7.4 Unity of logic

The considered sections of non-classical logic do not exhaust, of course, the whole variety of existing logical systems. Logic as a science is one. However, it is composed of many more or less private systems, none of which can claim to reveal the logical characteristics as a whole. In this aspect, modern logic is different from traditional logic. The latter did not know any many "logic". The problem of bringing together the fragmentary descriptions of thinking that are given by separate logical systems did not face it at all.

The intensive development of logic is accompanied by the expansion and enrichment of its apparatus, the emergence of new sections and systems. This differentiation should not at the same time overshadow those ideas and connections that transform a continuously expanding set of logical systems into a single science.

The unity of logic is manifested, first of all, in the fact that the individual “logic” that are part of it are used in the description of substantial logical processes by the same research methods. All these “logics” are diverted from the specific content of statements and conclusions and operate only with their formal, structural content. Each of them is a system that uses the language of symbols and formulas and is built in accordance with some common principles for all systems. And finally, the constructed “logic” raises a number of questions in the case of each system: is there a contradiction in it, does it cover all the truths of the kind in question, etc.

There are certain connections between different logical systems. Some systems may be equivalent to others, or included in them, or be their generalization, etc.

The unity of logic is also manifested in the fact that different "logic" do not contradict each other: the laws of one of them cannot be the negation of laws adopted in the other. This is true even for systems that can be called competing, since they describe the same reasoning processes in different ways. There are, as we have seen, “logic” that include the law of the excluded middle. There are also systems - and there are quite a few of them - designed to describe almost the same types of reasoning, but not including this law. In the infinite variety of logical systems there are not, however, such “logics” who proclaim the negation of the law of the excluded middle as their law.

The idea that a single modern logic is composed of a large number of individual “logics”, if unusual, then only in the form of its expression. A similar statement is true in the case of any developed science, say, physics or mathematics. They are also made up of many different theories, only in aggregate and in complex dynamic relationships that make up a kind of unity, called physics or mathematics.