Erkenntnistheorie der Zahldefinition und philosophische Grundlegung der Arithmetik unter Bezugnahme auf einen Vergleich von Gottlob Freges Logizismus und platonischer Philosophie (Syrian, Theon von Smyrna u.a.)

The epistomology of the definition of number and the philosophical foundation of arithmetic based on a comparison between Gottlob Frege's logicism and Platonic philosophy (Syrianus, Theo Smyrnaeus, and others). The intention of this article is to provide arithmetic with a logically and methodologically valid definition of number for construing a consistent philosophical foundation of arithmetic. The – surely astonishing – main thesis is that instead of the modern and contemporary attempts, especially in Gottlob Frege's Foundations of Arithmetic, such a definition is found in the arithmetic in Euclid's Elements. To draw this conclusion a profound reflection on the role of epistemology for the foundation of mathematics, especially for the method of definition of number, is indispensable; a reflection not to be found in the contemporary debate (the predominate ‘pragmaticformalism’ in current mathematics just shirks from trying to solve the epistemological problems raised by the debate between logicism, intuitionism, and formalism). Frege's definition of number, ‘The number of the concept F is the extension of the concept ‘numerically equal to the concept F”, which is still substantial for contemporary mathematics, does not fulfil the requirements of logical and methodological correctness because the definiens in a double way (in the concepts ‘extension of a concept’ and ‘numerically equal’) implicitly presupposes the definiendum, i.e. number itself. Number itself, on the contrary, is defined adequately by Euclid as ‘multitude composed of units’, a definition which is even, though never mentioned, an implicit presupposition of the modern concept ofset. But Frege rejects this definition and construes his own - for epistemological reasons: Frege's definition exactly fits the needs of modern epistemology, namely that for to know something like the number of a concept one must become conscious of a multitude of acts of producing units of ‘given’ representations under the condition of a 1:1 relationship to obtain between the acts of counting and the counted ‘objects’. According to this view, which has existed at least since the Renaissance stoicism and is maintained not only by Frege but also by Descartes, Kant, Husserl, Dummett, and others, there is no such thing as a number of pure units itself because the intellect or pure reason, by itself empty, must become conscious of different units of representation in order to know a multitude, a condition not fulfilled by Euclid's conception. As this is Frege's main reason to reject Euclid's definition of number (others are discussed in detail), the paper shows that the epistemological reflection in Neoplatonic mathematical philosophy, which agrees with Euclid's definition of number, provides a consistent basement for it. Therefore it is not progress in the history of science which hasled to the a poretic contemporary state of affairs but an arbitrary change of epistemology in early modern times, which is of great influence even today. This revised version was published online in August 2006 with corrections to the Cover Date.     

Neuroendocrine hemisphere asymmetries: Salivary cortisol secretion during lateralized viewing of emotion-related and neutral films

The study set out to examine whether the cerebral hemispheres differ in their ability to regulate cortisol secretion during emotion-related situations. One hundred twenty-three adult subjects were shown either an emotionally aversive or a neutral film in the left or right hemisphere by means of a technique for lateralizing visual input that allows prolonged viewing while permitting free ocular scanning. The film-related changes of cortisol secretion were determined by salivary cortisol radioimmunoassay. Right hemispheric viewing of the emotionally aversive film resulted in a significantly higher increase of cortisol secretion than left hemispheric viewing of the same film. No such differences were observed with respect to the neutral film. Comparing the effects of the two films separately for each hemisphere revealed that only the right hemisphere was able to respond neuroendocrinologically in a different manner to the emotional and the neutral film. Therefore, it is concluded that cortical regulation of cortisol secretion in emotion-related situations is under primary control of the right hemisphere. The potential implications of asymmetric control of cortisol secretion with respect to the pathogenesis of psychosomatic and immunological disorders are discussed.     

Exposure effects and associative learning

The contributions of initial stimulus affect and of associative learning to the effects of repeated stimulus exposures were examined in two experiments. Stimuli that were initially positive and stimuli that were initially negative were presented for different number of times, and subjects rated these stimuli afterward on a number of affective dimensions. In all cases, except when negative affect was associatively paired with every stimulus exposure, affective responses became increasingly more positive with increasing exposures. The results were taken to indicate that the exposure effect can overcome an initially negative stimulus affect when the conditions of the mere exposure hypothesis are satisfied. Initial stimulus affect and associative learning of affect were shown to be independent factors, the first influencing the intercept of the exposure function, the second its slope.     

Ambient Green and Creativity

This research examined an important applied question: whether viewing ambient green (relative to red) on the wall of a workspace would facilitate creativity. A methodologically sound experiment revealed no influence of green on creativity. Care must be taken when interpreting a null result, but these data do not provide support for the presence of a relation between ambient green and creativity. This research also highlights the need for more research in the area of ambient color and psychological functioning, and the need for caution regarding the tendency to move to real-world recommendations before a firm empirical base is established.     

Quantifying disablers in reasoning with universal and existential rules

People accept conclusions of valid conditional inferences (e.g., if p then q, p therefore q) less, the more disablers (circumstances that prevent q to happen although p is true) exist. We investigated whether rules that through their phrasing exclude disablers evoke higher acceptance ratings than rules that do not exclude disablers. In three experiments we re-phrased content-rich conditionals from the literature as either universal or existential rules and embedded these rules in Modus Ponens and Modus Tollens inferences. In Experiments 2 and 3, we also used abstract rules. The acceptance of conclusions increased when the rule was phrased with “all” instead of “some” and the number of disablers had a higher impact on existential rules than on universal rules. Further, the effect of quantifier was more pronounced for abstract rules and when tested within subjects. We discuss the relevance of phrasing, quantifiers and knowledge on reasoning.