Theoria: An International Journal for Theory, History and Foundations of Science

This is a multifaceted semantico-ontological investigation of different types of families of concepts and properties. One major result is that contrast between: (a) the ontologically egalitarian or democratic, but epistemologically hierarchical family of colors, and (b) the ontologically hierarchical or pyramidal familiy of negations. The different negations (of propositions, imperatives, properties, predication) are studied, and the unity of the whole family under a genus reveals the pyramidal structure of the family. The negation or properties has a powerful bearing on Russell’s paradox -- which shows different strands in negation. The connections between existence and negation provides an introduction to Guise Theory and reveals some limitations in Bertrand Russell’s analysis of definite descriptions.

A dix ans d’intervalle deux déontciens de premier plan, G.H. von Wright et H.N. Castañeda, ont abordé -indépendamment l’un de l’autre- le probleme du fondement des normes et des énoncés normatifs. Leurs solutions respectives méritent d’être attentivement examinées. Ne prêtent-elles pas a discussion? Pour qu’une norme juridique soit fondée, suffit-il qu’elle soit édictée par un législateur compétent conformément a la procédure législative en vigueur? Un énoncé nornlatif est-il fondé du moment que l’ordre en faisant partie est légitimé au sens conféré a ce terme par l’auteur de Thinking and doing? Et tout d’abord peut-on admettre que les ordres fassent partie des énoncés nomlatifs? L’article qui suit essaie de répondre à ces questions et aux questions connexes.

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 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.

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.

An impossible world is a world which necessarily does not exist. Besides the paradigm of necessity, wich is logical necesslty, we must consider physical necessity and ethical necessity, both of wich can beexpressed in terms of logical necessity, in the way suggested by Montague. Accordingly, an impossible world can be logically impossible, physically impossible or ethically impossible, but in every case the impossibility can be reduced to logical impossibility, and in consequence an impossible world is irrational and cannot be understood by us. An illustration is taken from the incongruities of Kafka’s story in Di Verwandlung.

A Fuzzy-Set Theoretical Framework -resting on a paraconsistent infinite-valued logic- is sketched, wherein a thorough ontological-reduction program can be carried out. The framework includes formulae of the form “x comprises z in the time-interval e”. Reducing aggregates to sets thus handled is shown to escape usual objections. Likewise, systems generally can be regarded as aggregates, hence as (fuzzy) sets -the purported nonextensionality of systems objection being disposed of owing to our system’s recognizing infinitely many membership degrees. So do bodies, too, which enables us to find a solutionto Unger’s sorites concerning ordinary material bodies.

EI gran filósofo catalón, español, iberoamericano y universal Juan David García Bacca, cuya obra inmensa y de impresionante variedad y proyección sobre todas las áreas cientfíicas y humanas se sigue acrecentando cada día, a sus 84 años de edad, con nuevas creaciones -hombre a quien THEORIA tanto debe como inspirador, colaborador y fiel apoyo, desde su exilio venezolano, en los tiempos dificiles de la primera salida de la revista, entre 1952 y 1956- ha querido hoy hacernos llegar, junto a su primer artículo para la nueva etapa, que publicamos en las páginas siguientes, su cordial saludo a la nueva THEORIA, que reproducimos a continuación.

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.