Re: The king of france is ...

On Apr 19, 5:58 pm, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
On Apr 19, 1:08 pm, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
If you express

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

as

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

But *who* has suggested doing this?

Who suggested it is not relevant for the problem before us, and the
problem is how to express

    (x)(Bx -> Rx)        (2)

when there is only one apple in the basket. Got it?

Er, *I* suggest it isn't relevant, since it (5) is true even if there
are zero apples in the basket.  

NOTE: Perhaps you would consider (5) to be neither true nor false if
there are no apples in the basket, but it makes no difference.  If
there are no apples in the basket, then (4) is false and so (5) does
not express the same thought as (4).

You're the only one who ever suggested that (5) could represent (4).
Sorry if you thought I agreed, but I do not.

Are you saying that the singular of "all the apples in my basket are
red" =  (x)[Bx -> (Rx & ~(y)(By -> y=x)] is not

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

but

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

?

I don't know what you mean by "the singular" of a sentence,

You should purchase a textbook of English grammar then. "All the
apples in my basket are red" is in plural. "The apple in my basket is
red" is in singular.

but I am
saying that "There is one apple in my basket and it is red" is
expressed by (7) and not (5).  

Sometimes, you really do surprise me.  I really think that you
understand classical logic well enough to be able to do such simple
translations, but the past week or so you seem utterly bumfuzzled.

For that matter, I would not agree that "all the apples in my basket
are red" is properly translated by (x)[Bx -> (Rx & ~(y)(By -> y=x)].
That formula expresses:

  "Every apple in my basket is red and there is not exactly one apple
  in my basket."

I.e., that every apple in the basket is red and there are either zero
apples in the basket or more than one apple in the basket.

Any suggestion for a better translation of "all the apples in my
basket are red"?

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

perhaps?
.