Frege, Russell

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Frege, Russell
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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.

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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.

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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))

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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.

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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)

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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)

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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.

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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.

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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.

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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

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• 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.

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• 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

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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.

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• 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.

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• (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.

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• 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))

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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.)

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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.

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• 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.

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• 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.

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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?)

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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.

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• 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

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• 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.

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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.

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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.

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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).

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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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.

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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?

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• 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

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• 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.