13.1 Logical paradoxes Paradoxes and development of logic

It is known that it is often more important and more difficult to formulate a problem than to solve it. “In science,” wrote the English chemist F. Soddy, “the task, properly set, more than half solved. The process of mental preparation, which is necessary for finding out that a certain task exists, often takes more time than solving the problem itself. ”

The forms in which the problem situation is manifested and realized are very diverse. Not always, she finds herself in the form of a direct question that arose at the very beginning of the study. The world of problems is as complex as the process of cognition that generates them. Identifying problems is connected with the very essence of creative thinking. Paradoxes are the most interesting case of implicit, problem-free ways of posing problems. Paradoxes are common in the early stages of the development of scientific theories, the first steps in a still unexplored area are drawn, and the most general principles of approach to it are groped.

In a broad sense, a paradox is a position that is in sharp disagreement with generally accepted, well-established, orthodox opinions. “Generally accepted opinions and what they consider to be a matter of long resolved deserve research most often” (G. Lichtenberg). Paradox - the beginning of such a study.

The paradox in its narrower and special meaning is two opposing, incompatible statements, for each of which there are seemingly convincing arguments.

The harshest form of paradox is antinomy, reasoning, proving the equivalence of two statements, one of which is the negation of the other.

The most famous are the paradoxes in the most rigorous and exact sciences - mathematics and logic. And it is no coincidence.

Logic - abstract spider. There are no experiments in it, not even facts in the usual sense of the word. Building its systems, logic proceeds, ultimately, from an analysis of real thinking. According to the results of this analysis are synthetic, undifferentiated. They are not statements of any particular processes or events that the theory should have explained. Obviously, such an analysis cannot be called observation: a specific phenomenon is always observed.

Constructing a new theory, a scientist usually goes from facts, from what can be observed in experience. No matter how free his creative fantasy is, it must reckon with one indispensable circumstance: a theory makes sense only if it agrees with the facts relating to it. A theory that diverges from facts and observations is far-fetched and has no value.

But if there are no experiments in logic, no facts and no observation itself, then what is the restraint of logical fantasy? What, if not facts, factors are taken into account when creating new logical theories?

The discrepancy between the logical theory and the practice of actual thinking is often found in the form of a more or less acute logical paradox, and sometimes even in the form of a logical antinomy, which speaks of the internal inconsistency of the theory. This explains the importance attached to paradoxes in logic, and the great attention that they use in it.