FOM: Infinite interpretation of "Liar", "Barber", etc.

[alexzen]

	Dear Colleagues,

	As is well known, the paradoxes problem is one of the most important 
problem in Logic, Foundations of Mathematics, Philosophy of Mathematics, 
etc.. The traditional formulation of famous Epimenides' "Liar", Russell's 
"Barber", etc. is as follows;

	[if A then NOT-A] and [if NOT-A then A] (1)

where A = "I am a liar", "the Barber does shave himself", "the set includes 
self as its own element", etc.
	Now I am writing a paper where a new interpretation of these paradoxes is 
proved and discussed. The interpretation has the following potentially 
infinite form:

	A -- > NOT-A -- > A -- > NOT-A -- > A -- > NOT-A -- > A -- > . . .  (2)

	It is obvious that (2) has a quite different logical, ontologhical and 
epistemological sense versus the traditional interpretation (1) and leads 
to new, quite not trivial consequences.
	Now I know only two papers considering the interpretation (2):
	1. Valentin F.Turchin, A Constructive Interpretation of the Full Set 
Theory. - The Journal of Symbolic Logic, vol. 52, Number 1, pp 172-201 
(1987), where the "Liar" is considered as an example of an infinte semantic 
resursion having the infinite form (2).
	2. Alexander A.Zenkin, New Approach to the Paradoxes Problem Analysis. - 
Voprosy Filosofii (Philosophy Problems), 2000, No. 10, pp. 79-90, where 
necessary and sufficient conditions of the paradoxicality are formulated 
and the interpretation (2) of the "Liar" is a natural concequence of these 
conditions.

	I would be very thankful for any other information (papers, references, 
WEB-addressess, etc. ) relating to such the infinite interpretation (2) of 
the paradoxes.

	Thanks in advance,

	Alexander Zenkin


= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
=
 Prof. Alexander A. Zenkin,
 Doctor of Physical and Mathematical Sciences,
 Leading Research Scientist of the Computing Center
 of the Russian Academy of Sciences,
 Member of the AI-Association and the Philosophical Society of the Russia,

Department of Artificial Intelligence problems,
Computing Centre of the Russian Academy of Sciences
Vavilov st. 40, 117967 Moscow GSP-1, Russia

e-mail: alexzen at com2com.ru
 WEB-Site   http://www.com2com.ru/alexzen/
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
=
 "Infinitum Actu Non Datur" - Aristotle.
"Drawing is a very useful tool <medicine> against the uncertainty of words" 
- Leibniz.