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EN
Among philosophical motifs brought up by Abp Józef Życiński (1948-2011), a crucial issue is the relation between the world of concretum, its psychological perception by people and the field of rationality, also called the field of the potential or the rational structure of the universe (by the co-author of ‘Universe and Philosophy’). Concrete objects seem to be more real than all sorts of theoretical objects of science, such as cosmological constants. Our mind, which was formed by the evolution, is responsible for that state of affairs. That mind was created in order to enable us survival, not in order to accurately learn the world. When closely examining relations between the three above mentioned spheres, there clearly appears an unusual role of abstract bonds of ontological structure of the world. In the arcticle, I am attempting to look at Życiński’s analysis from the angle of mental experiments presented by Stanislaw Lem, in which people meet earlier unknown forms of life (eg. solarian ocean) and enter interactions with them.
PL
In this article Whitehead’s philosophy of mathematics is characterized as a Structural Second-Order Platonism and it is demonstrated that the Whiteheadian ontology is consistent with modern formal approaches to the foundation of mathematics. We follow the pathway taken by model-theoretically and semantically oriented philosophers. Consequently, it is supposed that all mathematical theories (understood as deductively closed set of sentences) determine their own models. These models exist mind-independently in the realm of eternal objects. From the metatheoretical point of view the hypothesis (posed by Józef Życiński) of the Rationality Field is explored. It is indicated that relationships between different models can be described in the language of modal logics and can further be axiomatized in the framework of the Second Order Set Theory. In conclusion, it is asserted that if any model (of a mathematical theory) is understood, in agreement with Whitehead’s philosophy, as a collection of eternal objects, which can be simultaneously realized in a single actual occasion, then our external world is governed by the hidden pattern encoded in the field of pure potentialities which constitute the above mentioned Field of Rationality. Therefore, this work can be regarded as the first step towards building a Logic of Rationality.
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