A complete minimal logic of the propositional contents of thought

Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional identity than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation.Presented byJan Zygmunt     

Egocentric spatial framework effects from single and multiple points of view

In three experiments, we tested the one-place, one-perspective rule formulated by Franklin, Tversky, and Coon (1992). This rule proposes that subjects take a neutral, external perspective when they must use multiple viewpoints to make decisions about the locations of objects in memorized scenes. We compared responding from a single viewpoint with responding from two viewpoints. In Experiments 1 and 2, we used a sentence verification procedure, and in Experiment 3, we compared a true-false verification procedure with a six-alternative forced-choice procedure. Under these various conditions, we observed egocentric spatial framework effects in that above-below judgments were faster than front-back judgments and front-back judgments were faster than right-left judgments. When responding from two points of view in a single place, our subjects took multiple intrinsic perspectives rather than one neutral external perspective as proposed by the one-place, one-perspective rule.     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

Matter in its ‘infinity’

Consistent application of dialectical materialism leads Marxism-Leninism to the assertion that matter is infinite in its properties. However, the history of physics shows that the various levels of matter possess geometric dimensions that originate at the lowest level and continue through the others. The search for absolute natural constants — which Planck called the most pleasant task of physics — shows the conviction of the physicists that there is a limit to the parameters, a limit beyond which matter is no longer divisible. Translated by T. J. BLAKELEY     

The Skolem-Löwenheim theorem in toposes

The topos theory gives tools for unified proofs of theorems for model theory for various semantics and logics. We introduce the notion of power and the notion of generalized quantifier in topos and we formulate sufficient condition for such quantifiers in order that they fulfil downward Skolem-Löwenheim theorem when added to the language. In the next paper, in print, we will show that this sufficient condition is fulfilled in a vast class of Grothendieck toposes for the general and the existential quantifiers.     

Sheaves over Heyting lattices

For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.