FOM: The Liar

[Till Mossakowski]

charles silver wrote:
> 
>     The recent proposed solution to the Liar Paradox recommended by Till
> Mossakowski, which is the PhD thesis of Andreas Beck, is very impressive.
> I've read a fair amount of the work and it is both insightful as well as
> technically interesting.   However, the consequence that one instance of
> 'This sentence is False' may be true while another instance is false, is not
> acceptable, to my mind.   It also seems to me that there should be a
> "simple" answer to the faults of the Liar--one that does not require much
> technical machinery at all.   I think the "simple" answer is that we've
> expected something we shouldn't have expected in the first place.  Why
> should we have expected the Liar to deliver a single truth-value when we go
> to work on it?   Also, the Liar cannot really be said to be "inconsistent"
> proof-theoretically, since there are no rules of inference in ordinary
> language.  And, it also doesn't seem to make sense to assume that any
> sentence(s) constructed in ordinary language should have a model.
> Nevertheless, I still think Andreas Beck's work is impressive.   (His
> comments on the other well-known proposed solutions are worth reading on
> their own.)


Yes, a simple answer not requiring much technical machinery of course is
"the Liar should not tackled with technical machinery at all".

But once you want to treat the Liar formally, you will need some
technical machinery that is more complex than the logics that are used
to formalize non-paradoxial sentences. Beck's work has its complexity
in the analysis of the referential structure of the sentences (but
this is something also common to everyday reasoning: besides the
structure of a sentence, it is always also important who, and in which 
context, has uttered the sentence).
The gain is that the simplicity of a two-valued logic can be kept.

Till Mossakowski

-- 
Till Mossakowski                Phone +49-421-218-4683
Dept. of Computer Science       Fax +49-421-218-3054
University of Bremen            till at tzi.de           
P.O.Box 330440, D-28334 Bremen  http://www.tzi.de/~till