Re: The Case Against RosAsm (#2)

From: Beth (BethStone21_at_hotmail.NOSPICEDHAM.com)
Date: 01/18/04 

Date: Sun, 18 Jan 2004 12:30:24 -0000

Gerhard W. Gruber wrote:
> T.M. Sommers wrote:
> >A paradox of this type requires self-reference. The statement
> >'This statement is false' is paradoxical, as are the pair of
> >statements, 'The next statement is true. The previous statement
> >is false.'
>
> But when you say "All stamtents are false" then this includes the
very
> statement itself, which makes it false maening "All statements are
not false"
> in which case it is true. :)
>
> The self-reference is already included because "All statements"
includes that
> statement since it is a statement. :)
>
> It's the same with saying "All people are liars" which would include
myself
> because I also belong to the group of people, thus making myself a
liar.

Exactly, Gerhard...

You've saved me from making that exact same point myself...

Specifically:

If the statement "ALL statements are false" is true, then the
statement itself says that it cannot be true because all statements
are false...which itself is a contradiction...and, hence, we have
"self-reference" and the contradiction is _infinite_...thus, it is a
_paradox_...

If the statement "ALL statements are false" is false, then all
statements are true (or, if you like, "no statements are false") but
then the statement itself says that all statements are false so the
statement must itself be false...but, as we've just determined, if the
original statement is, indeed, false then we're going end up right
back where we started over and over again...the contradiction in
_infinite_...thus, it is a _paradox_...

Hence, I was correct in calling it _paradoxical_...

The simple little forgivable mistake you made was to _wrongly_ negate
"all statements are false"...the true opposite of "all" is "_none_",
NOT "some"...I'm sure you can know see and can substitute "none"
rather than "some" for the opposite of "all" and discover the
_paradox_ yourself...

But, fair enough, it's an easy enough mistake to make in wrongly
negating a statement like that...just remember, the opposite of "all"
is "none", NOT "some"...and you should happily avoid making the same
logical slip-up in future...

If you still can't see it, then wait for me to get some sleep first
and I could come back with the predicated logic for it all, if you
really, really insist...I don't particularly want to do that, mind
you, as it's really, really boring to do (and, also, to read ;)...but
that should make it clear as crystal and unambiguous (natural language
is _always_ a really bad place to be dealing in logic because of all
the very natural ambiguity in the words we use...infamously, Bertrand
Russell, in fact, made a wager that - by exploiting the ambiguity of
naturally language - he could logically prove _anything_...they tried
it out and got him to attempt to prove that he was the Pope _because_
"1 + 1 = 2"...yup, he succeeded to do so using only (apparently)
completely logical statements of which none you could reasonably
disagree with individually...of course, he could _only_ succeed by
exploiting the natural _ambiguity_ of natural languages...you know,
like using words that have "double-meanings" and sneakily "changing
context" without anyone noticing what you were doing...for example,
"one" is a number but it's also a way for "one" to refer to "one"'s
self in language...but only the very observant would notice a whole
series of these very minor "context changes" from sentence to
sentence, between "one and one equals two" followed by: "so, as one
myself, one must..." and that kind of "sneaky trick" of
_language_...it's actually a _language_ thing, not a logical thing at
all...but, if you're skilled in how to pull off these kinds of tricks
then most people won't even notice it happening at all...hence, if you
really want to insist on analysing logic, you've _got to_ insist on a
_formal proof_ (and nothing less than _FORMAL_ proof ;) or you can
still be "tricked" without even realising...after all, _HOW_ do you
think all those lawyers get away with often literally arguing that
"black is white"? As scholars of logic, language and law, you just
DON'T want to get into any _language-based_ arguments with them at
all...insist on mathematical or formal forensic proof or
something...that's about the only way to pin such people down...no
wonder lawyers are such often hated people...you just can't win with
them when they are particularly good with their "way with words" ;)...

Beth :)