Chapter 6: The Reasoning Process

Abstract

The main element of thinking that we have singled out—analysis through synthesis that detects more and more new properties in the analyzed objects when they are incorporated into new connections—is also highly important for an understanding of the reasoning for a proof and the derivation in the course of reasoning of more and more new propositions. It contains the key to the answer to a question that has constantly come up in the history of scientific and philosophical thought: How is it possible in reasoning, for example regarding geometry, based on a finite number of premises, to arrive at an infinite number of more and more new deductions? The answer to this question lies, above all, in the fact that in the course of any reasoning process, including a deductive one—which, however, is never performed in real life separately from induction—more and more new premises are introduced that are not given in the original conditions. These new premises are formed by means of an analysis that is done through synthesis, an analysis that, by incorporating objects into more and more new connections, “scoops out” more and more new content from them, “turns them around,” as it were, to their other side, and makes them function in a new capacity, with a new conceptual character. For example, in the conditions of a problem, it is only given that a certain segment is a bisector. By correlating the segment with other segments, angles, and figures it is determined that that segment is a median, then that it is also a transversal, and so forth. Each of these premises that emerge in the process of analyzing the problem represents a new, minor premise that is introduced into the reasoning by the course of analysis. The thinking process itself creates prerequisites and conditions for its further progress. The reason that the necessary reasoning for a proof and the derivation of certain propositions from others can lead to more and more new knowledge and deductions is that this process yields more and more new data and new, “minor” premises.