Russell, On Denoting

On Denoting

Key Question: What does "The" mean? It is Name or Quantifier Expression (QE)?

Russell's Two Arguments:

1. "The" is Quantifier Expression (QE)
2. Names should be analyzed like QEs

 

 

 

1. Traditional Picture of Language

1. Every sentence can be broken up into a SUBJECT and a PREDICATE

2. To determine the Truth-Value of a sentence you need to find

   • what does the SUBJECT picks out?
   • what property does PREDICATE picks out?

Example

Obama is tall - TRUE

• Subject = Obama
• Predicate = is tall

Obama is French - FALSE

• Subject = Obama
• Predicate = is French

Russell does not endorse this picture

• Problem

  1. Fido is happy
  2. Some dog is happy
  3. Every dog is happy
  4. No dog is happy

  Subject of [1] = "Fido"

  • it points to "Fido the dog"

  Subject of [2/3/4] = "Some / Every / No dog"

  • they do not point to specific things, many argue that these subjects point to abstract things

• Solution

  Distinguish Grammatical & Logical Forms

  Examples

  1. Alice is a Queen

  2. Some King is a Queen

  3. Every King loves some Queen

 

 

 

2. "The"

• Question

  What is "The"?

  • Name? (ex. "Alice" "Fido")
  • QE? (ex. "Some" "Every")

  Russell thinks "The" is a Quantifier Expression (QE), and there is only one $F$ (Uniqueness) when you say "The $F$ is $G$"

  Example

  • Grammatical Form

    The dog is happy

  • Logical Form

   

   

• Main Argument

  "The $F$ is $G$ but there's no $F$"

  • FALSE

  • "The King of France" does not exist

  • Comments from other Philosophers:

    • Meinong

      "the King of France" picks out something that does not exist

      Ex. The round square is weird - "round square" is a contradiction

    • Frege

      "The King of France has Sense but no Nominatum"

      Russell's Comment: Grey's Elegy

      No one knows what Russell is referring to

  • Why think that "The $F$ is $G$" is FALSE rather than Truth-Valueless?

    Russell thinks: If some part of the sentence is truth-valueless, then how could adding a predicate makes it have a truth-value?

    Example

    • Assume the son is not drowned

    $\to$ "the only child of mine" does not exist

    $\to$ the second half of the sentence is truth-valueless

    • However, the sentence is TRUE in general

    $\to$ how is it possible for the whole sentence being TRUE while its second half is truth-valueless?

    (Recall: Frege thinks that Truth-Value of a sentence contributes to that of a bigger Sentence)

 

 

 

3. Sentence Readings

Two different sentence readings

• De Dicto = "of the word"
• De Re = "of the thing"

Examples

• De Dicto Sentence

  Emphasis: "the President" $\to$ this applies to all presidents in the history of the US

• De Re Sentence

  Emphasis: "the Nominatum of the President" $\to$ the current president of the US is 79 years old indeed

Logical Forms of the two readings would be presented in the discussion of Russell's Three Puzzles

 

 

 

4. Russell's Three Puzzles

4.1 Frege's Puzzle

• Puzzle

  1. if $(a)=(b)$, then anything that is true of $(a)$ is true of $(b)$

  2. Scott is the author of Waverly

  3. George wondered whether Scott was the author of Waverley

  4. George wondered Scott was Scott

• Analysis

  According to Frege, switching a Names of the same Nominatum in a sentence should preserve its truth-value. Therefore, [4] should be TRUE

  But by the Meaning of Sentence [3] and [4]

  • [3] - TRUE
  • [4] - FALSE

  It is a substitution failure that Truth-Value of the sentence changed

• Solution

  To avoid the conclusion in [4], Russell promotes the Description Theory of Names on which "Scott" is a Unary Predicate $\textcolor{red}{S}\textcolor{blue}{y}$ (as applied to the variable $\textcolor{blue}{y}$) instead of a Logical Constant $\textcolor{green}{s}$

  As such, better logical forms of [2] and [3] are

  [2] Scott is the author of Waverly

  [3] George wondered whether Scott was the author of Waverley

  • De Dicto

    George wondered the following proposition is TRUE: There is one person that is the author of Waverley, and this person is Scott

  • De Re

    There is one person that is the author of Waverley, and George wonders if this person is Scott

 

 

4.2 Law of Excluded Middle (LEM)

• Puzzle

  According to this lemma, we have

  But if everything in the world is classified into two categories of

  Then you will find "the King of France" in neither of them

• Solution

  • De Re - Incorrect

    De Re reading is denying the "property" of the subject, hence it still assumes the existence of the subject (the King of France)

  • De Dicto - Correct

    De Dicto reading is directly denying the existence of the subject (the King of France), hence the meaning of this reading aligns with the Law of Excluded Middle

 

 

4.3 Existential Generation

• De Dicto - Correct

  1. If there is no golden mountain, then this is obviously TRUE
  2. If there are more than one golden mountain, then this is also TRUE because the Uniqueness of "The" becomes invalid

• De Re - Does not exist

  This does not exist. De Re reading usually places negation inside the Quantifier Expressions, which means it first assumes the existence of a subject and then deny its property.

  In this puzzle, it sounds very weird like this