On Denoting

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On Denoting

• Bertrand Russell

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Weve got some serious problems
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A Puzzle About Identity

• Indiscernibility of Identicals If a b then
  whatever is true of one is true of the other.
• If a is identical with b, whatever is true of
  the one is true of the other, and either may be
  substituted for the other in any proposition
  without altering the truth or falsehood of that
  proposition. Now George IV wished to know whether
  Scott was the author of Waverly, and in fact
  Scott was the author of Waverly. Hence we may
  substitute Scott for the author of Waverly and
  thereby prove that George IV wished to know
  whether Scott was Scott.
• Problem contexts in which substitutivity salve
  veritate fails, e.g.
• George IV wondered whether ___ wrote Waverly.
• Necessarily ___ is odd.

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A Puzzle About Excluded Middle

• The Law of Excluded Middle For any proposition,
  P, either P or not-P
• By the Law of Excluded Middle, either A is B
  or A is not B must be true. Hence either the
  present King of France is bald or the present
  King of France is not bald must be true. Yet if
  we enumerated the things that are bald and then
  the things that are not bald, we should not find
  the present King of France in either list.
• Problem When the subject term of a sentence
  fails to refer, excluded middle fails, e.g.
• The present King of France is bald.
• George W. Bushs son is a plumber

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A Puzzle About Negative Existentials

• A proposition cannot be about a non-entity to be
  either true or false the subject term of a
  singular statement must refer to something.
• Consider the proposition A differs from B. If
  this is true, there is a difference between A and
  B, which fact may be expressed in the formthe
  difference between A and B subsists. But if it
  is false that A differs from B, then there is no
  difference between A and B, which fact may be may
  be expressed in the form, the difference between
  A and B does not subsist. But how can a
  non-entity be the subject of a proposition?...If
  A and B do not differ, to suppose either that
  there is, or that there is not, such an object as
  the difference between A and B seems equally
  impossible.
• Problem Negative existentials, sentences of the
  form x doesnt exist seem to commit us to the
  existence of x and then say of it that it doesnt
  existwhich is a contradiction.
• Santa Claus doesnt exist
• Unicorns dont exist

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The Source of Our Problems

• We are mislead by language!
• Surface grammar obscures the true logical form
  of propositions
• Our failure to recognize the true logical form
  beneath the surface is responsible for the
  puzzles
• Subject-predicate form of some sentences is
  misleading
• Russell proposes an account of the true logical
  form of propositions that provides solutions to
  the puzzles
• He criticizes alternative approaches of Meinong
  and Frege
• And shows how his account deals with the puzzles

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An Ideal Language

• Disagreement about what philosophy is supposed to
  be doing
• Analyzing ordinary language or
• Translating into an ideal language that reveals
  true logical form
• Russell proposes translating ordinary language
  into an ideal language that will avoid puzzles
  and paradoxes.
• The language that reveals logical form and so
  allows us to explain validity and to provide
  solutions without getting into crazy metaphysics
  is . . .
• PREDICATE LOGIC WITH IDENTITY!

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Predicate Logic Vocabulary

• Connectives ? , ? , , ? , and ?
• Individual Constants lower case letters of the
  alphabet (a, b, c,, u, v, w)
• Predicates upper case letters (A, B, C,, X, Y,
  Z)
• Variables x, y and z
• Quantifiers
• Existential (? variable), e.g. (?x), (?y)
• Universal (variable), e.g. (x), (y)
• Identity (a special predicate)

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Basic Predicate Logic Translation

• Singular propositions
• Russell was a philosopher.Pr
• Russell was Moores friend.Frm
• Russell authored Principia Mathematica with
  Whitehead.Arwp
• General propositions
• Everything is material(x)Mx
• There is a God.(?x)Gx

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Identity

• Identity is an equivalence relation
• Reflexive everything is identical to itselfx
  x
• Symmetric if one thing is identical to another
  the other is identical to the firstIf x y
  then y x
• Transitive if one things identical to a second
  and the seconds identical to a third then the
  first is identical to the thirdIf x y and y
  z, then x z
• Identity is an indiscernibility relation
• Indiscernibility of Identicals if x y then
  whatever is true of x is true of y and vice
  versa.

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Ordinary language is deceptive!

• According to Russell, what appear to be simple
  singular statements are often really more
  complicated existentially quantified statements.
• I met a man
• Mm (wrong! a man is not the name of an
  individual!)
• (?x)Mx (correct translation)
• Even ordinary language statements that include
  ordinary proper names are deceptive ordinary
  proper names are really disguised descriptions
• Apollo lives on Mount Olympus
• (?x)(x is sun god and x is Letos son and
  Artemis twin brother andand x lives on Mount
  Olympus
• Puzzles arise because we think statements that
  involve denoting expressions are singular
  statements when they are really existential and
  generaland involve quantifiers and complicated
  logical machinery!

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Denoting

• The subject of denoting is of very great
  importance, not only in logic and mathematics,
  but also in the theory of knowledge.
• No general characterization of denoting is given,
  only a list of denoting phrases.
• A man
• Some man
• Any man
• Every man
• All men
• The present King of England
• A phrase is denoting solely in virtue of its
  form.

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Denoting Phrases and Denotation

• Russell considers three cases
• Denoting phrases that do not denote anything,
  e.g. the present King of France in 1905
• Denoting phrases that denote one definite object,
  e.g. the present King of England in 1905
• Denoting phrases that denote ambiguously, e.g. a
  man
• We want an account that will accommodate all
  three kinds of cases without paradox
• And explain how we can think and talk about many
  things with which we are not acquainted but
  only know by description.

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Paraphrasing Away Denoting Phrases

• I use C(x) to mean a proposition in which x is
  a constituent, where x, the variable, is
  essentially and wholly undetermined.
• We paraphrase away everything, nothing, and
  something as follows
• C(everything) means C(x) is always true (x)Cx
• Everything is material for all x, x is material
• C(nothing) means C(x) is is false is always
  true (x) ? Cx
• Nothing is free for all x, it is not the case
  that x is free
• C(something) means It is false that C(x) is
  false is always true ? (x) ? C(x) i.e. (?x)Cx
• Something smells there exists an x such that x
  smells.

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More Translations

• I met a man
• I met x and x is human is not always false
  (?x)(Mx ? Hx)
• All men are mortal
• If x is human then x is mortal is always true
  (x)(Hx ? Mx)
• No men are perfect
• If x is human then x is perfect is false is
  always true (x)(Hx ? ? Px)
• Some men are philosophers
• x is human and x is a philosopher is not always
  false (?x)(Hx ? Px)

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Definite Descriptions

• The denoting phrase in the sentence The father
  of Charles II was executed involves
• Existence x was father of Charles II, for some
  value of x.
• Uniqueness if y was father of Charles II, then y
  is identical with x, for any value of x who was
  father of Charles II and any value of y.
• To convey the uniqueness condition we need to
  introduce an additional special predicate, viz
  IDENTITY to produce the following translation
• There exists an x such that x is the father of
  Charles II
• For all y, if y is the father of Charles II then
  x y
• x was executed

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Denoting Phrases All Gone!

• We have now paraphrased away all denoting phrases
• A man
• Some man
• Any man
• Every man
• All men
• The present King of England
• Weve gotten rid of them in favor of logical
  machinery--and this will enable us to solve all
  three puzzles

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The Identity Puzzle

• Indiscernibility of Identiticals
  (substitutivity) If a is identical with beither
  may be substituted for the otherwithout altering
  the truth or falsity of the proposition
• Apparent Counterexample George IV wished to know
  whether Scott was the author of Waverly
• Scott the author of Waverly
• By substitutivity principle, George IV wished to
  know whether Scott was Scott
• But George IV did not wish to know whether Scott
  was Scott (he knew that!)
• So, contrary to the principle we have a case
  where substituting a different name for the same
  objects makes a true proposition falsewhich is
  unacceptable!

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Substitutivity Failures

• There are some contexts in which it looks like we
  cannot freely substitute identicals for
  identicals
• These include intentional contexts which occur in
  sentences that ascribe certain mental states,
  e.g.
• The Minoans didnt believe that the Morning Star
  was identical to the Evening Star.
• George IV wondered whether Scott was the author
  of Waverly.
• The Problem everyone knows that everything is
  identical with itself BUT
• The Minoans believed that the Morning Star was
  identical to the Morning Star, but not that the
  Morning Star was identical to the Evening Star.
• George IV didnt wonder whether Scott was
  identical to Scott but did wonder whether Scott
  was identical to the author of Waverly.

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Freges Puzzle

• How can true identity statements be informative?
• The Morning Star The Evening Star
• What makes this true is the fact that The
  Morning Star and The Evening Star refer to the
  same object, viz. the planet Venus so it looks
  like the identity statement just says that Venus,
  like everything else, is identical to itself!
• But everyone knows that everything is identical
  to itself so what do we know that the Minoans
  didnt know? And what did George IV wonder about?
  Surely not whether Scott was identical to
  himself!
• Russell discusses Freges way of dealing with
  this and related issues (pp 4 5) by
  distinguishing the meaning and denotation of
  denoting expressions well deal with this when
  we get to Fregenot now.

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Scope Ambiguity

• Guest I thought your yacht was larger than it
  is.
• Touchy Yacht Owner No, my yacht is not larger
  than it is.
• 1 The size I thought your yacht was is greater
  than the size your yacht is.
• Theres a certain size, x, and I thought that x
  was the size of your yacht but x is greater than
  the size of your yacht.
• 2 I thought the size of your yacht was greater
  than the size of your yacht.
• I thought that theres a certain size, x which is
  the size of your yacht but x is greater than the
  size of your yacht.
• In 1 the Guest does not believe that the size of
  the Owners yacht is greater than it is.
  Likewise, in the correct reading George IV
  wondered, George IV does not wonder whether
  Scott is Scott.

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Russells Solution

• George IV wished to know whether Scott was the
  author of Waverly
• 1 George IV wished to know whether one and only
  one man wrote Waverly and Scott was that man
• Secondary occurrence of the author of
  WaverlyGeorge IV wished to know whether
  (?x)Axw ? (y)(Ayw ? yx) ? xs
• 2 One and only one man wrote Waverly and George
  IV wished to know whether Scott was that man
• Primary occurrence of the author of
  Waverly(?x)Axw ? (y)(Ayw ? yx) ? George IV
  wished to know whether xs
• 1, not 2, is the correct interpretation of the
  original sentence. What George IV didnt know but
  wanted to know, was whether the proposition
  (?x)Axw ? (y)(Ayw ? yx) ? xs was true, and
  that is not the same proposition as ss which is
  the result of substituting s for x in 2.

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The Excluded Middle Puzzle

• Excluded Middle P or not P
• Consider the sentence P The present king of
  France is bald.
• P cant be true since there is no present king of
  France.
• Since its not true it must be false
• Therefore we conclude that the present King of
  France is not bald, i.e. not P
• But thats also false since there is no present
  king of France
• But this seems to violate Excluded Middle since
  we deny both P and not P

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Russells Solution

• Its false that the present King of France is
  bald is ambiguous.
• 1 There is an entity which is now king of France
  and is not bald.(?x)(Kx Bx)
• 2 It is false that there is an entity which is
  now king of France and is bald. (?x)(Kx Bx)
• Theres a scope ambiguity concerning negation!
• 1is false there is no x who is King of France
  and is either bald or non-bald.
• 2 is true.

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The Negative Existentials Puzzle

• Negative Existential A claim to the effect that
  something doesnt exist, e.g.
• Santa Claus doesnt exist
• There are no unicorns.
• Problem the following argument
• 1 If an individual denies the existence of
  something, then he refers to what he says does
  not exist.
• 2 Things which do not exist cannot be referred to
  or mentioned no statement can be about them.
• 3 Therefore, if an individual denies the
  existence of something, then what he says does
  not exist exists.

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The Paradox of Non-Being
Parmenides posed the Paradox of Non-Being
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Whats the problem???

• (F) If Ferdinand is not drowned, then Ferdinand
  is my only son (p. 3)
• Intuitively names dont have sense
  (dictionary-meaning) one cannot give a
  definition of, e.g. Ferdinand.
• So we may say that the meaning of a name is the
  object to it denotes, e.g. Ferdinand means that
  guy
• Therefore, if there is no object a name
  denotes,the name is meaningless
• And so is any sentence in which it occurs.
• If Ferdinand is drowned, i.e. there is no
  objectFerdinand denotes
• The sentence (F) is meaningless!

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Whats the solution???

• (F) If Ferdinand is not drowned, then Ferdinand
  is my only son (p. 3)
• But (F) is not meaningless, so we have a choice
• Meinongs Solution in addition to objects that
  exist, there are also possible objects that
  subsist and even impossible objects that dont
  either subsist or exist.
• Russells Solution Ferdinand is not really a
  name.
• Ferdinand is my only son is not really a
  singular, subject-predicate proposition
• Neither is The king of France is bald
  orUnicorns have one horn.
• So lets compare these two solutions

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Meinongs Bloated Ontology
Real things (things that actually exist)
Possibilia (dont actually exist but could they
subsist)
Impossibilia (dont exist, cant exist and dont
even subsist)
Round Squares
Married Bachelors
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Meinongs Solution

• It avoids the flat-out contradiction of having to
  say that some things that exist dont exist
• Zeus subsists so in saying that Zeus doesnt
  exist, were not saying that something that
  exists doesnt exist.
• But talk about impossible objects, e.g. round
  squares, lands us in contradictions.
• And we cant/shouldnt arbitrarily analyze talk
  about impossible objects differently from talk
  about things that exist or subsist.
• Furthermore, introducing impossible and merely
  possiblethings multiplies objects unnecessarily.

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Russells Solution

• We must abandon the view that denotation is
  what is concerned in propositions which contain
  denoting phrases.
• We have to deal with three kinds of cases,
  examplified by
• Unicorns dont exist.
• The Fountain of Youth doesnt exist.
• Apollo doesnt exist
• Note in 1 the surface-grammatical subject is a
  general term, in 2 its a definite description,
  and in 3 its a name

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Solution to Case 1

• Unicorns dont exist.
• It is not the case that there exists an x such
  that x is a Unicorn? (?x)(Ux)
• __is a unicorn is is a predicate
• We say theres nothing of which that predicate
  is true,
• i.e. it is not the case that something has the
  property of being a unicorn

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Solution to Case 2

• The Fountain of Youth doesnt exist.
• It is not the case that there is one and only
  one x thatsthe Fountain of Youth? (?x)Fx ?
  (y)(Fy ? y x)
• We note that the Fountain of Youth is a
  definite description and treat it accordingly.
• We say in effect Its false that theres a
  unique thing thats a fountain of youth.

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Solution to Case 3

• Apollo doesnt exist
• It is not the case that there is one and only
  one x which is C? (?x)Cx ? (y)(Cy ? yx)
• C is what the classical dictionary tells us is
  meant by Apollo--a description.
• Ordinary names are disguised descriptions!
• So Asw isnt strictly speaking (according to
  Russells metaphysical account) the correct
  translation of Scott was the author of Waverly
  since neither Scott nor Waverly are strictly
  speaking names.
• But well pretend it is to avoid getting into
  some heavy metaphysics.

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Genuine proper names

• Russell distinguishes knowledge by acquaintance
  and knowledge by description.
• Genuine proper names are names of things with
  which we are directly acquainted--our current
  sense data.
• Genuine proper names are simply tags.
• Ordinary names and definite descriptions attach
  to objects insofar as the objects have the
  characteristics that satisfy the descriptions.
  Theyre disguised descriptions

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Russells Theory of Descriptions

• On Denoting was (and by many is) viewed as the
  paradigm of analytic philosophy and one of the
  greatest pieces of philosophical writing of the
  20th century!
• It provides the standard analysis of definite
  descriptions.
• It stood unchallenged for over half a century.
• And then there was Strawson