Philosophical reflections on the foundations of mathematics

This article was written jointly by a philosopher and a mathematician. It has two aims: to acquaint mathematicians with some of the philosophical questions at the foundations of their subject and to familiarize philosophers with some of the answers to these questions which have recently been obtained by mathematicians. In particular, we argue that, if these recent findings are borne in mind, four different basic philosophical positions, logicism, formalism, platonism and intuitionism, if stated with some moderation, are in fact reconcilable, although with some reservations in the case of logicism, provided one adopts a nominalistic interpretation of Plato's ideal objects. This eclectic view has been asserted by Lambek and Scott (LS 1986) on fairly technical grounds, but the present argument is meant to be accessible to a wider audience and to provide some new insights.     

Effects of two-year treatment with the cholinesterase inhibitor rivastigmine on behavioural symptoms in Alzheimer's disease

Alzheimer's disease (AD) is accompanied by prominent behavioural disturbances. They cause significant distress for both caregivers and patients and can play a major role in the decision to institutionalise AD patients. Recent evidence suggests that cholinergic deficiencies not only contribute to the memory and cognitive abnormalities of AD but are also responsible for some behavioural abnormalities seen over the course of the disease. In this study we assessed the ability of rivastigmine, a pseudo-irreversible cholinesterase inhibitor, to improve behavioural and psychopathologic symptoms in AD. The analysis included 34 patients present in the Germanarm of the international study B303 who received and completed long-term treatment with rivastigmine in the open-label study B305. Assessments of behaviour and psychopathological symptoms were performed using the behavioural component of the Clinicians Interview Based Impression of Change Plus (CIBIC-Plus). Results show that long-term treatment with rivastigmine can slow the progression of behavioural and psychopathological symptoms of AD. Behavioural symptoms showing stabilisation included aggressiveness, activity disturbances, hallucinations and paranoid features. Results also suggest that patients treated earlier with rivastigmine may attain a greater benefit compared with patients whose treatment is delayed 6 months. Further studies examining the effects of rivastigmine on behavioural disturbances in AD are therefore warranted.     

Accentuation effects and illusory change in exemplar-based category learning

Examined the hypothesis that information enhancing category differences receives greater weight in estimates of category means than information that reduces such differences. In the first experiment, subjects estimated the cumulative means of test scores of two groups of students. The experimental manipulation involved a gradual shift of the true mean of one group either towards or away from the true mean of the other group. As predicted, changes of estimates were larger when the two means became more dissimilar than when they became more similar. The second experiment involved otherwise identical procedures, but the variance in one category was increased while the mean remained stable. Subjects perceived an illusory change of the mean away from the comparison category. It is suggested that accentuation effects of this kind may limit the reduction of social stereotypes.     

An examination of stimulus technology level and preference displacement during multiple stimulus without replacement preference assessments

Researchers have observed that preference for edible items may displace preference for leisure items when items from the stimulus classes are assessed together within multiple stimulus without replacement (MSWO) preference assessments. The current study extends previous research by examining patterns of preference and displacement when assessing preference for high-tech and low-tech leisure items. We conducted three separate MSWO preference assessments; one assessing low-tech items, another assessing high-tech items, and a combined assessment (using the top four high- and low-tech items from the previous assessments) to test for displacement. Preference for high-tech items fully or partially displaced preference for low-tech items in five of eight participants. We then conducted concurrent and single operant reinforcer assessments using the highly preferred high-tech and low-tech items. Reinforcer assessment results demonstrated similar levels of responding for the highest preferred high-tech and low-tech items, indicating that combining high- and low-tech items within preference assessments may influence the validity of results.     

Inhibited power motivation and persuasive communication: a lens model analysis

The authors tested the hypothesis that after motive arousal, individuals with an inhibited power motive (IPM) would excel at a persuasive task and explored the behavioral strategies IPM individuals use to that purpose. Sixty-eight participants presented their point of view on a controversial subject to another person. Power motivation and inhibition were both assessed by a picture-story test. Prior to their presentation, half of the participants imaginatively explored the ensuing task. The other half was assigned to a no-imagery control condition. Lens model analysis of videotaped presentations revealed that IPM participants in the imagery condition were judged to be the most persuasive of all participants. This interactive effect of power motivation, inhibition, and imagery condition was accounted for by three behavioral cues: verbal fluency, gesturing, and eyebrow lifts. No comparable effects emerged among no-imagery participants.     

Local contextual cuing in visual search

Previous research has indicated that covariations between the global layout of search displays and target locations result in contextual cuing: the global context guides attention to probable target locations. The present experiments extend these findings by showing that local redundancies also facilitate visual search. Participants searched for randomly located targets in invariant homogenous displays, i.e., the global context provided information neither about the location nor about the identity of the target. The only redundancy referred to spatial relations between the targets and certain distractors: Two of the distractors were frequently presented next to the targets. In four of five experiments, targets with frequent flankers were detected faster than targets with rare flankers. The data suggest that this local contextual cuing does not depend on awareness of the redundant local topography but needs the redundantly related stimuli to be attended to.     

The Semantic Theory of Truth: Field’s Incompleteness Objection

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection.