K.
Pkhakadze, R. Asatiani,
M. Ivanishvili
(Tbilisi
state University)
Logic
of Language and Paradoxes
According to Wittgenstein – Logic is Language. What does it mean? How we
understand the term “logic of Language”
In general, logic is the
rules of right thinking, but the right (correct) mental
processes i.e. the right
thinking we can understand only as some type of
language processes. The task of
mathematical logic was and is formalization of mental processes of mathematical
type. Frege’s mathematical formal language was the main ground of above
mentioned task. There’s a question – what nature has the natural language?-
the direct formal – logical description of natural Georgian language show us the possibility to find its isomorphical formal adequate.
The words of vocabulary of the Georgian natural language are described
by their placeness, by the
types of places, and by the type value of
this word – operator. On the basis of such described vocabulary the
conception of the well – formed expressions of so-called Georgian
natural formal language is defined. Classification of the words of
vocabulary gives the
possibility to
classify formally and
mathematically the well – formed expressions.
In any natural language as well
as in the Georgian natural language is the class of so called pure mental or
logical words. (For example: “da” – “and”,
“an”
– “or”,
“magram”
– “but”, “Tu” – “If”,
“SesaZlebloba” – “possibility”,
“aucilebloba”
– “necessity” . . .). In the formal adequate of
natural language we have
possibility to study thoroughly (fully) the logical formal – operatoral nature
of the above mentioned words.
This represents new perspectives to understand what is logic in general.
According to all above
mentioned we understand the sense of the term
‘logic of language’. Here
is also the answer of the question about Wittgenstein’s famous phrase.
Now very briefly about
Paradoxes, especially about the paradox of
‘liar’. From the
simplified point of view any natural language is the set of typicalized words.
Let us assume that W is language, i.e. W is the set of typicalized word. Logical
– semantical analysis of the languages shows that from W we can separate the w
subset of the basic words of language. We call the elements of W \ w set as non
– basic or definable or contracted words of the language. (For example: “vtyui” – “I lie” is non – basic
word, because of ‘I lie’ means
‘I say something and I know this something is not true’). The formal logical
description of the Georgian natural language clarifies that ‘I lie’ must be
regarded as 1 – placed operator which operates on L (logic) type words and
gives in the result the same type, i.e. the L type word. This means that ‘I
lie’ is L
®
L
type word and its value is the truth scheme. So, to define it as true or false
is absurd and forms the paradox.
References:
1. Bentem J, Essays on Logical Semantics, 1997; Logic and
Language, Handbook, 1998.
2. Frege G, Beguffsschrift, 1879.
3. Russel B, The Principles of Mathematics, 1938;
Ludwig Wittgenstein, 1951.
4. Wievtbicka A, Semantics Primes and Universals,
Oxford University, Press, 1996.
5. Wittgenstein L, Notebooks, 1914-1916, 1961.
6. Ãèëüáåðò Ä, Òåîðèÿ
äîêàçàòåëüñòâ, 1972.
7.
Ïõàêàäçå Ø, Íåêîòîðûå
âîïðîñû òåîðèé îáîçíà÷åíèé, 1978.
8.
Pkhakadze k, Ivanishvili M.; To Direct Formal –
Logical Description of Georgian Language Based on the Language as a
Natural Language, (Under publishing).