Abstract:
Tarski's Wahrheitsbegriff was published in German in 1936(35?).
In
an introductory section Tarski investigates what he calls colloquial
languages and his conclusions are entirely negative. "... not only
does the definition of truth seem impossible, but even the consistent
use of this concept in conformity with the laws of logic."
In 1935 Ajdukiewicz published his paper "Die syntaktische
Konnexität" in which he outlines a mathematical foundation for
the
study of the very same colloquial languages. There are mutual
references in these papers, but no meeting of minds. It was left to
others to see the close connection - contrary to Tarski's claim -
between the syntax of Ajdukiewicz and the semantics of Tarski.
We
should, in particular, mention Reichenbach, Curry and Montague
(Tarski's student).
Language and logic have been inseparably intertwined in the European
intellectual tradition. It has not always been an easy relationship,
but there were always issues of substance whether they were friends
or foes. In the first part of the lecture I will place the
Tarski-Ajdukiewicz episode within this larger context.
But there is a limit to the usefulness of logic in the study of
colloquial or natural languages. In the second part of the lecture
I
will survey some recent work emphasizing the need for geometry in the
study of semantics of natural languages.