Lecture
In the XIX century. The concept of “extended” formal logic has become widespread. Its supporters sharply shifted the center of gravity of logical research from studying the correct methods of reasoning to developing problems of the theory of knowledge, causality, induction, etc. The themes that were interesting and important in their own right, but not directly related to them, were introduced into logic. Actually the logical problematics receded into the background. The methodological problems that had supplanted it were interpreted, as a rule, in a simplified way, without taking into account the dynamics of scientific knowledge.
With the development of mathematical logic, this trend in logic, which confused it with superficially understood methodology and penetrated by psychologism, gradually became withering.
An echo of the idea of "extended" logic is, in particular, a conversation about the so-called basic laws of thinking, or the basic laws of logic.
According to this “broad” interpretation of logic, the basic laws are the most obvious of all the statements of logic, which are something of the axioms of this science. They form, as it were, the foundation of logic upon which all its building rests. They themselves are not deducible from anywhere, and they do not require any support due to their exceptional obviousness.
Under this extremely vague concept of fundamental laws could bring the most diverse ideas. Usually the law of contradiction, the law of the excluded middle and the law of identity were assigned to such laws. Often the law of sufficient reason and the principle of “about all and not one” were added to them.
According to the last principle, what has been said about all the objects of some kind is true about some of them and about each one individually; inapplicable to all subjects is also wrong for some and some of them.
Indeed it is. But it is completely incomprehensible how this truth relates to the foundations of logic. In modern logic, it is one of the infinite set of its laws.
The law of sufficient reason is generally not a principle of logic - neither basic nor secondary. He demands that nothing be taken for nothing, on faith. In the case of each statement, the reasons why it is considered true should be indicated. Of course, this is no law of logic. Most likely, this is some methodological principle, not particularly clear, but in general heavenly useful.
The law of identity, as interpreted in the “extended” logic, also had only a remote resemblance to the corresponding logical law. In the process of reasoning, the values of concepts and statements should not be changed. They must remain identical with themselves, otherwise the properties of one object imperceptibly will be ascribed to completely different. To avoid this, it is necessary to allocate the objects under discussion on fairly stable grounds.
The requirement not to change or substitute values in the course of the reasoning is, of course, absolutely true. But it is equally obvious that it does not belong to the laws of logic.
As for the laws of contradiction and the excluded middle, they also acquired a pronounced methodological bias in the framework of the “extended” logic. The first law usually turned into a ban on saying “yes” and “no” at the same time, asserting and denying the same thing about the same subject, considered in the same respect. The second was replaced by the requirement that the solution of each question be brought to full certainty. The analysis should be considered complete only when the truth of either the position in question or its negation is established.
These are useful tips, but not laws of logic.
As a result, it can be said that the reasoning of the “extended” logic about the basic laws of thinking obscures and confuses the problem of logical laws.
As modern logic has clearly shown, the laws of logic are infinite. Dividing them into core and non-core is illegal.
The substitution of logical laws by vague methodological advice is also untenable. There is no foundation in the form of a short list of fundamental principles in the science of logic. This is no different from all other scientific disciplines.
The basic principles from which the rest of the content would be derived or on which none of mathematics, psychology, or any other science has any other science. Sometimes, however, they talk about such principles or about the foundation of any branch of knowledge. In the XIX century. The term "basic principles" often appeared in the titles of scientific books. But all this should not be taken literally and straightforwardly.
It is surprising that the conversation about the basic principles of logic sometimes arises even in our time.
There is another prejudice that has been cultivated by “extended” logic and has survived to our days — it is a discussion of the laws of logic in complete separation from all other important topics and concepts, and even in their isolation from each other.
When reading old books on logic, one gradually gets the impression of fragmentation, non-commitment and incoherence of the topics covered in them. If we remove from the old textbook of logic, say, the section on the law of the excluded middle, this will not affect the interpretation of other laws. Any mention of fundamental laws can be eliminated altogether from such a textbook. And while all the rest will not even need to rephrase.
Logical laws are interesting, of course, by themselves. But if they really are important elements of the mechanism of thinking - and this is undoubtedly so - they must be inextricably linked with other elements of this mechanism. And above all with the central notion of logic - the notion of logical following and, therefore, with the notion of proof.
Modern logic establishes such a connection. To prove an assertion means to show that it is a logical consequence of other assertions whose truth has already been established. The conclusion follows logically from the accepted assumptions, if it is connected with them by a logical law.
Without a logical law there is no logical following and there is no proof itself.
Comments
To leave a comment
Logics
Terms: Logics