The logic of turmoil: some epistemological and clinical considerations on emotional experience and the infinite

The idea of the infinite has its origins in the very beginnings of western philosophy and was developed significantly by modern philosophers such as Galileo and Leibniz. Freud discovered the Unconscious which does not respect the laws of classical logic, flouting its fundamental principle of non-contradiction. This opened the way to a new epistemology in which classical logic coexists with an aberrant logic of infinite affects. Matte Blanco reorganized this Freudian revolution in logic and introduced the concept of bi-logic, which is an intermingling of symmetric and Aristotelic logics. The authors explore some epistemological and clinical aspects of the functioning of the deep unconscious where the emergence of infinity threatens to overwhelm the containing function of thought, connecting this topic to some of Bion's propositions. They then suggest that bodily experiences can be considered a prime source of the logic of turmoil, and link a psychoanalytic consideration of the infinite to the mind-body relation. Emotional catastrophe is seen both as a defect-a breakdown of the unfolding function which translates unconscious material into conscious experience-and as the consequence of affective bodily pressures. These pressures function in turn as symmetrizing or infinitizing operators. Two clinical vignettes are presented to exemplify the hypotheses.     

On the logic of theory change: Safe contraction

This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and under various natural constraints.     

The logic of misperceived distance (or location) theories of the Poggendorff illusion

For the Poggendorff display (transversal interrupted by parallel lines), the typical distance-misperception theory postulates that a particular linear distance extending across the empty space between parallels is underestimated; examples are the intertransversal slant distance defined by the closest ends of the transversal segments (a “wings-in Müller-Lyer like” underestimation) or the perpendicular distance between parallels (parallels “attract”). Distance misperception by itself, however, can neither establish that perceived transversal misalignment exists for a Poggendorff display nor specify the perceivedlocation conditions) that will produce perceptual collinearity. The perceptual displacement vector is introduced as a means of specifying fully the perceptual mislocation (displacement) of one transversal segment with respect to the other. Given this vector information (direction as well as distance), the logical soundness of theories postulating distance or location misperception were evaluated, and they were compared on the basis of extant data. Such vector information can be used to evaluate other classes of theories as well.     

The logic of viewpoints

In this paper a propositional logic of viewpoints is presented. The language of this logic consists of the usual modal operatorsL (of necessity) andM (of possibility) as well as of two new operatorsA andR. The intuitive interpretations ofA andR are “from all viewpoints” and “from some viewpoint”, respectively. Semantically the language is interpreted by using Kripke models augmented with sets of “viewpoints” and with a new alternativeness relation for the operatorA. Truth values of formulas are evaluated with respect to a world and a viewpoint. Various axiomatizations of the logic of viewpoints are presented and proved complete. Finally, some applications are given.