Mathematics is often considered as a body of knowledge that is essen-
tially independent of linguistic formulations, in the sense that, once
the content of this knowledge has been grasped, there remains only the
problem of professional ability, that of clearly formulating and
correctly proving it. However, the question is not so simple, and P.
Weingartner's paper (Language and Coding-Dependency of Results in Logic
and Mathe- matics) deals with some results in logic and mathematics
which reveal that certain notions are in general not invariant with
respect to different choices of language and of coding processes. Five
example are given: 1) The validity of axioms and rules of classical
propositional logic depend on the interpretation of sentential
variables; 2) The language- dependency of verisimilitude; 3) The proof
of the weak and strong anti- inductivist theorems in Popper's theory of
inductive support is not invariant with respect to limitative criteria
put on classical logic; 4) The language-dependency of the concept of
provability; 5) The language- dependency of the existence of ungrounded
and paradoxical sentences (in the sense of Kripke). The requirements of
logical rigour and consistency are not the only criteria for the
acceptance and appreciation of mathematical proposi- tions and theories.
