Arithmaetical Platonism: Reliability and Judgement-Dependence

Philosophical Studies -     

Further Antidotes: a Response to Gundersen

In my 'Dispositions and Antidotes', The Philosophical Quarterly , 48 (1998), I raise an objection to the conditional analysis of dispositions, both in its simple formulation and in a more sophisticated version due to David Lewis, The Philosophical Quarterly , 47 (1997). The objection suggests that a disposition may be continuously present and the appropriate stimulus occur without the manifestation occurring, because some outside influence, an antidote, interferes. Gundersen in The Philosophical Quarterly, 50 (2000), argues that my objection rests on an equivocation about which object possesses the disposition and more particularly on an equivocation about the context in which the events referred to take place, and that when the equivocation is resolved the counter-example disappears. I respond by showing that the counter-example does remain if we take contextual and mereological issues into account, and I conclude by remarking that the difference with Lewisdepends on whether certain features are seen as significant for the semanticsand metaphysics of dispositions or as merely characteristic of the pragmaticsof common usage.     

The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability

In theory, the greatest lower bound (g.l.b.) to reliability is the best possible lower bound to the reliability based on single test administration. Yet the practical use of the g.l.b. has been severely hindered by sampling bias problems. It is well known that the g.l.b. based on small samples (even a sample of one thousand subjects is not generally enough) may severely overestimate the population value, and statistical treatment of the bias has been badly missing. The only results obtained so far are concerned with the asymptotic variance of the g.l.b. and of its numerator (the maximum possible error variance of a test), based on first order derivatives and the asumption of multivariate normality. The present paper extends these results by offering explicit expressions for the second order derivatives. This yields a closed form expression for the asymptotic bias of both the g.l.b. and its numerator, under the assumptions that the rank of the reduced covariance matrix is at or above the Ledermann bound, and that the nonnegativity constraints on the diagonal elements of the matrix of unique variances are inactive. It is also shown that, when the reduced rank is at its highest possible value (i.e., the number of variables minus one), the numerator of the g.l.b. is asymptotically unbiased, and the asymptotic bias of the g.l.b. is negative. The latter results are contrary to common belief, but apply only to cases where the number of variables is small. The asymptotic results are illustrated by numerical examples.This research was supported by grant DMI-9713878 from the National Science Foundation.     

On the nature of the foreign accent syndrome: A case study

A detailed acoustic analysis was conducted of the speech production of a single patient presenting with the foreign accent syndrome subsequent to a left-hemisphere stroke in the subcortical white matter of the pre-rolandic and post-rolandic gyri at the level of the body of the lateral ventricle. It was the object of this research to determine those changes which contribute to the perception of a "foreign accent." A number of acoustic parameters were investigated, including features of consonant production relating to voice, place, and manner of articulation, vowel production relating to vowel quality and duration, and speech melody relating to fundamental frequency. The results indicated that many attributes which might have contributed to the foreign quality of the patient's speech were similar to those of normal English speakers. However, a number of critical elements involving consonant and vowel production and intonation were impaired. It was hypothesized that the acoustically anomalous features are linked to a common underlying deficit relating to speech prosody. It is suggested that the normal listener categorizes this speech pattern as a foreign accent because the anomalous speech characteristics, while not a part of the English phonetic inventory, reflect stereotypical features which are a part of the universal phonetic properties found in natural language.