FOM: Infinite interpretation of "Liar", "Barber", etc.
alexzen
alexzen at com2com.ru
Fri May 25 08:44:20 EDT 2001
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
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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/
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"Infinitum Actu Non Datur" - Aristotle.
"Drawing is a very useful tool <medicine> against the uncertainty of words"
- Leibniz.
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