On Denoting

BERTRAND RUSSELL

- A proponent of analytic philosophy

- He had Ludwig Wittgenstein as his protégé

- Main goal was to reduce mathematics to logic

- His intentions and aspirations, as regards the creation and development of his theory of description, is still a topic of endless scholastic and historic discussions.

- Before his theory of description, logic was never really the criterion of meaning.

BRIEF HISTORY ON BERTRAND RUSSELL & HIS THEORY OF

DESCRIPTION

BRIEF HISTORY ON BERTRAND RUSSELL & HIS THEORY OF

DESCRIPTION

- A proponent of analytic philosophy

- He had Ludwig Wittgenstein as his protégé

- Main goal was to reduce mathematics to logic

- His intentions and aspirations, as regards the creation and development of his theory of description, is still a topic of endless scholastic and historic discussions.

- Before his theory of description, logic was never really the criterion of meaning.

- Presents the theory- Gives his criticism- Tests the strength of the theory- Explores the implications of his theory

PROCEDURE

IMPORTANCE OF HIS THEORY

Direct implications to logic, math, and epistimology.

The distinction between…

Aquaintance - Knowledge about

“The distinction between acquaintance and knowledge about is the distinction between the things we have presentations of, and the things we only reach by means of denoting phrases.”

3 KINDS OF DENOTING PHRASES

A. “The present prime minister of the Republic of the Philippines.”Non-referential denoting phrase

B. “The present drummer of Dreamtheater.”

Specific Referent

C. “A man.”

Ambiguous

THEORY

BR’s formulation of a proposition: C(x)“Nix is handsome.”

True proposition

He applies it to the most fundamental of denoting phrases e.g. everything, nothing and something.

E C(x) is always true.

N “C(x) is false” is always true.

S It is false that “C(x) is false” is always true

- Double negation

This becomes very important in his solution to non-referential phrases, and the distinction between primary and secondary occurrences.

“All humans are mammals.”

“THE NOTION OF THE VARIABLE IS FUNDAMENTAL.”

If we look at the logical form of a denoting phrase, it would seem that they have no meaning per se.

“…every proposition in whose verbal expression they occur has meaning.”

Denoting phrases really have no meaning in themselves, whether or not it has a referent because it only affects the truth value.

Meaning - Truth Value

“Moriarty is the Napoleon of crime.”

There being no referent for “Moriarty”, it does not make the proposition nonsensical/meaningless because it is plainly false.

This proves to be a very advantageous view.

A. “I met a man.”Ambiguous DP

“ ‘I met x, and x is human’ is not always false.”

“ ‘C(x) and x is human’ is not always false.”

B. “All men are mortal.”“ ‘If x is human, x is mortal’ is always true.”

“ ‘If x is human’ implies ‘x is mortal’ for all values of x.”

“C (all men)” means “ ‘If x is human, then C (x) is true’ is always true”.

“C (no men)” means “ ‘If x is human, then C (x) is false’ is always true”.

“C (a man)” means “It is false that ‘C (x) and x is human’ is always false”.

If we substitute “x is human” for “x is a man”

PUZZLES AND CRITICISM

A. “The” phrases Uniqueness

If so-and-so had a plurality of sons:“The father of Charles II. was executed.”

Singularity

“It is not always false of x that x begat Charles II., and that x was executed, and that ‘If y begat Charles II., y is identical with x’ is always true of y.”“ x begat Charles II” - Father

“if y begat Charles II., y is identical with x” - Uniqueness

“x begat Charles II., and ‘if y begat Charles II., y is identical with x’ is always true of y.”

The son of so-and-so

A son of so-and-so

“Charles II. had one father and no more.”

If this condition fails, all propositions in the form C(the father of Charles II) are all false.

Russell’s suggestion:

“There is one and only one entity that begat Charles II., and that one was executed.”

“The pope called me on my phone.”

B. Non-referential phrases

Meinong Gramatically correct denoting phrases stand for object.

“These do not subsist, but are still objects.”

An infringement of the law of non-contradiction.

FREGE

“The king of France is bald” should be nonsensical since it has no referent.

It is not because it is plainly false.

Frege seems to answer this problem by saying that the “The king of France” denotes the null class.

It doesn’t really necessarily answer the question completely!

Another infringement of the law of contradiction.

It refers to the null class.

It actually has no referent.

Puzzles

A. Scott = Scott? - Identity

B. Excluded middle - “A is B” or “A is not B”

C. Difference - “The difference between A and B does not subsist.

Frege’s theory suffers mostly when both sense and reference are present!

C “C”

“Meaning of C”

“ Meaning of ‘C’ ”

Meaning of C = “C”

“…if we speak of “the meaning of C,” that gives us the meaning if any, of the denotation. “The meaning of the first line of Gray’s Elegy” is the same as “The meaning of the ‘The curfew tolls the knell of parting day,’ “ and is not the same as “The meaning of ‘the first line of Gray’s Elegy’ “. Thus in order to get the meaning we want, we must speak not of “the meaning of C, “ but of “the meaning of “C,’ “ which is the same as “C” by itself. Similarly “the denotation of C” does not mean the detonation we want, but means something which, if it denotes at all, denotes what is denoted by the detonation we want.

“According to the view which I advocate, a denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account. If I say “Scott was a man,” that is a statement of the form “x was a man,” and it has “Scott” for its subject. But if I say “the author of Waverly was a man,’ that is not a statement of the form “x was a man,” and does not have “the author of Waverly” for its subject.”

IMPLICATIONS

Non-complex phrases

“The author of Waverly” > C(x)

“Scott was a man”

“One and only one entity wrote Waverly, and that one was a man.”

Primary and Secondary occurence

C(x)

SUMMARY

- Where does meaning reside?

- Author of Waverly ≠ Scott

We can reduce it to logical terms where “Scott” cannot be replaced with “Author of Waverly.”

- Denoting phrases have both truth value and meaning; the two being mutually exclusive.