Frege, Russell

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Frege, Russell

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Title: Frege, Russell

1
Frege, Russell
2
1. De re de dicto distinction

Notice that the following sentence
(1) He wants to talk to the store manager.
is, in a subtle way, ambiguous.

3
Consider the following two situations

Case 1 in a store, the cashier tries to cheat me
when giving me back change. Then she exclaims I
want to talk to the store manager! This
statement is of de dicto form I say I want to
talk to whoever the store manager is. My goal is
to pick out the relevant person through the role
/ via the definite description uttered.
Case 2
Jack entering the store I want to talk to
Bill. (Bill is the store manager.)
In this case what we can correctly say of Jack is
this
The store manager is such that he wants to talk
to him.
This is de re mode the latter paraphrase (in
italics) does not imply that Jack wants to talk
to the store manager under the description the
store manager.

4
Logical forms Russellian analysis

Case 1 Someone can correctly say of me he
wants that, whoever the store manager is, he talk
to him .
In de dicto mode the definite description takes
narrow scope
He wants that the x x is the store manager(he
talk to x)
Case 2 Jack wants to talk to Bill who, by the
way, is the store manager.
In de re mode the definite description takes wide
scope
The x x is the store manager want (Jack,
talk(Jack, x))
?x (St_man(x) ?y(F(y)? yx) want(J, talk(J,x))

5
Moral de re de dicto analyzed as scope
ambiguity(terjedelmi kétértelmuség)

The original, everyday interpretation of these
phrases is of the thing, and of the word
respectively.
This subtle intuitive difference is clarified by
means of the Russellian analysis.
Russell calls the de re reading primary
occurrence (of descriptions) ? when the
description takes wide scope
The de dicto reading is called secondary
occurrence.

6
Another example de re vs. de dicto belief

(1) Tracy believes that John is the candidate
most likely to be elected
? de dicto belief, because Tracy takes the guy in
question under the name Jones. Here believes
takes wide scope.
(2) John is such that Tracy believes him to be
the candidate most likely to be elected.
De re belief believes takes narrow scope. This
form does not presuppose that Tracy knows the guy
by the name Jones. Perhaps she knows him only
by a nickname, say, Baldguy. So what Tracy
believes, and is disposed to utter, is that
Baldguy is the candidate most likely to be
elected. Still, in this case (2) can be truly
said of her, although not (1). (I.e., if
Baldguy and Jones refer to the same person)

7
Russell on denoting and semantic puzzles

Some terminology
What Russell calls denoting phrases are, in
contemporary terminology, noun phrases consisting
of a predicate and a quantifier expression (e.g.
every man) ? quantifying noun phrases.
(1) I met a man.
?x(x is human I met x)
Certain pronouns, like everything, nothing,
are simpler they are interpreted as quantifiers
binding variables. Bare quantifiers are simpler
still (e.g., every, some, no).
(2) Nothing lasts forever.
?x(x lasts forever)

8
Reference and denotation

J. S. Mill A system of logic, 1872 put forth a
purely referential theory of proper names
According to Mill, the role of proper names is
"to enable individuals to be made the subject of
discourse. Names are "attached to the objects
themselves, and are not dependent on any
attribute of the object"
Russell The point in using a name is not to
represent its object as having certain
properties, but rather, "merely to indicate what
we are speaking about the name is no part of
the fact asserted it is merely part of the
symbolism by which we express our thought
(Russell, 1919)
This is unmediated reference.

9
However

Russell thought that most ordinary proper names
are in reality, disguised (abbreviated) definite
descriptions.
Descriptions are quantificational phrases which
pick out their object (if it exists) via some of
their properties cited.
In other words, descriptions denote.

10
Surface grammar and logical form

Grammatical form is misleading as to logical
form. The following sentences
(3) The inventor of the zipper is smart.
(4) Smith is smart.
both are of subject-predicate form grammatically,
but not logically.

11
Three puzzles (and a fourth one)

1. Substitution.
(a) here the substitution is truth-preserving
Tully Cicero.
Cicero limped.
? Tully limped.
(b) here it is not, in fact the conclusion does
not follow.
Scott the author of Waverley.
George IV wished to know whether Scott was the
author of Waverley.
? George IV wished to know whether Scott was
Scott.
Solution should be clear by now

2. The excluded middle.
A sentence (proposition) must be either true or
false there can be no middle course. So, either
The present king of France is bald or The
present king of France is not bald must be true,
and the other false. But the present king of
France cannot be found among the (existing) bald
entities nor can it be found among the non-bald
ones.

Solution If we notice the ambiguity created by
the negation, we can properly assign truth
values.
The sentence
The present king of France is not bald has two
readings
The king of France is such that he is not bald.
That is ?x(KF(x) ?y(K(y) ? yx) B(x))
Primary occ. de re FALSE
It is false that the king of France is bald.
?x(K(x) ?y(K(y) ? yx) B(x))
Here the occurrence of the definite description
is secondary ? it is within the scope of the
negation TRUE

14
Note Freges view

For Frege, both of these sentences
The present king of France is bald
The present king of France is not bald
fail to have a truth value (or were assigned the
TV fictitious). The reason was that these
sentences contained an expression that had no
reference.

3. Statements of non-existence
Try to formalize the following sentence
(5) The present king of France does not exist.
The following sentence is strange as well
(6) The present king of France exists.
Contrary to the first two puzzles, that are
solved elegantly, this is a catchy one for the
Russellian system.

(5) The present king of France does not exist.
?x(K(x) ?y(K(y) ? yx))
(6) The present king of France exists.
?x(K(x) ?y(K(y) ? yx))
Regarding logical form, exists adds nothing to
the picture it seems to have no content that
could complete the definite description.
Russell also claimed that in general, quantifying
noun phrases like a man, some children have
no meaning in themselves. If this is applied to
the definite case as well, we have an additional
problem the logical form of (6) does not suggest
that it is meaningless, but according to the
above stipulation it is, because it too is a
quantifying noun phrase.

Russell introduced a dummy predicate for exists
(E!) in order to be able to complete the logical
form of (6)
E!(the x Fx) df ?x(F(x) ?y(F(y) ? yx))
Notice that we must not insert the dummy
predicate in the definiens (right side). Why?
Because then (5)
(5) The present king of France does not exist
Will be outright contradictory
?x(K(x) ?y(K(y) ? yx) E!(x))

18
A fourth problem well-established fictitious
characters

There is a difference between (5) above
(5) The present king of France is bald.
and this one
(7) Bugs Bunny has long ears.
Intuitively, (7) is true. But prima facie the
Russellian system has no resource to distinguish
it from (5), and explain how (7) can be true
whereas (5) false.
(What remains open is to reject the common-sense
intuition about (7). But given the role fiction
plays in our thinking, this would be an unhappy
result.)

19
The nature of propositions

In general, propositions are what sentences or
utterances of sentences express.
For Frege, propositions (or thoughts, as he
sometimes calls them) are the senses of
sentences. According to Frege, propositions are
abstract objects.
Since Russell wanted to eliminate the need for
Fregean senses, he could not regard propositions
as abstract objects. (For if propositions are
abstract objects, why cant they be the Fregean
meanings of sentences?)
Still, Russell relies on the notion of a
proposition. For him, propositions have entities
as their subjects moreover, propositions are the
denotations of declarative sentences.

What are propositions then?
In his writings, Russell used the word
proposition in several different ways.
Sometimes he seems to use it on a par with
sentence.
One way to understand Russell might be this
A propositon is like a state of affairs
(admitting compositionality).
e.g., the state of affairs that Grandma drinks
beer consists of two relevant objects and a
relation between them, all three being perfectly
real.
If some of the relevant objects are missing, then
there is no real state of affairs consequently
there is no proposition. (Cf. The present king
of France is bald.)
So if something is the subject of a proposition,
then that thing must exist.

But this account of the nature of propositions
yields an annoying problem there can be no false
propositions only true propositions and true or
false sentences.
This is because only existing states of affairs
can be propositions, and they make certain
sentences true. If a sentence is not backed by a
proposition (an actual state of affairs), then it
is a false sentence.
What is the problem here?
? True sentences express propositions, okay.
? Intuituvely, however, false sentences express,
or mean, something just as well as true ones.
? But, on this understanding of Russell, false
sentences are not backed by propositions,
therefore there is nothing false sentences
express. An unhappy result.

22
Quiz

Formalize, accoring to the Russellian system, the
statement
(8) The person named Tully is the person named
Cicero.
vagy ezt
(8) A legnagyobb magyar a Tudományos Akadémia
alapítója.
(That is, what is the logical form of a statement
of identity that contains two definite
descriptions?)

23
Linguistic contexts and the substitution of
co-referential singular terms

Linguistic contexts (logical operators) differ in
what aspects of their operand they are sensitive
to.
1. Truth-functional contexts (extensional
operators) are sensitive only to the truth value
of their operand. Examples negation and logical
connectives.

2. Intensional contexts are sensitive to the
truth value and the truth conditions of their
operand.
Examples the modal operators necessary and
possible. For example,
(9) 9gt7 and
(10) The last president of the USSR is M.
Gorbachev.
are both true. However,
(11) necessarily(9gt7) is true whereas
(12) necessarily(The last president of the USSR
is M. Gorbachev) is false.
Note also that merely intensional contexts admit
the substitutivity of coreferentials
(13) Mark Twain might not have written The
Adventures of Huckleberry Finn. I.e., ?(M.T. did
not write The Adventures of H.F.) TRUE
(14) Samuel Clemens might not have written The
Adventures of Huckleberry Finn. I.e., ?(S.C. did
not write The Adventures of H.F.) TRUE

3. Hyperintensional contexts are those which are
neither extensional, nor intensional.
Example propositional attitude contexts.
The sentences
(15) Mark Twain authored The adventures of
Huckleberry Finn.
(16) Samuel Clemens authored The adventures of
Huckleberry Finn.
have the same truth value and truth conditions,
still, when prefixed by Tom thinks that__, they
will not necessarily have the same truth value.
Another key example of hyperintensional contexts
direct quotation. Tom said Mark Twain authored
The adventures of Huckleberry Finn.

26
The Slingshot argument

There is a famous argument in the philosophy of
language one version of which attempts to
demonstrate that the situation is much simpler
than this there are, in fact, only two types of
context extensional, and hyperintensional (or
opaque).
Furthermore, hyperintensional contexts can be
traced back to direct quotation. (I.e., being
directly quoted is the ultimate reason for
hyperintensionality.)
At least for W. v. O. Quine, this was the
conclusion from the argument.

27
Why is this conclusion important for Quine?

Quine famously argued against such notions as
intension, possibility, and proposition claiming
that they are unintelligible.
Therefore these notions cannot serve any useful
function in a theory of meaning.
Abstract objects, and merely possible concrete
objects are entia non grata, in Quines
ontology, since, according to him, they only
create confusion in our thinking, raising
problems about identity in particular.
The Slingshot was one of Quines arguments in
establishing this general conclusion.

28
The argument

Summary of the argument If a linguistic context
allows the substitution of co-referential
singular terms, and it also allows the
substitution of logically equivalent sentences,
then that context is extensional.
For supposedly (merely) intensional contexts
like necessary, possible (or causes), the
argument goes through and leads to unacceptable
conclusions.
Take the following two sentences
(17) Necessarily, two plus two equals four.
(18) Necessarily, the author of The adventures of
Huckleberry Finn is Mark Twain.
Intuitively, (17) is true, whereas (18) is false.
However, through logical steps, the Slingshot
argument takes us from (17) to (18).

Premises
P1. Substitution of co-referential singular terms
is allowed in the scope of necessary it does
not affect the truth value of the whole.
P2. Substitution of logically equivalent
sentences in the scope of necessary does not
affect the truth value of the whole.
Comment
(i) This much (P1 and P2) has been assumed.
(ii) Two sentences are regarded as logically
equivalent if they are true and false together.

Premises continued
P3. The singular term x xx 224 is
coreferential with the term x xx the author
of The adventures of Huckleberry Finn is Mark
Twain.
Oops. Comment and proof
Both sentences (224 and The author of The
adventures of Huckleberry Finn is Mark Twain)
are true.
The expressions in curly braces define sets. The
formula x xx is to be understood thus the
set that contains any individual x such that x is
identical to itself this is the set of all
individuals. However, it is also true that
everything is such that it is identical to
itself and 224 we add a condition to the
definition which is satisfied and does not in any
way exclude individuals from the set defined by
x xx. For the same reason, x xx the
author of The adventures of Huckleberry Finn is
Mark Twain refers to the same set as well.

P4. The sentence
(19) x xx the author of The adventures of
Huckleberry Finn is Mark Twain x xx
is logically equivalent to the sentence
(20) The author of The adventures of Huckleberry
Finn is Mark Twain.
Proof.
(20) is true, therefore the two formulas flanking
the identity sign in (19) both denote the set of
all individuals. Now suppose, for the sake of
argument, that (20) is false. In this case the
left side of (19) denotes the null set (since
there is no individual for which it is true that
it is self-identical and (20) is true remember,
we just assumed the opposite), and the right
side, the set of all individuals. So the equation
is false, as is, by assumption, (20). So (19) and
(20) are true and false together.

P5. The sentence
(21) x xx 224 x xx
is logically equivalent to the sentence
(22) 224
Since (22) is true it can be derived from the
axioms of number theory (21) is true as well.
Hence the two are logically equivalent.

Now the derivation
Necessarily 224.
Necessarily x xx 224 x xx (P2,
P5)
Necessarily x xx The author of The
adventures of Huckleberry Finn is Mark Twain
x xx (P1, P3)
Necessarily The author of The adventures of
Huckleberry Finn is Mark Twain (P2, P4).
Thus we get the absurd conclusion.

34
Summary notes

According to the argument, there is no such thing
as a merely intensional context the kind of
context we would like to think modal operators
belong.
?That is, IF WE SUPPOSE THAT modal contexts are
merely intensional, then it follows by the
Slingshot that they are no different from
extensional contexts.
Quine, however, has another argument that is
supposed to show that modal operators are
hyperintensional (or opaque), that is, they do
not allow the substitution of co-referential
singular terms.

35
Quines other argument

1. necessarily(9gt7)
2. 9 the number of planets
3. necessarily(the number of planetsgt7)
This shows, according to Quine, that necessary
is opaque, since it does not allow the
substitution of coreferential singular terms.
Moreover, Quine says, quantification into opaque
contexts is unintelligible. Therefore, logic has
to dispense with modal operators.
Quiz2 What could we respond to this argument,
in Russells spirit?

Observation 1
What happens in the above argument is NOT a
substitution of coreferential singular terms
(i.e., 9 ? the number of planets).
Observation 2
The third line in the argument has two readings.
De re
the x x numbers the planets necessarily (x gt
7) TRUE
De dicto
necessarily the x x numbers the planets (x gt
7) FALSE
Now the big question is

Which reading can we derive from the correctly
formulated Quinian premises
1. necessarily(9gt7)
2. ?x(Planets(x) ?y(Planets(y)?yx) x9)
It turns out that, following Russellian logic, we
can derive the de re reading, which is true.
(We skip the derivation here Neale, 1990 has
it.)
Thus Quines second argument loses force.
Not so the Slingshot that we have not rebutted
yet.