> On Jun 16, 2012, at 1:36 AM, Rich Cooper wrote: (01)
>>> But we can all agree there are no statements
>>> agreed by everyone, right? (02)
>> If we all did agree to a statement, then that
>> agreement would have been agreed by everyone, (03)
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. (04)
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. (05)
The original statement can be logically encoded as: (06)
(forAll ?ONEofUS (memberOf ?ONEofUS We)
(canAgree ?ONEofUS
(not (thereExists ?STATEMENT)
(forAll ?PERSON (memberOf ?PERSON Everyone)
(agrees ?PERSON ?STATEMENT))))) (07)
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. (08)
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. (09)
-- doug foxvog (010)
>> 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 (011)
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