I thought that we had stopped doing this. (01)
On 18/06/2012 3:41 PM, doug foxvog wrote:
>> On Jun 16, 2012, at 1:36 AM, Rich Cooper wrote:
>>>> But we can all agree there are no statements
>>>> agreed by everyone, right?
>>> If we all did agree to a statement, then that
>>> agreement would have been agreed by everyone,
> 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
> 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.
> The original statement can be logically encoded as:
> (forAll ?ONEofUS (memberOf ?ONEofUS We)
> (canAgree ?ONEofUS
> (not (thereExists ?STATEMENT)
> (forAll ?PERSON (memberOf ?PERSON Everyone)
> (agrees ?PERSON ?STATEMENT)))))
> 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.
> 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.
> -- doug foxvog
>>> 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
>>> 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.
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