What the Liar Taught Achilles

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.     

When Hyperpropositions Meet ...

With each proposition P we associate a set of proposition (a hyperproposition) which determines the order in which one may retreat from accepting P, if one cannot fully hold on to P. We first describe the structure of hyperpropositions. Then we describe two operations on propositions, subtraction and merge, which can be modelled in terms of hyperpropositions. Subtraction is an operation that takes away part of the content of a proposition. Merge is an operation that determines the maximal consistent content of two propositions considered jointly. The merge operation gives rise to an inference relation which is, in a certain sense, optimally paraconsistent.     

Neuropsychological Characteristics of Adolescents With Conduct Disorder: Association With Attention-Deficit–Hyperactivity and Aggression

The purpose of this study was to determine whether an association exists between neuropsychological deficits and conduct disorder (CD) with and without concurrent attention-deficit–hyperactivity disorder (ADHD). In addition, we explored the differential neuropsychological performance of aggressive and nonaggressive CD adolescents and the combined effect of this behavioral status and ADHD on performance. Fifty-nine adolescents (mean age of 15.4 years) who met the criteria for CD were compared with 29 controls comparable in age, gender, and socioeconomic status. A neuropsychological battery of current tests measuring executive functions and a battery of language tests were used in the study. Multivariate analyses showed that, compared with controls, CD adolescents had significantly lower verbal skills but did not differ on executive function measures. However, the lower verbal performance of CD adolescents is not explained by the existence of a CD subgroup with concomitant ADHD or aggressiveness. The study confirms with a sample of CD adolescents the association between verbal deficits and antisocial behavior when socioeconomic status is controlled. Our results also demonstrate that CD per se can be a sufficient condition for such deficits.     

Familiarity and pronounceability of nouns and names

Ratings of familiarity and pronounceability were obtained from a random sample of 199 surnames (selected from over 80,000 entries in the Purdue University phone book) and 199 nouns (from the Ku?era-Francis, 1967, word database). The distributions of ratings for nouns versus names are substantially different: Nouns were rated as more familiar and easier to pronounce than surnames. Frequency and familiarity were more closely related in the proper name pool than the word pool, although both correlations were modest. Ratings of familiarity and pronounceability were highly related for both groups. A production experiment showed that rated pronounceability was highly related to the time taken to produce a name. These data confirm the common belief that there are differences in the statistical and distributional properties of words as compared to proper names. The value of using frequency and the ratings of familiarity and pronounceability for predicting variations in actual pronunciations of words and names are discussed.     

Why Dynamical Self-Excitation Is Possible

In Pérez Laraudogoitia (1996), I introduced a simple example of a supertask that involved the possibility of spontaneous self-excitation and, therefore, of a particularly interesting form of indeterminism in classical dynamics. Alper and Bridger (1998) criticised (among other things) this result. In the present article, I answer their criticisms. In what follows I assume familiarity both with Pérez Laraudogoitia (1996) and Alper and Bridger’s subsequent article. This revised version was published online in June 2006 with corrections to the Cover Date.     

Vienna Indeterminism: Mach,Boltzmann, Exner

The present paper studies a specific way of addressing the question whether the laws involving the basic constituents of nature are statistical. While most German physicists, above all Planck, treated the issues of determinism and causality within a Kantian framework, the tradition which I call Vienna Indeterminism began from Mach’s reinterpretation of causality as functional dependence. This severed the bond between causality and realism because one could no longer avail oneself of a priori categories as a criterion for empirical reality. Hence, an independent reality criterion had to be sought, a problem which all three physicists to be studied solved in different ways that were mainly conditioned by their different concepts of probability. In order to prevent a dissipation of intuited facts, Mach had to resort to a principle of unique determination as his reality criterion, especially when discussing the Principle of Least Action. Giving theories more independence, Boltzmann understood atomism as property reduction to precisely defined theoretical entities and their interactions. While this served as a relative reality criterion, he also advocated a constructivist one because atomism was already implied by our finitary reasoning power. Finally, Exner contemplated the idea that all apparently deterministic laws are only a macroscopic limit of an irreducible indeterminism, because by adopting the frequency interpretation, observable collectives could be considered as the real basic entities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Every Finitely Reducible Logic has the Finite Model Property with Respect to the Class of ♦-Formulae

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators.     

Perceptual restoration of missing sounds in a group of hallucinating schizophrenics.

17 subjects diagnosed with schizophrenia and having auditory hallucinations in their case history were compared with 15 control subjects in an experiment on perceptual restoration. A tone pattern was presented, then interrupted by noise, under conditions such that the tone pattern could be heard as going on continuously (restoration). A series of 16 stimuli with a distractor of varying amplitude (noise) were presented. Healthy controls reliably reported restoration in Presentations 9 and 10. Four schizophrenics reported no restoration at all. Three of them reported restoration earlier than controls, and four others reported it later than controls and continued to report the phenomenon after a point at which no healthy controls did. Six other presented an irregular pattern of response to the phenomenon. The results are discussed with respect to the neurophysiological functioning of the auditory pathway and schizophrenic symptoms.     

Are European and American golf players different? Reply to Engelhardt (1997)

Analysis of 1998 statistics for individual performance in the PGA European Tour yielded significant differences between some shot-making skills (drive distance, total driving, greens in regulation, and sand saves) between the top 10 and bottom 10 money winners, replicating (with partially different results) a result found for the 1995 American PGA Tour by Engelhardt.