Dear Chris,
While I see your point when viewed solely from the
perspective of logic, I find much more subtlety in the statement than you did,
apparently.
From Google: define can
1.Be able to: "they can run fast"; "he
can't afford it".
Removing the "can" modal, as you suggested,
does indeed ruin the magnificent elegance of a plurality of agents who CAN
agree, even if they find it less than logically consistent, that there are no
statements on which they do agree.
By sticking forlornly to the purely logical
interpretation of the statement (S as you called it after removing the significant
modal "can") renders an otherwise very colorful statement in projected,
washed out black and white form.
Let me be more specific.
Although language can be translated into logic after
removing a lot of linguistic functionality, that doesn't mean that the
translation is accurate, faithful or complete in its translated form to the
original statement.
The original statement (T, lets call it), pays
attention to the possibility
of agreement in addition to its logical structure.
T: But
we can all agree there are no
statements agreed by everyone, right?
The subjectivity of each of the “all” observers
comes in when such actions as compromises are considered. It is common
for groups of observers to reach compromise on a law, or on other action, even
when they don't agree with the logic expressed, or even with the pragmatics of
the action, because they feel that their own subjective requirements will be met
by the action regardless of how it is described; the anticipated effect is more
significant to each observer than the debatable parts. That is why
subjectivity is a significant factor in laying bare the magnificent elegance of
the statement.
But I agree that, seen purely logically, it isn't
anywhere near as compellingly magnificently elegant. I don't consider
that factor (pure logic) as important as the mind-to-mind transfer of a complex
linguistic statement experienced by many observers. That complexity is
what I find magnificently elegant about it, not the purely logical
interpretation per se.
HTH,
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher Menzel
Sent: Saturday, June 16, 2012 1:45 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Social
interaction and teamwork
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.
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
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