The logical study of science

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4).I would like to thank David Pearce and Veikko Rantala for their helpful comments.     

The level of organization of the motor schema

The interpretations of Piaget and Schmidt on the level on which the motor schema is supposedly effective were evaluated in pre-school children of different ages in a throwing task. In an analysis of variance on the accuracy scores, significant main effects for age, sex, and throwing arm were found. Further, the results showed no relationship between accuracy scores with the preferred and non-preferred arm in the younger group, while in the older group a moderate relationship was found. This result was interpreted in terms of structural development and as a warning for studies where Schmidt's variability-of-practice hypothesis is tested.     

Some kinds of modal completeness

In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability and preservation under ultrafilter extensions are introduced and studied as well.     

Perceptual interpretation of complex line patterns

Leeuwenberg's coding system for the representation of line pattern interpretations is tentatively applied to the interpretation of complex line patterns, that is, line patterns with intersecting lines. Perceptually preferred interpretations of complex line patterns can only be predicted correctly if two requirements are met: (a) The codes of line patterns should contain information about the objects represented by the line patterns, not about the line patterns as drawings; and (b) effects of the gestalt law of good continuation have to be taken into account.     

Stiffness as a control variable in motor performance

In the experiments described in this article we investigated the control of stiffness of the effector system in relation to parameters of the movement. If the velocity of a movement is chosen, it appears that at the same time the stiffness of the effector system is set to a preferred value. By changing the instruction given to the subject it is possible to change the relationship between velocity and stiffness without changing the kinematic parameters of the movement.Finally, the changes of stiffness and velocity in a learning process are studied. In conformity with what might be expected on intuitive grounds, it is found that velocity increases spontaneously during learning while stiffness decreases. The results are discussed in connection with the generation of motor programmes.     

Effects of visual-field and matching instruction on event-related potentials and reaction time

Vertical letter pairs were presented randomly in the left and right visual hemifields in a physical identity match and name identity match condition. The reaction times showed a right visual field superiority for name matches, and a left visual field superiority for physical matches. Event-related potentials to letter pairs showed a sequence of three waves: a negative wave (N2, around 270 msec), a positive wave (P3, around 500 msec), and a broad positive slow wave (SW, around 600-700 msec), respectively. P3 and SW amplitudes were consistently larger at the left hemisphere than at the right hemisphere, regardless of the field of stimulation. At both hemispheres, N2 waves were always larger to stimuli presented in the visual field contralateral to a hemisphere than stimuli presented in the visual field ipsilateral to a hemisphere. The positive waves (P3, SW) showed the opposite pattern: smaller amplitudes to stimuli that were presented contralaterally than stimuli that were presented ipsilaterally to a given hemisphere. These results were attributed to a shift in sustained negativity on the directly stimulated hemisphere, relative to the indirectly stimulated hemisphere, reflecting either sensory at attentional processes in the posterior cerebral hemispheres.     

The variety of consequence,according to Bolzano

Contemporary historians of logic tend to credit Bernard Bolzano with the invention of the semantic notion, of consequence, a full century before Tarski. Nevertheless, Bolzano's work played no significant rôle in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, and still quite relevant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their meta-theory. There are certain analogies with Tarski's concerns here, although the main thrust seems to be different, both philosophically and technically. Thus, if only obliquely, we also provide some additional historical perspective on Tarski's achievement.