Scott was the author, but already knew the tautology that Scott was Scott.
Frege’s solution here is that George knew the two senses, but did not know that
each sense had the same referent, namely, Scott.
The puzzle of excluded middle is that by this law either A is B, or, A is not
B must be true. So either the present king of France is bald, or the present king
of France is not bald must be true. Yet, in order to check whether this is true,
we must check whether property is true of the referent, but there is no referent
for either sentence. So it seems that neither is true. Frege says that the referent
is the empty set and that the truth-value corresponds to this, which is odd.
The puzzle of negative existentials is a problem with referring to nonexistent
objects. When we denote something, we, in a loose sense, linguistically point at
it. But how can we point at a non existing object? It is like saying ‘the thing
at which I am pointing is nothing.’
2.2
What is Russell’s Solution?
Russell solves these problems by providing a three-part analysis of denoting
phrases like ‘The present king of France is bald.’
Russell’s Analysis (sentential) There exists some x such that x has the
property of being the king of France and the property of being bald and
further, there is only one x that satisfies these properties. So anything
else that might seem to satisfy them must be equivalent to x.
Russell’s Analysis (logical) (∃xKx) ∧ (Bx) ∧ (∀yKy → y = x)
2.3
How does Russell’s Solution solve the problems?
Russell’s solution solves the first problem in the following way: once we break
the denoting phrase into its three parts, then what it is that George wanted to
know is whether substituting Scott for x satisfies the three disjuncts. That is
whether the following is true:
Scott Case (As) ∧ (s = Scott) ∧ (∀yKy → y = s)
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Russell’s solution solves the second problem by introducing the distinction
between primary and secondary occurrences of denoting phrases. What we need
is for the sentence ‘the present king of France is bald’ to take one truth value
and for its negation to take the other. This is possible when we formalise the
sentence using the ‘secondary occurence analysis’ for the negation formalisation,
so:
Normal formalisation: (∃xKx) ∧ (Bx) ∧ (∀yKy → y = x)
Negation formalisation: ¬(∃xKx) ∧ (Bx) ∧ (∀yKy → y = x)
The first sentence is false, the second is true. Therefore, we have preserved the
law of excluded middle.
Russell’s solution to the third problem also depends on the primary/secondary
occurrence distinction. The denoting phrase, ‘the square circle’ is a denoting
phrase that doesn’t denote anything. Now give the sentence, “The square circle
is round.” Russell’s treatment.
Russell’s formulation: (∃xZx) ∧ (Rx) ∧ (∀yKy → y = x)
Again, no ‘a’ that we could substitute for x exists. Thus, the first disjunct is
false; thus, the sentence is false.
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Strawson’s Critique
Srawson draws a number of distinctions: one between expressions and sentences,
another two between these entities, their uses and their utterances. He uses these
distinctions to critique Russell’s account.
3.1
Strawson’s Distinctions
Strawson notes that sentences are denoting phrases, proper names etc. And
sentences are those things that begin with such expressions. So, ‘the present
king of France is bald’ is a sentence and ‘the present king of France’ is an
expression. Taken in general these are expressions and sentences, but they may
also be indexed to, for example a time or place. That is, a context. A sentence
or expression in a particular context is a ‘use’. And finally, particular instances
of each are ‘utterances.’
3.2
Strawson’s Critique of Russell
Strawson argues that Russell fails to distinguish uses from the context independent status of sentences and expressions. Meaning, according to Strawson, is
a property of the general sentences; but mentioning (as Strawson calls it) or
referring is a property of uses of sentences and expressions. So, whether or not
a sentence is true depends on the context in which it is uttered. This, in a
nutshell is Strawson’s point.
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The most important difference between the two is the relation of implication
between:
1. The present king of France is bald.
and
2. There is a king of France.
If we take the relation of implication to be one of logical entailment (as Russell
does), then both of the following are true: a)1 cannot be true unless 2 is true
and b) If 2 is false, then 1 is false. On the other hand, if we take the relation to
be that the former presupposes the latter (as Strawson does), then c) 1 cannot
be true or false unless 2 is true and d) If 2 is false, then 1 is neither true or
false hold.
3.3
Russell’s Response
One thing that can be said of Russell’s response is that is is a bit curmudgeonly.
But, despite this, what are its merits? What is Russell trying to accomplish in
his claim that “if for the word ‘present’ I had substituted the words ‘in 1905’,
the whole of [Strawson’s] argument would have collapsed”? It seems that he is
eroding the distinction Strawson draws between the non-indexical general status
of stentences and their indexical use. Why does this matter? I’ll leave this for
you to think about.
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