И.Кант и финитная установка Д. Гильберта.

Аннотация

The problem under consideration concerns the question of whether examined by K.Goedel an extension of finitistic point of view would be the way out beyond the limits of knowledge by means of concept constructing.

An idea is pursued that D.Hilbert's finitistic point of view underlie the Kantian idea of demarcating the knowledge obtained in accordance with concepts and the knowledge obtained by concepts constructing. The clue of understanding genuine D.Hilbert's proposals is the notion of pure contemplation while following along the lines of Kant's treatment.

In Hilbert's approach ideal elements play the role of transcendental ideas of reason in Kantian interpretation. An indispensable condition of introducing ideal elements would therefore be the requirement of their eliminability from the context of the whole theory (see [3, ch. VJ). Thus their introduction does not mean the way out beyond the limits of finitistic point of view.

It is shown that the extension of Hilbert's finitistic point of view intends the deviation from the consecutive nominalism in philosophy of mathematics. An idea is preserved, the "schematism" of I.Kant's pure contemplation, and meanwhile an extension in question intends the denial of Kantian idea of the representation of the general in concrete in case of yielding the respective notion of contemplation.