Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics

We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes' own earlier work in functional analysis. Connes described the hyperreals as both a "virtual theory" and a "chimera", yet acknowledged that his argument relies on the transfer principle. We analyze Connes' "dart-throwing" thought experiment, but reach an opposite conclusion. In S, all definable sets of reals are Lebesgue measurable, suggesting that Connes views a theory as being "virtual" if it is not definable in a suitable model of ZFC. If so, Connes' claim that a theory of the hyperreals is "virtual" is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren't definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in his Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes' criticism of virtuality. We analyze the philosophical underpinnings of Connes' argument based on Goedel's incompleteness theorem, and detect an apparent circularity in Connes' logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace (featured on the front cover of Connes' magnum opus) and the Hahn-Banach theorem, in Connes' own framework. We also note an inaccuracy in Machover's critique of infinitesimal-based pedagogy.Comment: 52 pages, 1 figur

Critical Care Nursing of the Elderly, 2nd Edition

Meredith Wallace [Kazer] (with E. Flaherty) is a contributing author, Assessment and Management in Pain . Book description: This volume, like the first edition, is an important milestone in the field of gerontological nursing, reflecting the growing number of nurses actively involved in geriatric care and clinical research in hospitals. Thoroughly revised and updated, the second edition provides the collective thinking of experts who strive to ask and answer such key questions as: Who should receive advanced technological care? When should care stop? and Who determines vitality? The comprehensive coverage includes sound guidelines for nursing assessment and management; basic clinical issues with elderly populations; specialized practice protocols and advances; and lively discussion of social and policy issues.https://digitalcommons.fairfield.edu/nursing-books/1066/thumbnail.jp

Psychometric properties of the Flemish translation of the NEECHAM Confusion Scale

BACKGROUND: Determination of a patient's cognitive status by use of a valid and reliable screening instrument is of major importance as early recognition and accurate diagnosis of delirium is necessary for effective management. This study determined the reliability, validity and diagnostic value of the Flemish translation of the NEECHAM Confusion Scale. METHODS: A sample of 54 elderly hip fracture patients with a mean age of 80.9 years (SD = 7.85) were included. To test the psychometric properties of the NEECHAM Confusion Scale, performance on the NEECHAM was compared to the Confusion Assessment Method (CAM) and the Mini-Mental State Examination (MMSE), by using aggregated data based on 5 data collection measurement points (repeated measures). The CAM and MMSE served as gold standards. RESULTS: The alpha coefficient for the total NEECHAM score was high (0.88). Principal components analysis yielded a two-component solution accounting for 70.8% of the total variance. High correlations were found between the total NEECHAM scores and total MMSE (0.75) and total CAM severity scores (-0.73), respectively. Diagnostic values using the CAM algorithm as gold standard showed 76.9% sensitivity, 64.6% specificity, 13.5% positive and 97.5% negative predictive values, respectively. CONCLUSION: This validation of the Flemish version of the NEECHAM Confusion Scale adds to previous evidence suggesting that this scale holds promise as a valuable screening instrument for delirium in clinical practice. Further validation studies in diverse clinical populations; however, are needed.status: publishe

Psychometric properties of the Flemish translation of the NEECHAM Confusion Scale

Research articl