Validity and quantification in intuitionism

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the most natural reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.This paper was partly written while the first author, H. C. M. de Swart, was a Visiting Fellow at Princeton University for the academic year 1976–1977. This opportunity was given to him by the Niels Stensen Stichting in Amsterdam, the department of philosophy of the Catholic University in Nijmegen and by Princeton University. He is happy to express his appreciation for that opportunity.     

Group psychotherapy in chronic psychiatric outpatients: a Toronto model.

Seventy to 80 chronic psychiatric patients are treated in an aftercare clinic with a goal of tertiary preventive care. The major component of the treatment approach is reality-oriented group psychotherapy with an emphasis on interpersonal relationships. Attention to three factors in group psychotherapy with this population of patients has facilitated our work and outcome. These are the concept of the core group, diagnostic heterogeneity, and staff structure.     

The enhancement of retention induced by vasopressin in mice may be mediated by an activation of central nicotinic cholinergic mechanisms.

Immediate post-training subcutaneous administration of lysine vasopressin (LVP, 0.003-1.00 microgram/kg) enhanced retention, whereas the vasopressin antagonist AAVP (0.01-0.30 microgram/kg) impaired it, in male Swiss mice tested 48 h after training in an inhibitory avoidance task. Both effects were dose-dependent. Neither LVP nor AAVP affected response latencies in mice not given the footshock on the training trial. The simultaneous administration of AAVP at a dose (0.01 microgram/kg) which had no effect on retention shifted the dose-response curve of LVP to the right. Nicotine (1.0-30.0 micrograms/kg, sc), a central nicotinic cholinergic agonist, also facilitated retention in a dose-related manner without affecting the retention performance of unshocked mice. The effect of nicotine was prevented by the central acting nicotinic cholinergic receptor antagonist mecamylamine (5 mg/kg, sc.). In contrast, neither hexamethonium (5 mg/kg, sc), a peripheral acting nicotinic receptor blocker, nor atropine (0.5 mg/kg, sc) or methylatropine (0.5 mg/kg, sc), two anticholinergic drugs which are known to act on muscarinic cholinergic receptors, prevented the effect of post-training nicotine. The effects of LVP and nicotine were time-dependent, suggesting that both treatments enhanced retention by influencing post-training processes involved in memory storage. Low doses of nicotine (1.50 microgram/kg, sc) or the central anticholinesterase physostigmine (35 micrograms/kg, sc) and LVP (0.003 microgram/kg, sc), which had no effect on retention when administered alone, produced a synergistic interaction when given together following training. The influence of LVP (0.03 microgram/kg, sc) on retention was prevented not only by AAVP (0.01 microgram/kg, sc) but also by mecamylamine (5 mg/kg, sc), whereas the effects of nicotine (10.0 micrograms/kg, sc) were prevented only by mecamylamine. These results suggest that the enhancement of retention induced by vasopressin is probably due to an activation of central nicotinic cholinergic mechanisms which are critical for memory formation.     

A note on partitioned determinants

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.     

Generalized eigenvalue problems with positive semi-definite matrices

In a recent paper in this journal McDonald, Torii, and Nishisato show that generalized eigenvalue problems in which both matrices are singular can sometimes be solved by reducing them to similar problems of smaller order. In this paper a more extensive analysis of such problems is used to sharpen and clarify the results of McDonald, Torii, and Nishisato. Possible extensions are also indicated. The relevant mathematical literature is reviewed briefly.     

Demonstration of an aftereffect occurring in the tactile-kinesthetic domain

Summary The aim of this work is the demonstration of a tactile-kinesthetic aftereffect. A sequence of stimuli was offered to adult subjects whose task was to compare two weights presented simultaneously to both hands by means of a Piéron gravimeter. In Experiment 1 the inspection stimuli consisted of two successive presentations of unequal weights for a period of 2 × 10 s. The test stimuli consisted of two equal weights rapidly following an inspection stimulus. Control stimuli consisting of two equal weights not preceded by an inspection stimulus were interspersed in the sequence. The results obtained confirm the existence of a contrast effect after presentation of an inspection stimulus. In Experiment 2 the inspection stimuli consisted of a single presentation of two unequal weights for a period of 20 s. The results confirm those of the first experiment and provide data enabling the contrast effect obtained to be interpreted as a Köhler-type aftereffect. In order to avoid confusion with the kinesthetic-figural aftereffect, we propose to call the effect demonstrated here the Gravimetric Aftereffect.     

Correctness of Kruskal's algorithms for monotone regression with ties

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.Comments by Dr. J. B. Kruskal have been most helpful.