Lecture 6: Bertrand Russell, “On Denoting” - BenBayer.com

Bertrand Russell
Lecture 6: Bertrand Russell,
“On Denoting”
Philosophy A465:
Introduction to Analytic Philosophy
Ben Bayer, Spring 2011
1. Introduction
2. Knowledge by acquaintance and by description
3. Three puzzles involving denotation
4. The theory of descriptions
5. Solutions to the puzzles
6. Critical questions
Introduction
• Bertrand Russell (1872–1970)
o English aristocrat, logician,
mathematician, philosopher, peace activist
o brought Frege to the attention of English
philosophy (and the world)
o like Frege, concerned with grounding math in logic
(in Principia Mathematica, with Whitehead)
• “On Denoting”
o called a “paradigm of philosophy” for use of modern
(Fregean) logic in solving puzzles (unsolved by Frege)
o like “Sense and Reference,” the subject is the
“meaning of ‘meaning’”
o but Russell is no fan of meaning as sense
Knowledge by acquaintance
and knowledge by description
• Russell was also a critic of idealism
o this meant rejecting the claim that we can know of
nothing existing external to the mind
o like Moore, Russell thinks objects external to the mind
are conceivable
• to make sense of this, Russell distinguishes two
kinds of knowledge
o knowledge by acquaintance
o knowledge by description
Knowledge by acquaintance
and knowledge by description
• Q: Which of these two types of knowledge seems
more likely to have objects in the mind
o we know by acquaintance things of which we’re directly
aware, not mediated awareness
o most of Russell’s objects of knowledge by acquaintance are
mental things:
• sense data
• memories
• introspection
• the self ()
o only possibly non-mental exception:
• universals
• Q: So what kinds of objects are likely to be objects of
knowledge by description
o objects external to the mind: bodies and other minds
Knowledge by acquaintance
and knowledge by description
• Q: which of these is known by acquaintance by
description
physical objects
o a table
o the color brown, a trapezoidal shape sense data
• Q: by what kind of description would we come to
know the table
o “the physical object which causes
such-and-such sense data.”
• Q: so how does this distinction help him
overcome idealism
• Descriptions are any phrase of the form:
o “a so-and-so” (ambiguous)
o “the so-and-so” (definite)

Knowledge by acquaintance
and knowledge by description
• Russell: a proper name is often shorthand for a
definite description
o exception: we use a proper name to refer to our self, if we
are directly acquainted with it
ex.
“I, Bismarck, am an astute diplomatist”
“I, , am an astute diplomatist”
o a friend of Bismarck’s is only acquainted
with sense data associated with him
(if not with him directly)
The mustachioed graying man is an astute diplomatist.
o a student of history is only acquainted with testimony:
“The first chancellor of the German empire is an astute diplomatist.”
“The first chancellor of the land of beer and philosophers is an astute
diplomatist.”
ex
ex
Knowledge by acquaintance
and knowledge by description
• this leads Russell to a strong claim about meaning:
“
The fundamental principle in the analysis of propositions contained descriptions is
this: Every proposition which we can understand must be composed wholly of constituents
with which we are acquainted.
--Russell, “Knowledge by Acquaintance and Description,” p. 5
o this model of analysis will be adopted later by logical
empiricists (positivists)
• Q: what happens if we’re acquainted with the
constituents, but not as going together
o “The just and kind German chancellor who succeeded
Kurt von Schleicher lived a long and happy life.”
• Q: what would Frege say
o The statement has no truth value
o Russell will disagree
”
Three puzzles involving
denotation
• Puzzle #1: a problem about identity
o if descriptions denote like names, we should be able to
substitute them for names of equivalent meaning
ex
Scott is the author of Waverley
George IV wonders if Scott is the author of Waverley.
George IV wonders if Scott is Scott.
TRUE
FALSE
o but we can’t, so why not
• Q: Which other puzzle does this remind you of
o Frege’s puzzle about belief
o but Russell doesn’t like Frege’s solution appealing to sense
o Russell: do descriptions denote like names
Three puzzles involving
denotation
• Puzzle #2: a problem about sentences with non-referring
terms
o by the law of the excluded middle:
• either A is B, or A is not B
ex
So either
The present King of France is bald.
or
The present King of France is not bald
should be true
o but if we examine all the bald and non-bald things,
we find no present King of France
o neither statement appears to be true, even though one should be
• Q: What was Frege’s solution to this problem:
o a concession, they’re both neither true nor false
o but Russell is convinced that every sentence is either true or false:
how might these be
Three puzzles involving
denotation
• Puzzle #3: a problem about negative existentials
o if descriptions denote like names, they should denote something
real
ex
“It’s false that A differs from B.”
“The difference between A and B does not exist.”
These are no different from:
“The present King of France does not exist.”
“Santa Claus does not exist.”
o but if a term is non-denoting, how can it be used to deny the
existence of anything
o if the term does denote, then what it denotes is said not to exist,
so it doesn’t denote: that’s a contradiction!
• Q: How did Frege solve this problem
o said that negative existentials are not about referents, but sense:
ex
“The present King of France” does not refer.
The theory of descriptions
• We need an analysis of definition descriptions
o but his method of analysis is different than usual
• Q: Normally, if you analyze the concept “king,”
what can you do with a sentence using it
ex
Louis is [king].
An analysis of “king” should yield something substitutable for that term:
Louis is a [ male aristocratic head of state ].
• Q: Can you do the same kind of analysis for
grammatical particles
ex
[If] Louis is King, [then] Louis is an aristocrat.
The best you can do is to translate this into a whole other sentence:
Louis is King, or Louis not an aristocrat.
o this is analysis by contextual definition

The theory of descriptions
• Russell’s contextual definition of definite
descriptions:
ex
The Prince of Wales is large-eared.
means the same as
1. There is a Prince of Wales.
2. A Prince of Wales is large-eared
3. One and only one Prince of Wales is large-eared.
• But this analysis won’t help unless it’s presented
in a more formal, rigorous notation
ex
The Prince of Wales is large-eared.
means the same as
x [Px & Lx & y(Py → x=y) ]
The theory of descriptions
• Updated symbolic logical notation:
• Predicates
• A, B, F ( is an apple, is a banana, is a fruit)
• Terms
• Variables: x, y, z,
• Names: a, b, c
• Atomic formulas: Ax, Ab, Bxy, Bcd
• Complex formulas:
Where φ is an atomic formula, a complex formula can be:
~ φ (φ ψ) (φ & ψ) (φ ψ) (φ ↔ ψ)
• Complex formulas involving variables:
x (Ax) [“” is an “existential quantifier”]
x (Ax) [“” is a “universal quantifier”]
• A sentence is a formula with no free variables:
Ab Bcd x Ax y (By Fy)
• Sentences involving and are intertranslatable:
x (Ax) :: ~x (~Ax) x (Ax) :: ~ x (~Ax)
The theory of descriptions
• How this relates to Russell’s older notation:
C(everything)
means
‘C(x) is always true’
(x) Cx
C(nothing)
means
‘”C(x) is false’” is always true’
(x) (~Cx)
C(something)
means
‘It is false that “C(x) is false” is always true
‘C(x) is not always false’ ~(x) (~Cx) ::
x (Cx )
15
The theory of descriptions
• Descriptions analyzed in logical notation
ex
The Prince of Wales is large-eared.
means the same as
1. There is a Prince of Wales.
x (Px)
There is an x, such that x is a Prince of Wales
2. A Prince of Wales is large-eared
x (Px) & (Lx)
There is an x, such that x is a Prince of Wales and x is large-eared.
3. One and only one Prince of Wales is large-eared.
x [(Px) & (Lx) & y(Py → x=y) ]
There is an x, such that x is a Prince of Wales, x is large-eared, and
if any other y is a Prince of Wales, then y is x.
The Theory of Descriptions
• Q: What is wrong with the following way of
representing the same description
ex
x (Px) & (Lx) & y(Py) → x=y
compared to the original:
x [(Px) & (Lx) & y(Py → x=y) ]
o the missing parentheses are an important omission:
• without the parentheses, Lx is not bound to a quantifier
• without the parentheses, x=y is not bound to any quantifiers
• without the parentheses, we don’t know if any of the x’s are
the same
o the extent of the parentheses defines the scope of the
operator, in this case the x
17
Solutions to the puzzles
• Puzzle #2: a problem about sentences with nonreferring
terms
ex
Either
(1) The present King of France is bald or
(2) The present King of France is not bald
should be true
o but neither seems to be true: why
• Russell: analyze “the present King of France is
bald”
• Q: is “the present King of France” a name
ex
Bp
x [(Kx) & (Bx) & y(Ky → x=y) ]
o no: a denoting phrase is not independently
meaningful, only contextually

Solutions to the puzzles
• Q: How would you express that (1) is false with the
same notation
ex
(1) The present King of France is bald.
x [(Kx) & (Bx) & y(Ky → x=y) ]
FALSE
There is an x such that x is a King of France, x is bald, and if any
y is a King of France, then x is y.
(2) The present King of France is not bald.
x [(Kx) & (~Bx) & y(Ky → x=y) ]
FALSE
There is an x such that x is a King of France, x is not bald, and if
any y is a King of France, then x is y.
(3) It’s not the case that the present King of France is bald.
~ x [(Kx) & (~Bx) & y(Ky → x=y) ]
TRUE!!
It’s not the case that there is an x such that x is a King of France, x is
bald, and if any y is a King of France, then x is y.
• So “Either the present King of France is bald, or the
present King of France is bald” is true
o provided that we mean “Either (1) or (3)” is true
Solutions to the puzzles
• Puzzle #3: a problem about negative existentials
ex
The present King of France does not exist.
Santa Claus does not exist.
o How can we deny the existence of anything
• Russell: analyze “The present King of France
exists”
• Q: is this the correct way to assert existence
ex
A present King of France exists.
x (Kx & Ex)
o no!: existence claims are made with the “x” operator,
not with predicates.
o existence is not a predicate
Solutions to the puzzles
• Q: Simplify: how do we analyze “a present King
of France exists”
ex
A present King of France exists
x (Kx)
The present King of France exists.
x [(Kx) & y(Ky → x=y) ]
(There is an x such that x is a King of France, and if any y is a King of
France, x is y)
• Q: So how is existence denied
ex
A present King of France does not exist.
~ x (Kx)
It’s not the case that there is an x such that x is a King of France.
~ x [(Kx) & y(Ky → x=y) ]
It’s not the case that there is an x such that x is a King of France, and
if any y is a King of France, x is y.
Solutions to the puzzles
• Q: Does this kind of denial involve any terms
that denote non-existing objects
ex
~ x (Kx)
(It’s not the case that there is an x such that x is a King of France)
~ x (Kfx )
(It’s not the case that there is an x such that x is a King of f.)
• Q: Suppose this statement is false: why does it
not involve the suspected contradiction
ex
Santa Claus exists.
x (Sx )
FALSE
“Santa Claus” is not really a name, but means an associated definite description:
The man who lives at the North Pole and who brings presents to all the
world’s good little boys and girls on Christmas exists.
x [(Mx & Nx & Pbgcx) & y(My & Ny & Pbgcy → x=y) ]
~ x [(Mx & Nx & Pbgcx) & y(My & Ny & Pbgcy → x=y) ] TRUE
Solutions to the puzzles
• Puzzle #1: a puzzle about identity
ex
Scott is the author of Waverley
(1) George IV wonders if Scott is the author of Waverley.
(2) George IV wonders if Scott is Scott.
TRUE
FALSE
o why is (1) true but (2) is false
• Russell: analyze “Scott is the author of Waverley”
o suppose “Scott” is a regular name (maybe we’re Scott)
o suppose we treat identity like a predicate
o suppose Ax = “x is an author of Waverley”
ex
Scott is the author of Waverley
x [(Ax) & y(Ay → x=y) & (x = Scott)]
Solutions to the puzzles
• So how does George IV wonder about this
o suppose we leave “George IV wonders” unanalyzed
ex
George IV wonders whether Scott is the author of Waverley
This can be translated one of two ways:
Primary occurrence of “the author of Waverley”
(1) x [(Ax) & y(Ay → x=y) & George IV wonders whether (x =
Scott)]
Secondary occurrence of “the author of Waverley”
(2) George IV wonders whether x [(Ax) & y(Ay → x=y) & (x =
Scott)]
o in neither (1) nor (2) does George IV wonder whether Scott
= Scott, but whether x = Scott.
o there is no single denoting phrase “the author of
Waverley” to equate with “Scott”