The paper enriches the conceptual apparatus of the theory of meaning and denotation that was presented in Part I (Section 3). This part concentrates on the notion of interpretation, which is defined as an equivalence class of the relation possessing the same manner of interpreting types. In this part, some relations between meaning and interpretation, as well as one between denotation an interpretational denotation are established. In the theory of meaning and interpretation, the notion of language communication has been formally (...) introduced and some conditions of correctness of communication have been formulated. (shrink)

We argue that E. Wigner’s well-known claim that mathematics is unreasonably effective in physics is only one side of the hill. The other side is the surprising insufficiency of present-day mathematics to capture the uniformities that arise in science outside physics. We describe roughly what the situation is in the areas of everyday reasoning, theory of meaning and vagueness. We make also the point that mathematics, as we know it today, founded on the concept of set, need not be a (...) conceptually final and closed system, but only a stage in a developing subject. (shrink)

En este artículo una paradoja es un tipo de argumentación con respecto a un sujeto X (sea un individuo o una comunidad) en un determinado momento T. Muchas argumentaciones paradójicas tienen lugar en el desarrollo histórico y práctico de las ciencias. Algunas suponen grandes sorpresas acompañadas de profundas crisis, como ocurre con las llamadas antinomias. Solventar, y eventualmente resolver, una paradoja en este sentido supone avances revolucionarios que se obtienen al precio de rechazar creencias previamente asumidas o tenidas por verdaderas (...) por la comunidad científica. El concepto de paradoja que se propone es relativo a sujetos y dinámico en el tiempo. Una argumentación que resulta paradójica para X pudiera no ser paradójica para Y, simplemente porque X e Y no tienen por qué compartir las mismas creencias. Asimismo, X puede descubrir que tiene una paradoja en T, y dejar de tenerla ulteriormente en virtud de un cambio de sus creencias. (shrink)

The duality of truth and falsity in a Boolean algebra of propositions is used to generate a duality of belief and disbelief. To each additive probability measure that represents belief there corresponds a dual additive measure that represents disbelief. The dual measure has its own peculiar calculus, in which, for example, measures are added when propositions are combined under conjunction. A Venn diagram of the measure has the contradiction as its total space. While additive measures are not self-dual, the epistemic (...) state of complete ignorance is represented by the unique, monotonic, non-additive measure that is self-dual in its contingent propositions. Convex sets of additive measures fail to represent complete ignorance since they are not self-dual. (shrink)

We here report the findings of our investigation into the validity of the conjunction fallacy (Tversky & Kahneman, 1983), bearing in mind the role of conversational rules. Our first experiment showed that subjects found a logically correct answer unacceptable when it implied a violation of the conversational rules. We argue that tautological questions, such as those which concern the relationship of inclusion between a class and its sub-class, violate conversational rules because they are not informative. In this sense, it is (...) not understood that the question in a Linda-type problem involves a comparison between an inclusive and included class, but presumed that a different type of comparison is intended. Tautological questions (and, consequently, also their answers) do not become a matter of discussion except under certain specific conditions. Our second experiment showed that, providing the context was adequately marked (such as in the case of a rhetorical question), the conjunction fallacy disappears. In two further experiments, the implications of our view were compared with those of the other critical approaches to the heuristic programme: the classical pragmatic view (which we call logical complementarity) and the frequentist view. (shrink)