Re: Liars Paradox - resolution

On Thu, 22 Jan 2009 23:12:08 +0000, John Jones <jonescardiff@xxxxxxx>
wrote:

I thought you had pinched my idea. But then I realised that you had not
given the conditions that must obtain if we want to assert 'always'.

At best, I've semi-formalised, and I even did a lot of that wrong.

Anyway, I posted hoping to tidy up my understanding, check that I'm
not missing something important in an area I thought I understood, and
pick up related ideas from people who understand what I'm saying
better than I do. Apart from messing up the initial post, that's
mostly what happened. I don't get to claim any credit for anything,
AFAICS.

That said, I don't get why I need to specify conditions for the
"always". Maybe its something about the broken post of mine you
replied to, rather than my slightly more sane second post.

The way I see it, in any logical statement, you always have the option
of adding a "forall" of arbitrarily defined irrelevant cases. It's
just normally pointless to do so - unless dealing with the liars
paradox, in which case its necessary. After Bill Taylors post, I'm now
thinking of those cases as integer level numbers, but it doesn't
really change the logic.

Without the model of levels, the only condition I can think of is that
the cases form a non-empty set.

Also, one key thing I have learned is that any resolution probably
needs to be based on some additional model (e.g. levels) and the
axioms etc to suit. As I said in reply to abo, I've come to believe
that the paradox is real after all - until you define an alternative
model in which it can be reinterpreted and resolved. The levels model
is just one such model.

As for avoiding the need for any additional model, I've re-read the
Wikipedia page and decided that I probably agree with the A. N. Prior
resolution - I have reservations, but I can't work out what they are,
which is a bad sign where logic is concerned. Intuition is very often
a liar.

http://en.wikipedia.org/wiki/Liar_paradox

.

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