Re: The king of france is ...

Newberry <newberryxy@xxxxxxxxx> writes:

We note that the expression

(x)(Fx -> Gx) (1)

is neutral with respect to the grammatical number. Even if the set {x:
Fx} has only one element, (1) still applies. So

(x)(Bx -> Rx) (2)

expresses either "all the apples in my basket are red" or "the apple
in my basket is red." One would certainly agree that if there are
three apples in my basket and they are all red then the state of
affairs is expressed as (2). If there are two apples in my basket and
they are both red the state of affairs is also expressed as (2). If
there is one apple in my basket and it is red then it is certainly the
case that (2). The singular of

"All the apples in my basket are red" (3)

is

"The apple in my basket is red" (4)

Therefore (2) expresses both (3) and (4).

No, we don't agree that (2) expresses (4). If I utter the English
sentence (4), then I am conveying more information than is conveyed in
the formal sentence (2), namely that there is a single apple in my
basket and that apple is red.

One could object however that since and English sentence must carry
the information about the cardinality of the subject class, neither
(3) nor (4) are equivalent to (2). In that case we would have to
express (2) as

"The apple in my basket is red or all the apples in my basket are
red."

(4) would be expressed as

(x)[Bx -> (Rx & (y)(By -> y=x)] (5)

and (3) would be expressed as

(x)[Bx -> (Rx & ~(y)(By -> y=x)] (6)

However it is not clear how (2) could possibly become

(Ex)[Bx & Rx & (y)(By -> y=x)] (7)

It is not clear what the hell you mean when you say "(2) could become"
some other sentence. The sentence (2) says that every apple in my
basket is red. It does not convey any information about how many
apples there are. There could be zero, one, or 23. (7) says
something more about the situation. Why do you suppose that (2) is
supposed to "become" (7)?

Anyway, another way to express "there is one apple in my basket and it
is red" is:

(x)(Bx -> Rx) & (Ex)(Bx & (Ay)(By -> x=y)). (8)

Is it clear how (2) could "become" (8)?

--
Jesse F. Hughes

"You see 300 of something, anything, and you go `[Man], that's a lot of
stuff.'" -- Jim Bigler, quoted in the Pittsburgh Post-Gazette.
.

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