A conjunction in closure spaces

This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of ω-conjunctive closure spaces (X is ω-conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:

1. For every closed and proper subset of an ω-conjunctive closure space its interior is empty (i.e. it is a boundary set).
2. If X is an ω-conjunctive closure space which satisfies the ω-compactness theorem and \(\hat P\) [X] is a meet-distributive semilattice (see [3]), then the lattice of all closed subsets in X is a Heyting lattice.
3. A closure space is linear iff it is an ω-conjunctive and topological space.
4. Every continuous function preserves all conjunctions.

     

Erotetic arguments: A preliminary analysis

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.     

Undecidability without Arithmetization

In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas.     

The logic of questions as a theory of erotetic arguments

This paper argues for the idea that the logic of questions should focus its attention on the analysis of arguments in which questions play the role of conclusions. The relevant concepts of validity are discussed and the concept of the logic of questions of a semantically interpreted formalized language is introduced.This paper was presented at the symposium Erotetic Logic. A Dialogue organized by the Center for the Philosophy and History of Science of Boston University (February, 1994) and prepared during my stay at the Department of Philosophy, University of California, Riverside as a Fulbright grantee.I would like to thank Professors David Harrah and Sylvain Bromberger for valuable suggestions and comments.     

Axiomatic extensions of the constructive logic with strong negation and the disjunction property

We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B εV, thenA×B is a homomorphic image of some well-connected algebra ofV. We prove:

• each varietyV of Nelson algebras with PQWC lies in the fibre σ^?1(W) for some varietyW of Heyting algebras having PQWC,
• for any varietyW of Heyting algebras with PQWC the least and the greatest varieties in σ^?1(W) have PQWC,
• there exist varietiesW of Heyting algebras having PQWC such that σ^?1(W) contains infinitely many varieties (of Nelson algebras) with PQWC.

     

Changes in anaclitic–introjective personality dimensions,outcomes and psychoanalytic technique: a multi-case study

This study investigates changes in latent mental structures along the anaclitic and introjective dimensions in relation to outcomes in 14 cases of publicly financed psychoanalysis. The method of prototype matching was adapted for personality assessment, and multiple outcome measures were applied. For the anaclitic cases, symptom reduction was accompanied by more mature integration of anaclitic and introjective personality dimensions, while the introjective cases showed symptom reduction without such improvement. This could indicate that sustainable change in latent mental structures is more difficult to achieve in introjective than in anaclitic patients. Further research is needed to validate these preliminary results.