G I Wall; The Concept of Vocational Education, Journal of Philosophy of Education, Volume 2, Issue 1, 30 May 2006, Pages 51–65, https://doi.org/10.1111/j.1467-9.

It is common knowledge that many problems in contemporary physics, particularly in microphysics and cosmology, present various infinities of which it is difficult to dispose, and that their role in mathematics is so considerable that it is often defined as the discipline of the infinite. Therefore it would be difficult to deny that infinity exists. But it is just as well known that, over the entire history of science, recognition of infinity has resulted in various difficulties, contradictions, aporias, antinomies, paradoxes (...) — in a word, "much that is impossible," as Aristotle puts it. As phrased by one of the outs tanding mathematicians of the last century, David Hilbert, infinity offers a real challenge to our thinking. (shrink)

In recent years, as a result of the extensive employment of the ideas and methods of mathematical logic in cybernetics and computer mathematics here and abroad, there has been a noticeable rise in interest in the methodological problems of this science. One of these is the problem of the relations between mathematical logic and traditional and even modern formal logic. However, when this problem is discussed in our philosophical literature it appears to us that three of its significant factors are (...) neglected by many writers. (shrink)

In the system of the philosophical and sociological ideas of the Frankfurt School the "critical theory" of society occupies the central place. In the "critical theory" are interwoven all the most significant aspects of the philosophical, economic, political, sociological, psychological, aesthetic, and ethical ideas dealt with by the representatives of this school. And therefore it is not accidental that the concept of the "critical theory" of society is employed frequently as a synonym of the social philosophy of the Frankfurt School. (...) The multi-leveled problematique of the "critical theory" of society, and the contradictoriness of the theoretical positions of its adherents, complicate critical analysis. Therefore, the explanation of its methodological orientation, which can help us to understand better the existence and actual philosophical nature of this theory, has important significance for our discussion. (shrink)

The problem of self-knowledge, originally ethnic, and then national, always excited and continues to worry humanity. At different times, she was sharper, then she calmed down, then stepped forward, then she became one in line with other issues of political, economic and social life. But this problem was inevitable. It was one of the sources of the spirit and activities of the people.