A system S has the “converse Ackermann property” (C.A.P.) if (A -> B) -> C is unprovable in S whenever C is a propositional variable. In this paper we define the fragments with the C.A.P. of some well-know propositional systems in the spectrum between the minimal and classical logic. In the first part we succesively study the implicative and positive fragments and the full calculi. In the second, we prove by a matrix method that each one of the systems has the C.A.P. Thus, we think the problem proposed in Anderson & Belnap (1975) § 8.12 has been solved.

The paper investigates the problems whether a concrete individual can be defined as a set or be characterized by an abstract theory. In particular, Jesês Mosterín’s objection to a theory of things proposed by the present author is discussed. Also, the view of scientific theories held by Sneed, and adopted by Mosterln, is analyzed. It is concluded that any adequate description of a concrete individual calls for more than a mathematical formalism.

The pascalian use of indivisibles is here considered in the context of the theological and mathematical debates of the time, by distinguishing it clearly from this of Cavalieri. The combinatory and geometrical approaches are closely linked in Pascal’s work. His use of indivisibles has a heuristic, inventive character and not only a demonstrative one. Ontologically speaking, it stems out from the acceptance of actual infinite. The use of the symmetry axiom of Archimedes is the basis of the pascalian use of the infinitesimals, which has, in other respects, some close connexions with the Leibnizian conception of infinitesimals.

The purpose of this paper is to outline a thesis which in some ways attemts to retrieve the value of meaning as a constituent element of theories. It will be argued that theories possess in common a more or less explicit relational structure, but, at the same time, they possess a meaningful function by means of which they are instruments of knowledge or, rather, by means of which theories have the value ofknowledge in science. In conclusion, it will be suggested that this approach to theories allows those with weak relational structure (social, historical theories, etc.) to be treated with a degree of adequacy by the philosophy of science. Likewise, it will be suggested that the method of semantic analysis linked to the theory of “possible worlds” could be fruitful for this purpose.

The article starts from previous contributions by the author about “Languages of History” (Dianoia, 1970), in which he distinguished three types of statements used by historians. In this context, he analyzes the various relationships between these three following languages (I, 11 and III): the positivist, the hermeneutic, and the recursive ones. After analyzing the two first ways in their strong and weak versions, the author decides in favour of the third one, in its weak or informal version.

There are two kinds of philosophical problems in the theory of partial truth: semantical and methodological problems. The semantics of partial truth must be clarified by some standard system of multivaluedlogic. Fuzzy set theory should be applied to solve some methodological problems.