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, thus
> contradicting the many subjective models we each
> had previously mentally formed in reaching said
> agreement simultaneously. (01)
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. (02)
> So then none of us
> would agree to the first such, statement. The
> elegance of that thought is magnificent. (03)
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. (04)
> Great paradox, Paul, and great wit! (05)
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": (06)
S: Everyone agrees that there are no statements agreed upon by everyone. (07)
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. (08)
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. (09)
So again, not a paradox, just a (moderately clever) logical falsehood. (010)
-chris (011)
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