Witti-Buch2 2001.qxd - Austrian Ludwig Wittgenstein Society

Jan Werszowiec Plazowski, Marek Suwara
The standard solution to the paradox consists in narrowing the spectrum of
acceptable (sensible) sentences to prevent the construction of liar’s statement. Such
solution comes directly from applying the postulate (4) of formalisation. This can be done
only within the formal language structure and as A. Tarski suggests is impossible in
natural language.
The interesting is, however, that in natural language liar’s paradox is rarely observed
as a logical problem. For instance, mathematicians seem to ignore it even when they
realise that the language they use is not the formal one.
The explanation is fairly simple. When we examine the problem in the perspective
of information “filtering”. The problem one has to solve is not limited to assigning the
logical value to the liar’s statement. This gives us nothing unless we know that he/she
IS the SOURCE of information WE CAN TRUST. The situation is just the case of
obtaining any information from a given source. First we have to decide whether we can
trust the source then we can assign a logical value to the sentence, which carries the
information. From the point of logical analysis this can be reduced to the question of
assigning the logical values to the following set of sentences:
i) X is a trustworthy source of information
ii) The statement “I am a liar” produced by X is true
The failure to assign any logical value to (ii) results in:
X is not a trustworthy source of information.
and consequently no sentence coming from that source is worth logical analysis.
Therefore we can safely ignore it.
It is not, however, true that from liar’s statement we cannot learn anything. The
information that such a person cannot be trusted is very useful especially if he/she were
going to provide us with some more data, some of them maybe contradictory. Treating
the “liar” as just a liar simply comprises with the rule of epistemological scepticism.
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