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Friday, February 27, 2015

The Three Grices


In "Scope and Truth Value Gaps", R. B. Jones writes: "The King of France is not bald" can be translated in two different ways depending on whether the negation is considered to be in the context for elimination of the description or outside it. There are two options for representing this sentence according to Russell's theory[...]:
[(inverted iotax)(Kx)] . ~B(inverted iotax)(Kx)
~[(inverted iotax)(Kx)] . B(inverted iotax)(Kx)

where the placement of the notation "[(inverted iotax)(Kx)]" serves to identify the relevant context for the elimination of the definite description, and we can see that in the first case the negation is inside that context and in the second case it is not."

While Whiteheand and Russell focus on "the king of France is bald", there seem to be another range of definite descriptions. Whitehead and Russell were aware of the plural 'the', as in

"The Three Graces were beautifully represented by Canova."


"If some philosophers speak of the two Wittgensteins, I shall speak of the three Grices."


Quine has

"The twelve apostles were all charismatic, even if some more than others."

And then there is

"The three stooges I've always found funny -- especially Larry."


There are occurrences of 'the' which while singular, implicate plural:

"The cow is a sacred animal in India".

"The zebra is the animal that tourists most appreciate when doing a safari in Africa".

"The black-necked swan is typical of the Southern lakes."

----- This may relate to KEYWORDS: definiteness, but the point about UNIQUENESS is controversial.

For 'twelve apostles', the keyword should be: NUMERICAL QUANTIFIER.

Plurarity in general is dealt with logically by Altham et al.

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