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Re: [ontolog-forum] Social interaction and teamwork

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <chris.menzel@xxxxxxxxx>
Date: Sat, 16 Jun 2012 22:45:09 +0200
Message-id: <6271D2EB-BB33-4E94-8075-11D3A1022352@xxxxxxxxx>
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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