Обзор круглого стола «Возможна ли современная трансцендентальная философия?», проведенного в рамках работы VII Российского философского конгресса
Kant's transcendentalism is associated with the study and substantiation of objective value as a human way of cognition as whole and individual kinds of our knowledge. This article is devoted to Kant’s understanding (substantiation) of mathematics as cognition via constructing of concepts. Unlike the natural sciences the mathematics is an abstract – formal cognition, “[its] thoroughness is based on definitions and axioms” [B754].
The article consequently analyzes each of these components. Mathematical objects are determined by the principle of Hume. Transcendentalism considers the question of genesis and ontological status of concepts. To solve them Kant suggests the doctrine of schematism, which is compared with the modern concepts of mathematics. We develop the dating back to Kant original concept of the transcendental constructivism (pragmatism) as the programme of substantiation of mathematics. We also give a brief comparison of the axiomatic method of Kant and Hilbert.
“Constructive” understanding of mathematical constructions (calculations) is a significant innovation of Kant. Thus mathematical activity is considered as a two-level system, which supposes a “descent” from the level of rational understanding to the level of sensual contemplation and a return “rise”. The article also examines the difference between the mathematical structures and logical proofs.
In his concept Kant highlights ostensive (geometric) and symbolic (algebraic) design. The article analyses each of them and shows that it is applicable to modern mathematics, in activity of which both types of Kant's constructing are intertwined.
This paper is devoted to Kant’s transcendental philosophy as a special type of philosophy (philosophizing), or the transcendental paradigm. For this purpose we introduce new methodological concepts as the transcendental shift, perspective and paradigm. The basis for our interpretation of transcendentalism is cognitive-semantic reading of the Critics and the theory of "two aspects". Transcendentalism is defined as a new «experimental» (Erfahrung) metaphysics and «transcendental» — as the intermedia domain (between the immanent and the transcendent) of reality, as the "instrumental" part of our cognition (consciousness).
The theory of consciousness adequately describing processes of human thinking is necessary for construction of the complete argumentation theory. We take for such theory Kant`s transcendental consciousness model, in which the important role belongs to schematic synthesis. The article suggests some modification of schematic synthesis — the image–image synthesis (image–concept (or schematic) synthesis vs. image–image synthesis). It is claimed that the image–image synthesis is fundamental for metaphorical thought the basic model of which is the theory of metaphor of I.A. Richards — M. Black.
The article contains an original attempt to create a transcendental theory (philosophy) of science (experience). The conceptual basis of the author’s position is the Kant’s transcendentalism as theory of experience and his original interpretation and development in new conditions. The author shows that the modern (postpositivistic and analytical) philosophy of science follow spirit of the Kant’s «Copernican revolution» as «the new method of thought» [CPR, B XVIII].
How is metaphysics possible? The answer to this question can be received by means of Kant’s transcendental method. According to Kant, the basis (background) of any metaphysics is metaphysica naturalis, which is conceived as human reason speculation demand to arise and solve questions that are beyond possible experience and exceed the limits of a current ‘physical’ situation. Thereby the man is homo metaphysicus (Aristotle. Kant). Possibility of metaphysica naturalis roots in the human faculty of imagination and is connected with our language, its metaphysics. There are two modus of the academic metaphysics. Possibility of metaphysica generalis is connected with presence in our language (resp. Mind) special metaphysical (ontologic) predicates (categories). Possibility of metaphysica specialis is connected with presence in our language (resp. Mind) wholeness, or encompassing totalities (comp. with the Encompassing of K. Jaspers).