Re: The king of france is ...

On Apr 19, 1:08 pm, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
On Apr 19, 11:23 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
On Apr 19, 4:17 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
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.

This is very true.

  (7) says
something more about the situation.  Why do you suppose that (2) is
supposed to "become" (7)?

That is what Russel said.

Who said what?  Where?  

If you mean Russell's article on denoting, I don't think that he ever
claims a particular formula somehow "becomes" some other formula.

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)?

The problem is not how to express "there is one apple in my basket in
it is red." The problem is that (3) cannot be used to express (2) when
there is only apple in the basket.

You seem to have changed direction and now you're talking about
whether a certain English sentence expresses a formula or not.  Before
you were asking whether a formula expresses an English sentence or
not.  Was this intentional?

I was NEVER interested in formalizing "there is one apple in my basket
and it  is red"

That didn't answer my question, but whatever.

Anyway, if you intend to point out that plain English treats
quantification somewhat differently than formal logic, then surely we
agree.  If someone told me "All the apples in my basket are red" in a
normal conversational context, I'd be a little surprised to learn that
there was only one (or no) apples in the basket.  But so what?  What
consequence do you want to draw from this observation?

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?


 Not me.  After all, (5) expresses
something like "There is no more than one apple in my basket and it is
red."

then (4) cannot at the same time mean

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

Got it?

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)

?
.