LUKASIEWICZ'S CAUSAL INTERPRETATION OF LOGICAL FATALISM AND ROBINSON'S NONSTANDARD ANALYSIS
Vladimir Moiseevich Reznikov1,2
1Institute of Philosophy and Law, SB RAS, 8, Nikolaev st. , Novosibirsk, 630090
2Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
Keywords: причина, принцип причинности, транзитивность, бесконечность, факт, событие, нестандартный анализ Робинсона, гиперреальные числа, cause, causality principle, transitivity, infinity, fact, event, nonstandard analysis of Robinson, hyper-real numbers
Abstract
The article dealing with foundations of Łukasiewicz’s causal model of logical fatalism defines a relation of global transitivity. This relation means that in a succession of causes, each new event is the cause for all following events. We substantiate that Lukasiewicz's interpretation is not quite adequate for describing fatalism, since it does not take into account the influence of background factors, which may be neutral with regard to the occurrence of new events or prevent them, but they do not necessarily contribute their occurrence. We show that the solution of the problem of logical fatalism on the basis of ineffability of the smallest number following one half through real numbers proposed by Lukasiewicz has an ad hoc character. Thus, in Robinson's non-standard analysis, hyper-real numbers are closer to positive numbers than real numbers, so the unknown number equals the sum of one half and a hyper-real number.
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