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Lecture notes, cheat sheets
Logics. Logical laws (lecture notes)
Directory / Lecture notes, cheat sheets Table of contents (expand) LECTURE No. 14. Logical laws 1. The concept of logical laws The laws of logic have been known since ancient times - law of identity, non-contradiction and excluded middle. All of them were discovered by Aristotle. The law of sufficient reason was discovered by Leibniz. They are of great importance for science, they are the pillars of logic, because without these laws logic is unthinkable. logical laws - these are objectively existing and necessary applied rules for the construction of logical thinking. Like any laws of the surrounding world, discovered within the framework of science (for example, natural), the laws of logic are objective. Logical laws differ from the laws of jurisprudence in that they cannot be repealed or changed. Thus, they are characterized by constancy. You can compare the laws of logic, for example, with the law of universal gravitation. It exists independently of anyone's will. Therefore, logical laws are the same for everyone. However, despite the presence of common features with the laws of nature, logical laws have their own specifics. The laws of logic are the laws of correct thinking, but not of the surrounding world. As mentioned above, the laws of logic represent a kind of foundation for the science of logic. Everything in it is based on these fundamental rules. Sometimes they are also called principles, and their application is widespread. Consciously or unconsciously, every person in everyday life - at work, on vacation, in a store or on the street - applies logical laws in practice. Sometimes statements, whether by accident or design, do not obey logical laws. More often than not, this is immediately noticeable and, as they say, “catchy.” That is why many people talk about the uselessness of logic as a science - after all, it is always clear when a person makes his judgment incorrectly. However, we should not forget that, in addition to everyday life, where philistine logic is sufficient, there is science, which is characterized by a higher level of knowledge. This is where precision and correct thinking are needed. What can be forgiven in a simple conversation is unacceptable in a scientific discussion. And there should be no doubt about this. Just imagine for a moment a nuclear power plant designer drawing diagrams by eye, and the importance of logical laws becomes obvious. 2. The law of identity. Law of non-contradiction Identity law (a = a). To characterize it, it is first necessary to understand what identity is in general. In the most general sense Identity means equivalence, sameness. At the same time, it is rarely possible to talk about absolute identity, since it is difficult to find two completely identical objects. In this sense, it is logical to talk about the identity of an object with itself. However, there are pitfalls here too - the same object, taken at different periods of time, most likely will not be characterized by identity. For example, you can take a person at 3 years old, 20 and 60 years old. Obviously, this is the same person, but at the same time they are three “different” people. Therefore, absolute identity in the real world is impossible. But since the world does not live according to absolute laws, we can talk about identity, moving away from complete abstraction. The law of identity follows from what has been said above. It means that in the process of constructing judgments and statements, it is unacceptable to replace one object with another. That is, you cannot arbitrarily replace the subject from which the logical construction began with another. One cannot call objects identical that are not identical, and one cannot deny the identity of identical objects. All this leads to a violation of the law of identity. Also, a violation of the law of identity occurs when a person incorrectly names things. In this case, he can convey correct information, which nevertheless does not concern the named subject. There are cases when the subject is changed in a dispute. That is, the arguing imperceptibly move from a discussion of a previously chosen subject to a new one or narrow the concept of the subject to its linguistic expression. That is, they are no longer discussing the subject itself, but the words, phrases, etc. expressing it. This change can occur for various reasons. Here is the intent of one of the participants, and a mistake, also intentional or unintentional. Often the law of identity is violated when using ambiguous words. These can be pronouns, homonyms. For example, homonymous words in a sentence taken out of context are often difficult to limit to one or another of their meanings. That is, it is not clear in what sense the word was used. In this case, instead of one value, another can be taken, and then the law of identity will be violated. Often arising from ambiguity, violation of the law of identity also creates ambiguity, and with it confusion. Speaking about the law of identity and its violations, these violations must be named. The first one is called "change of concept" and means that the subject of the concept was lost, i.e., the originally understood meaning has changed. Substitution of the thesis - the second type. It means changing the thesis initially understood in the process of discussion. The law of identity is widely used not only within the framework of logic, but also by other, including applied, sciences: computer science and mathematics, physics, chemistry, jurisprudence, forensic science, etc. Law of non-contradiction. Probably, everyone in his life has encountered a situation when the subject he undertook to talk about turned out to be so difficult that the thread of reasoning soon slipped away and confusion began in his thoughts. This happens because the subject is not well known to the narrator or he has not made the necessary preparation. As soon as a clear “path” of reasoning is lost, contradictions begin. The reasoner can, often without noticing it, express contradictory judgments one after another. The law of non-contradiction speaks precisely about the inadmissibility of a contradiction between what was said earlier and what was said again. It is also a contradiction to attribute previously rejected properties to one and the same object, and vice versa. Such a contradiction is called formal-logical. Not to mention the time factor. In this case, it is of immediate importance. We are talking about the inadmissibility of a contradiction between two or more statements, that is, if it was previously approved, say, that an object has one or another feature, the subsequent denial of this feature is unacceptable. However, do not forget about time and the fact that everything in our world tends to change. So, a judgment is not contradictory, which, although it contains mutually exclusive information about the subject, but implies the same subject at different intervals of time. 3. Law of the excluded middle Law of the excluded middle associated with conflicting opinions. It means that there can be only two contradictory judgments, there cannot be a third. Hence the name of this law. If two judgments deny each other, one affirms something, and the other contradicts the existence of what is being affirmed, we can say that these judgments are contradictory. Each of these judgments is independent and is considered separately due to the fact that it contains information that denies the opposite judgment. Consideration of them in this regard is carried out in order to determine which of them is true and which is false. Since such judgments are completely mutually exclusive, that is, if one is true, the other is always false, there is no third option. That is, it means that there is no intermediate state between true and false. This means that there can be no third judgment regarding one object, reflecting the same properties that are reflected (affirmed or denied) by two contradictory judgments. For a more complete understanding of the issue, examples should be given. To begin with, consider the schematic reflections of the contradictory judgments: "No S is P" and "Some S are P"; "All S are P" and "Some S are not P"; "This S is P" and "This S is not P". As you can see, all three given pairs of judgments are, respectively, general, particular and singular, as well as contradictory (i.e., type A and non-A). The judgments "Yuri Gagarin is the cosmonaut who first flew into space" and "Yuri Gagarin is not the cosmonaut who first flew into space" are contradictory judgments. When considering the law of the excluded middle, the question always arises of its differences from the law of non-contradiction. This is due to the fact that both these laws apply to the contradictory judgments now considered. However, there is a difference between them. It becomes clear if one considers counter-judgments (for example, "All men have limbs" and "No man has limbs") judgments. The law of the excluded middle does not apply to them. 4. Sufficient reason Any assertion must have a basis. It is obvious. When one of the parties to a dispute claims something, the other often demands: "Justify." sufficient reason wherein is reliable information. Any true thought must be sufficiently substantiated. Of course, the absence of a sufficient reason does not entail the falsity of a judgment; it can be true. However, this fact remains unknown until justification is received. It must be said that only a true judgment needs justification. What is false cannot have sufficient reason at all. Despite the fact that in some cases there have been attempts to substantiate false judgments with varying success, this approach cannot be called correct. The law of sufficient reason is not expressed in the form of a formula, since there is no such formula. When we say that true information is a sufficient basis for a judgment, we mean various kinds of data based on reliable sources. For mathematics, these are digital expressions derived without errors using axioms, theorems, various systems that allow reliable calculations (such a system, for example, is the multiplication table). Information obtained on the basis of scientific laws will also be considered reliable. To substantiate a new judgment, one can use previously derived judgments, in relation to which it has been proven that they are true. The law of sufficient reason, perhaps more than any other, operates in the realm of human daily life, and also applies within various professions. This is due to the fact that in the process of cognition, a person first of all thinks about what the new, received information is based on. For example, you can often hear in the media that information was obtained "from reliable sources", or sometimes the expression "according to unverified data" is used. Of course, the law of non-contradiction and the excluded middle, as well as the law of identity, play a huge role in correct thinking. However, they seem to follow the law of sufficient reason. The need for them arises only when there is a substantiation of one or another fact, concept, judgment. What has been said should be attributed, of course, not to the scientific significance of the laws of logic, but rather to the necessity of these laws for the life and activity of the average person. Within the framework of this question, it is necessary to say about one feature that is characteristic of the logical reason and consequence in their relationship with the real reason and consequence. If in real life the foundation always comes first, and the consequence is derived from it, then in logic the opposite situation can take place. This is due to the order of things - in the real world, the foundation process first passes, and only then the consequence is derived from it. A person, who did not have the opportunity to observe the reason, can rely only on the consequence. Thus, having received a consequence, a person mentally, virtually can recreate the foundation. Author: Shadrin D.A. << Back: Truth and modality of judgments (Modality of judgments. Truth of judgments) >> Forward: Conclusion. General characteristics of deductive reasoning (The concept of inference. Deductive inferences. Conditional and disjunctive inferences)
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