Dear Doug, (01)
What an interesting interpretation! The "we"
doesn't designate the same set of agreers (the
"all") and therefore the statement could be
interpreted on the basis of two groups, one that
"can agree" and one that "agrees". (02)
It seems the entire difference between the
interpretation you proposed below and
interpretation Chris and I were first using (that
the "we" and the "all" codesignate the same
group). (03)
As always, language is a slippery wrapping for
ideas. There is nothing in Paul's statement that
indicates the two groups are identical, nor that
they are separate, so both interpretations fit the
statemnt. (04)
Thanks,
-Rich (05)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (06)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On
Behalf Of doug foxvog
Sent: Monday, June 18, 2012 12:41 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Social interaction
and teamwork (07)
> On Jun 16, 2012, at 1:36 AM, Rich Cooper wrote: (08)
>>> But we can all agree there are no statements
>>> agreed by everyone, right? (09)
>> If we all did agree to a statement, then that
>> agreement would have been agreed by everyone, (010)
Not at all. I interpret the "we" to mean the
ontolog-forum participants,
and "everyone" to be a far greater set of people
(which includes the
ontolog-forum participants. Since the set of
agreers is different from
the set of disagreers the statement can be true,
even if the predicates
(verbs) were the same (e.g., "agree"). With the
predicates different
(i.e., "agree" vs. "can agree") it is also
possible for the statement to be
true or false even if the subjects were the same
for the inner and outer
clause. (011)
I do not think that any of us is omnipotent, thus
i suggest that it is quite
possible that each of us *can* agree to something
that is false. (012)
The original statement can be logically encoded
as: (013)
(forAll ?ONEofUS (memberOf ?ONEofUS We)
(canAgree ?ONEofUS
(not (thereExists ?STATEMENT)
(forAll ?PERSON (memberOf ?PERSON
Everyone)
(agrees ?PERSON
?STATEMENT))))) (014)
I would suggest that this statement is true. *We*
all *can*
agree that there is no statement that *every
person* does
agree with. This does not imply that we all *do*
so agree. (015)
Simultaneously, the statement that *we* all *can*
agree that
there is a statement that *every person* does
agree with
*could* also be true, although i doubt that it
currently is. (016)
-- doug foxvog (017)
>> thus contradicting the many subjective models
we each
>
>> had previously mentally formed in reaching said
>
>> agreement simultaneously.
>
>
>
> Paul's statement has nothing whatever to do with
> subjective mental models so they don't play any
> role in determining its truth or falsity.
>
>
>
>> So then none of us
>
>> would agree to the first such, statement. The
>
>> elegance of that thought is magnificent.
>
>
>
> Well, there's two thoughts here. There's what
Paul
> wrote. And then there's what you wrote. Either
> way, you seem to have set a very low bar for
> magnificence.
>
>
>
>> Great paradox, Paul, and great wit!
>
>
>
> Actually, it's not a paradox, it is simply a
> logical falsehood, a contradiction, like
"Socrates
> is a philosopher and there are no philosophers".
> Let's call Paul's statement S and rewrite it
> without the modal "can":
>
>
>
> S: Everyone agrees that there are no statements
> agreed upon by everyone.
>
>
>
> It is clear that S cannot be true. For if it is,
> then everyone agrees upon the statement "There
are
> no statements agreed upon by everyone" and,
hence,
> there is a statement that everyone agrees upon,
in
> which case S is false. So S implies it's own
> falsity and, hence, is (logically) false.
>
>
>
> However, unlike the case with a genuine paradox
> (like the Liar, "This statement is false"), from
> the assumption that S is false, it does not
follow
> that it is true. For if S is false, then someone
> (call such a person A) doesn't agree that there
> are no statements agreed upon by everyone. That
> could happen either because A has simply never
> considered the matter, or because A has
considered
> it and believes instead that there are in fact
> statements that everyone agrees upon. But there
> is nothing logically problematic about either of
> those scenarios.
>
>
>
> So again, not a paradox, just a (moderately
> clever) logical falsehood.
>
>
>
> -chris (018)
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