Philosophy, Mathematics, Linguistics: Aspects of Interaction (PhML 2012)
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This contribution to a volume on the“ultimate why-question” discusses ambiguities in Leibniz’s formulation of the question, “[. . . ] pourquoi il y a plus tôt quelque chose que rien”. This formulation poses two problems: Leibniz does not explain how to understand the concepts of “something” and “nothing”. And it is not clear, whether “something” and “nothing” are contradictory opposites, so that there is either nothing or something, or whether both concepts denote principles which are effective in the world at the same time. My analysis rests on the hypothesis that the relevant context for Leibniz’s question is the theology of creation.
Hence, the paper compares eight different approaches to “creation from nothing” (Thomists, Scotists, Taurellus, Lubinus, Timpler, Keckermann, Kircher, Knorr von Rosenroth, van Helmont). Candidates for the nihil the world was created from include absolute non-being, thoughts in God’s mind, unformed matter, imaginary space, or a self-contraction of the Divine spirit. These different approaches can be translated into different versions of the “ultimate why-question”. The paper concludes that Leibniz’s formulation contains a comparison between two Divine acts of creation, because not only “something”, but “nothing” as well owes its subsistence to the Divine will. This rises substantial questions: either God created first an imperfect entity in order to create the world as a whole, or Leibniz subscribes to an emanative understanding of creation that either levels the difference between creation and (natural) generation or is based on misunderstanding God as a material entity.
The form whose main function is to express indirect commands, called the third person Imperative, Jussive or Exhortative, when compared to the prototypical (second person) Imperative, shows semantic and formal similarities and distinctions at the same time. The study describes formal and functional patterns of Jussive and places this category within the typology of the related categories, such as Imperative and Optative, based on data from six East Caucasian languages (Archi, Agul, Akhvakh, Chechen, Icari and Kumyk). Five formal patterns of Jussive are attested in these languages, including a specialized form, constructions derived from want, from tell him to do and from make him do and the Optative. Jussive forms may express such meanings as third person command, indirect causation, permission, indifference towards the accomplishment of an action and an assumption. While the Jussive is crucially different from the second person Imperative in that it introduces a third participant, this article shows that it is the addressee, not a third person, who is the central participant of a Jussive situation from both formal and functional points of view.
This article presents the results of a pilot study assessing the level of formation of a stochastic competence among teachers of mathematics. Besides, the indicators that reflect the competence of formation of stochastic students are identified and ranked in order of importance. Different instruments (questionnaires, tests, assignments) have been used to solve the problem under study.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.