Kripke, Naming and Necessity

Naming and Necessity

Criticize Russell's Description Theory of Names
Criticize Traditional Thesis on Types of Knowledge & Modality

Informally,

1. Concepts

Modality
- Necessary Truth: Truth that couldn’t have been otherwise
  - No bachelor is married
  - 50 is an even number
- Contingent Truth: Truth that could have been otherwise
  - Some bachelors have brown hair
  - There are 50 states in the USA

Possible Worlds: Possible ways that the whole world could have been
Modal Arguments

Modals are, in a sense, statements about possible worlds
Modal Operators

2. Against Description Theory of Names

Russell's Description Theory of Names: Names are Definite Descriptions in disguise

Kripke, in Naming and Necessity, criticized Russell’s theory

2.1 CRITICISM 1: Names & Modals

Names and Definite Descriptions operate differently under modals

Russell's theory predicts following sentences to be equivalent

But actually they are not
Example 1 Aristotle is the Tutor of Alexander
- "It is possible that Aristotle died in infancy" - TRUE
- "It is possible that the Tutor of Alexander died in infancy" - FALSE
It is impossible for an infant to tutor Alexander
Example 2

St. Anne is the Mother of Mary
- "It is possible that St. Anne died in infancy" - TRUE
- "It is possible that the Mother of Mary died in infancy" - FALSE
It is impossible for an infant to be the mother of Mary
According to Kripke, Names are Rigid Designators (like tags)

Rigid Designators: Denotes the same thing across possible worlds

Names are, but Definite Descriptions are not!
Example

"The president could have been a woman"
- De Dicto - TRUE
Modal Operator $\Diamond$ is OUTSIDE the Quantifier Expression $\exist x$ , "The President" here is a Definite Description

It is possible that the president is a woman
- De Re - FALSE
Modal Operator $\Diamond$ is INSIDE the Quantifier Expression $\exist x$ , "The President" here is "Trump", which is a Name

It is impossible that Trump is a woman

2.2 CRITICISM 2: Incomplete Descriptions

Russell's theory predicts that we cannot use incomplete descriptions to talk about things or individuals

But actually we can

Example

Who is Richard Feynman?

A physicist

"A physicist" or "A Roman orator" is NOT definite description, it doesn’t pick out anyone uniquely since there are so many Roman orators or physicists

Yet, since I know that Feynman is a physicist, even I don’t know anything more about him, I still can say something like "Feynman is in the physics building" to talk about him

2.3 CRITICISM 3: Incorrect Descriptions

Russell's theory predicts that we cannot use incorrect descriptions to talk about things or individuals

But actually we can

Example

Who is Christopher Columbus?

The first European to visit the Americas

In fact, the first European to visit the Americas is Leif Erikson, not Columbus

Yet, we still seem to be talking about Columbus when we say things like "Columbus was the first European to visit the Americas"

2.4 The Historical Chain Picture of Reference

Initial Baptism: An initial naming event, in which a name is bestowed upon on an object or person, either through acquaintance or definite descriptions)
Chain of Reference: People use this name in conversations with others, and grant them the ability to use the name to reference the object or person in the Initial Baptism

Counterexample

Way back, there was a man in Turkey named Nicholas who was extremely generous and helped a family out of poverty from the kindness of his heart. Word got out about the man, and he was soon bestowed sainthood: becoming Saint Nicholas.

Overtime, stories about Saint Nicholas grew more and more fantastical, and the name "Saint Nicholas" gradually transformed in pronunciation to become "Santa Claus".

When children today, however, talk about "Santa Claus", like "Santa Claus lives in the north pole", they are clearly NOT talking about Nicholas from Turkey.

3. Against Traditional Thesis on Types of Knowledge & Modality

Types of Knowledge
- A Priori: Acquired with no appeal to Experience
  
  Example
  
  "50 is even" or "no bachelor is married" is A Priori Truth
- A Posteriori: Acquired by appealing to Experience
Traditional Thesis on Types of Knowledge & Modality
Kripke's Idea
- Contingent A Priori
  Example 1
  
  "I exist"
  - Why Contingent?
    
    There is a possible world in which "I" was not born
  - Why A Priori?
    
    "I" do not need any experience to recognize self-existence
  Example 2
  1. "If water exists and has a boiling point, it boils at $100\degree C$ "
  2. "Stick $S$ is $1\text{m}$ long at $t_0$ "
  3. "If some planet is causing those perturbations (of Uranus' orbit), it is Neptune"
    - Why Contingent?
      
      There is a possible world in which the thing that is actually causing the perturbations (which we call "Neptune") doesn’t cause the perturbations
    - Why A Priori?
      
      NOTE: Neptune is not visible to the unaided eye and is the only planet in the Solar System that was not initially observed by direct empirical observation
      
      We know there is perturbations on Uranus' orbit, but we did not see the source of those perturbations
      
      We have named whatever planet is causing the perturbations (if there is one) "Neptune"
- Necessary A Posteriori
  
  Typical Case: Necessity of Identity
  
  where $x, y$ are Names (Rigid Designators)
  Examples
  1. "Water is $H_2O$ "
  2. "Hesperus is Phosphorus"
    - Why Necessary?
      
      There are two names co-designated to the same object
    - Why A Posteriori?
      
      We had to learn that they refer to the same thing through empirical investigation
  3. "Gold has atomic number 79"
    
    NOTE: This is not an identity statement like [1] or [2]
    - Why Necessary?
      
      Gold is defined as the element with 79 protons, which means "atomic number 79"
    - Why A Posteriori?
      
      We had to learn that Gold has 79 protons through empirical investigation