PIERDANIELE GIARETTA LIAR, REDUCIBILITY AND LANGUAGE ABSTRACT. First, language and axioms of Church’s paper ‘Comparison of Russell’s Resolution of the Semantical Antinomies with that of Tarski’ are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made in order to justify the Russellian, and perhaps Churchian, idea that language should not be fragmented beyond what is required by type distinctions. After all, because of reducibility, which seems to allow a semantics without propositions, this comes out to be possible only at the cost of resorting to two disputable theses. The relationship between ramification of types and Tarskian distinction of languages is analysed by Church (1976). Introducing some modifications and additions, Church presents a formalized version of Russell’s ramified type theory. The main change, with respect to the original versions given by Russell (1908; 1910), is the addition of predicate constants express- ing semantical relations. This allows a formal analysis and resolution of Grelling’s paradox. In his comments Church shows how to extract an ana- logue of the Tarskian hierarchy of languages from the language in which his theory is formulated. Since the intended semantics of this theory is intensional, he seems to suggest that the ramified type theory provides a more general and a better grounded point of view. In this paper Church’s language and axioms are slightly modified and a version of the Liar paradox tentatively reconstructed, using a device in- troduced by Myhill in connection with Grelling’s paradox. With reference to such a version of the Liar paradox, it is possible to point out that a hier- archy of truth predicates can be defined which is of a different kind from the one defined by Church: it depends on the enlargement of the semanti- cal vocabulary and its levels do not differ in the ramified-type-theoretical sense. Finally, an alternative point of view is outlined in order to try to justify the Russellian, and perhaps Churchian, idea that language, understood as the ideal language used by an ideal community in its whole history, is not, or should not be, fragmented beyond what is required by type distinctions, Synthese 117: 355–374, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.