Varzi, Achille. 1991. "Truth, Falsehood and Beyond." In Topics in Philosophy and Artificial Intelligence, edited by Albertazzi, Liliana and Poli, Roberto, 39-50. Bozen:
Istituto Mitteleuropeo di Cultura.
Papers from the International Summer Schools in Bozen - 1989-1990.
Always in the background and sometimes in the foreground of any semantic approach to cognitive reasoning is a straight, twofold assumption on the admissible state
 Every sentence must be either true or false
 No sentence can be both true and false.
Arguably, such a standard course is intuitively well-grounded, and the resulting accounts have generally proved to be not only simple, but formally powerful as well. As things are,
however, some concern arises in connection with their range of application. For on the one hand, it appears that any but the most artificial set-ups may violate , while on the other hand, any but
the most simplistic situations are liable to violate . In fact, even if we assume that the purpose of a language's sentences is to be always true or false, there is no a priori reason to
suppose that the underlying conditions will be always completely fulfilled (for instance, ordinary language sentences may involve expressions whose intended reference is only partially
defined, or vaguely defined, or not defined at all). And since there is no general syntactic criterion for incompleteness, there is no general way that incompletenesses can be ruled out without
ruling out a variety of unproblematic cases as well. Conversely, even if we assume that the intention of a language's sentences is never to be true and false, there is in fact no a priori
guarantee that the underlying conditions can be always consistently fulfilled (for example, ordinary language sentences may, in unfavourable circumstances, turn out to be self-referential,
thus leading to such well-known troubles as the liar paradox). And again, since there is no general decision procedure for inconsistency, there is no general and effective way that inconsistencies
can be ruled out without rendering a great deal of perfectly unproblematic reasoning impossible.
For these reasons, a more general semantic framework, where representational gaps and/or gluts are admitted bona fide, is arguably desirable. Of course the task is by no
means straightforward. Dropping  and  from the foundations of semantics is a true "revolution", and it might be difficult to keep it under logical control. Nevertheless it can be done. My
purpose here is to outline a concrete proposal in this direction."