On the notions of indiscernibility and indeterminacy in the light of the Galois–Grothendieck theory

We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to \(K\) -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry.     

Bad company generalized

The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable constraint on mathematical practice.     

The Use of Contextual Information by Right Brain-Damaged Individuals in the Resolution of Ambiguous Pronouns

Two experiments were conducted with the primary purpose of investigating the ability of right brain-damaged (RBD) individuals to use contextual information—at the level of the single sentence, in terms of the integration of information between clauses, and at the level of a minimal discourse (i.e., two sentences)—in the resolution of ambiguous pronouns. The investigation was extended to a group of left brain-damaged (LBD) and non-brain-damaged (NBD) individuals. Contrary to the prevailing view that RBD patients have difficulty in the use of contextual information to process language, both experiments were consistent in demonstrating that the RBD group was influenced by contextual information in a manner similar to that demonstrated by both the LBD and NBD groups.     

An observation on the spontaneous noticing of prospective memory event-based cues

In event-based prospective memory, current theories make differing predictions as to whether intention-related material can be spontaneously noticed (i.e., noticed without relying on preparatory attentional processes). In 2 experiments, participants formed an intention that was contextually associated to the final phase of the experiment, and lures that overlapped to differing degrees with the features of the intention-related cues were embedded in the initial phase. When participants were outside of the appropriate responding context (i.e., the initial phase), they exhibited slower latencies to lures that exactly matched the features of their intention compared with other types of lures and control words. In addition, on a final remember/know recognition test, participants reported having greater subjective recollection for the occurrence of the exact-match lures. These results suggest that exact-match lures were spontaneously noticed and differentially processed in the absence of any observable preparatory attentional processes. The findings have implications for the theoretical debate over whether preparatory attention must always be relied upon to notice intention-related material.     

Depression, Marital Satisfaction and Communication in Couples: Investigating Gender Differences

The correlation between depression and dysfunctional marital interaction is well documented, but only a few studies have examined gender-related differences in marital interaction patterns of couples with a depressed partner. In this paper we examined differences in observed marital communication in a sample of 62 Swiss couples presenting for treatment of depression. There were 16 maritally distressed couples with a depressed wife, 21 maritally nondistressed couples with a depressed wife, 18 maritally distressed couples with a depressed husband, and 7 maritally nondistressed couples with a depressed husband. Marital interaction behavior was found to depend on gender, depression, marital distress, as well as gender of the depressed partner. Our results suggest the need for a gender-sensitive model of the link between marital interaction and depression.     

Adaptation in Visuomanual Tracking Depends on Intact Proprioception

The role of arm proprioception in motor learning was investigated in experiments in which, by moving the arm, subjects followed the motion of a target displayed on a monitor screen. Adaptive capabilities were tested in visuomanual tracking tasks following alterations in the relationship between the observer's actual arm movement and visual feedback of the arm movement given by a cursor motion on the screen. Tracking performance and adaptive changes, measured in terms of spatiotemporal error, tracking trajectory curvature, and spatial gain, were compared in 7 control subjects (CSs) and in 1 deafferented subject (DS). CSs adapted appropriately to altered visuomanual relationships; those changes were present in trials immediately after restoration of normal scaling. In contrast, although the DS modified his tracking strategy from trial to trial according to the altered conditions, he did not show plastic changes in internal visuomanual scaling. Like the results of prismatic adaptation experiments, the present results suggest that arm proprioception contributes to the plastic changes that follow alterations in the scaling of visuomanual gain.     

Revisiting the suitability of antisaccade performance as an endophenotype in schizophrenia

Poor performance on the antisaccade task has been proposed as a candidate endophenotype in schizophrenia. Caveats to this proposal, however, include inconsistent findings in first-degree relatives of individuals with schizophrenia, and substantial heterogeneity in individuals with the disorder. In this study, we examined antisaccade performance in patients and relatives, and sought to establish whether antisaccade measures could differentiate between two patients clusters identified in the Western Australian Family Study of Schizophrenia with either pervasive cognitive deficits (CD) or cognitively spared (CS). Ninety-three patients (CD = 47, CS = 46), 99 relatives and 62 healthy controls carried out a standard antisaccade task. Results showed: (i) significantly greater error rate, and prolonged latencies to correct responses and self-correction saccades in patients compared with controls; (ii) high error rates in relatives of poorly performing patients; (iii) longer latencies of self-correction saccades in relatives compared to controls; and (iv) higher error rate and longer latencies of self-correction saccades in the CD subgroup compared with CS. Unaffected relatives as a group were unimpaired in error rate as compared to healthy controls. These findings suggest that the antisaccade error rate and latency of self-correction saccades are useful measures in specific applications of genetic research in schizophrenia, without fully meeting endophenotype co-familiality requirements.     

Exploring the informational sources of metaperception: the case of Change Blindness Blindness

Perceivers generally show a poor ability to detect changes, a condition referred to as “Change Blindness” (CB). They are, in addition, “blind to their own blindness”. A common explanation of this “Change Blindness Blindness” (CBB) is that it derives from an inadequate, “photographical” folk-theory about perception. This explanation, however, does not account for intra-individual variations of CBB across trials. Our study aims to explore an alternative theory, according to which participants base their self-evaluations on two activity-dependent cues, namely search time and perceived success in prior trials. These cues were found to influence self-evaluation in two orthogonal ways: success-feedback influenced self-evaluation in a global, contextual way, presumably by recalibrating the norm of adequacy for the task. Search time influenced it in a local way, predicting the success of a given trial from its duration.     

Color and intensity discrimination in <Emphasis Type="Italic">Xenopus laevis</Emphasis> tadpoles

Investigations into the physiology of Xenopus laevis have the potential to greatly accelerate biomedical research, especially concerning neural plasticity and sensory systems, but are limited by the lack of available information on behavioral learning in this species. Here, we attempt to lay the foundations for a behavioral assay in Xenopus that can be used in conjunction with biological manipulations. We tested cohorts of Xenopus tadpoles across four light-mediated active-avoidance experiments, using either wavelength or intensity as the salient discriminative cue. In the wavelength task, we determine a baseline learning rate and characterize retention of learning, identifying active extinction effects as far more potent than the passage of time in the loss of behavior. In the intensity task, we examine the effects of varying differences between the discriminative stimuli on acquisition and extinction and identify a critical range of intensity differences where learning changes. The results of our experiments demonstrate that Xenopus is a tractable model organism for cognitive research and can learn a variety of associative tasks in the laboratory settings. These data reveal new aspects of the Xenopus larval visual processing system and facilitate future research between cognitive methods and biological/chemical manipulations to study mechanisms of brain structure and function.     

Dynamic time warping: a new method in the study of poor handwriting

Poor handwriting is a diagnostic criterion for developmental coordination disorder. Typical of poor handwriting is its low overall quality and the high variability of the spatial characteristics of the letters, usually assessed with a subjective handwriting scale. Recently, Dynamic Time Warping (DTW), a technique originally developed for speech recognition, was introduced for pattern recognition in handwriting. The present study evaluates its application to analyze poor handwriting. Forty children attending Dutch mainstream primary schools were recruited and based on their scores on the Concise Evaluation Scale for Children's Handwriting (Dutch abbreviation: BHK), 20 good and 20 poor writers (of whom 13 were scheduled for handwriting intervention) were identified. The groups were matched for age (7-9 years), school grade (grades 2 and 3) and handedness. The children subsequently wrote sequences of the letter "a" on a graphics tablet in three conditions (normal, fast, and accurate). Classical kinematics were obtained and for each individual letter DTW was used to calculate the distance from the mean shape. The DTW data revealed much higher variability in the letter forms of the poor writers that was independent of the kinematic results of larger trajectories, faster movements, and higher pen pressure. The current results suggest that DTW is a valid and objective technique for letter-form analysis in handwriting and may hence be useful to evaluate the rehabilitation treatments of children suffering from poor handwriting. In education research it may be exploited to explore how children (should) learn to write.