Re: The king of france is ...

On Apr 19, 4:17 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:
Newberry <newberr...@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),

Indeed. But (3) also conveys more information than (2). Namely that
there is more than one apple in the basket.

namely that there is a single apple in my
basket and that apple is red.

Please stop regurgitating. It is not a pretty sight.

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.

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.


.

Relevant Pages

  • Re: Class Hierarchy design problems...
    ... My opinion is that your intent doesn't make sense. ... How does the fact that the apple is in a basket influence the nature of the ... Is it THAT MUCH more elegant than writing the following? ...
    (microsoft.public.dotnet.languages.csharp)
  • Re: The king of france is ...
    ... expresses either "all the apples in my basket are red" or "the apple ... they are both red the state of affairs is also expressed as. ... there is one apple in my basket and it is red then it is certainly the ... then I am conveying more information than is conveyed in ...
    (sci.logic)
  • Re: The king of france is ...
    ... in my basket are red" is true when there are no apples in the basket. ... I'm not convinced that we always interpret such sentences as having an ... implicit claim that there are more than one apple in my basket. ...   ...
    (sci.logic)
  • Re: The king of france is ...
    ... when there is only one apple in the basket. ... Are you saying that the singular of "all the apples in my basket are ... "So why are mathematicians NOT what most people suppose? ...
    (sci.logic)
  • Re: The king of france is ...
    ... nothing about the number of apples in the basket. ...   ... that there is more than one apple in the basket. ... is most implausible and I was not suggesting that we interpret the ...
    (sci.logic)