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Lecture notes, cheat sheets
Логика. Истинность и модальность суждений (конспект лекций)
Directory / Lecture notes, cheat sheets Table of contents (expand) LECTURE No. 13. Truth and modality of judgments 1. Modality of judgments modal judgment - this is a separate type of judgments, which has its own characteristics and is characterized both by the presence of features common with assertoric judgments, and by difference from the latter. Modal judgments are studied within the framework of modal logic, which is heterogeneous in its content and is divided into several branches. Among them: logic of time, logic of action, logic of norms, deontic logic, logic of decision making and more From the point of view of classical logic, one or another judgment can be called assertoric or modal. It is obvious that these two types are different from each other. Modal judgments can be called clarifying. Judgments of this kind do not just characterize this or that object, describe, define it and its inherent properties, but also clarify and supplement such a characterization. In a simplified form, we can say that modal judgments express our attitude towards the object in question. Of course, this feature of modal judgments is reflected in natural language. So, unlike assertoric judgments (read - simple), modal ones contain a number of special words. For example, "proven", "necessarily", "possibly", "good", "bad", etc. These words are called modal operators. One can show the difference between assertoric and modal judgments by giving the following sentences: "Tomorrow it will be cold" - this judgment is assertoric; "Perhaps it will be cold tomorrow" - as is already clear, this is a modal judgment. From these positions, it can be argued that modal judgments are assertoric judgments supplemented by a specific relation. However, the role of modal statements is not limited to a simple transfer of the speaker's attitude to the subject. There is a more complex and noticeable pattern that is not at first glance: modal judgments reflect the nature of the connection between the subject and the predicate. In a sense, they create it themselves. Modal judgments are judgments that reflect the relationship and connection between the subject and the predicate and show the relationship to the subject with the help of modal operators. In order to better understand the nature of this type of judgment, let us consider a number of examples. We will first give an example of an assertoric judgment, and then a modal one formed from it. “There is not a cloud in the sky, and the sun is shining brightly,” “It’s good that there is not a cloud in the sky and the sun is shining brightly”; “Correct posture improves performance”, “Correct posture has been proven to improve performance” and “Pouring cold water improves health”, “Dousing cold water has been proven to improve health.” And also: “The runner in the second lane will come first,” “It is possible that the runner in the second lane will come first”; “Two multiplied by two makes four,” “Obviously, two multiplied by two makes four”; “An electric current, as it passes, heats the conductor” and “It is imperative that the current, as it passes, heats the conductor.” The difference between assertoric and modal judgments in the examples given is obvious. Let's say the first pair of judgments. “There’s not a cloud in the sky...” is just a statement of fact, a description of two components of clear weather, devoid of evaluation, and with it any feelings and emotions. With the addition of the word “good” to the judgment comes the speaker’s assessment of this weather. From this judgment we can clearly conclude that he likes this kind of weather. The first type of judgment, like the second (i.e., both assertoric and modal judgments) can be either true or false. There is no third option. However, one cannot but agree that modal judgments have more variations and shades. They can often be interpreted differently, which makes it possible for errors to occur in determining their truth or falsity. Here it is necessary to mention that logic in general and modal logic in particular approach the consideration of the meaning of the words “possible”, “necessary”, “proven”, “obligatory”, as well as “necessity”, “obligatory”, “obligatory” derived from them. chance", "impossibility" from a special point of view. If, from the point of view of natural language, the above words are only words and have different shades and meanings, then logic elevates them to the rank of categories. From this point of view, their interrelations and dependencies are considered. These categories are also considered within the framework of philosophy, which is most interested in their substantive side. In this way, assertive judgments - These are simple judgments in which certain information about a particular subject is affirmed or denied. They are also characterized by what they say about the relationship between the objects reflected in them. There may be two or more such items. To clarify the above, we give an example: "All professional skiers are athletes." In this judgment, the concepts of "professional skiers" and "athletes" are correlated, and the first is narrower than the second and is fully included in its scope, but richer in content, due to the fact that it has more features. A modal judgment, in contrast to an assertoric one, indicates the proof or lack of proof of what is reflected in the judgment, the need for a connection between objects or its accident, the relation to the subject of judgment from the point of view of morality, morality, etc. Modal judgments have a structure: M (S is (or not to eat) P). It must be said that assertoric judgments (as already described in other chapters) can be combined into complex ones using logical connectives (conjunctions, disjunctions, equivalences, implications, denials). Modal operators are great for complex judgments as well. In other words, even complex judgments can be modal. In this case, their structure will be: M (a ^ b) or M (a V b), etc. It is only necessary to remember that there are five logical connectives and, accordingly, complex judgments formed from them. Words in a natural language (including Russian) are characterized by a certain ambiguity. In other words, many words have different meanings with the same sound. Others, despite the fact that they differ in sound and spelling, mean the same thing. The latter also applies to modal operators. Thus, one of the modal operators can easily be replaced by another, and without losing the implied meaning of the judgment. For example, the judgment "Probably this athlete will run first" will not lose what he has and will not gain a new one if you replace "probably" with "maybe". Judge for yourself: "Perhaps this athlete will come running first." This can be done in other cases as well. Combining the above, we can call complex modal judgments such complex judgments that, with the help of modal operators, reflect the relationship and connection between the simple judgments that make up its composition. As described above, modal statements are formed using modal operators. The modality of judgments has a number of modal concepts. They are well studied and systematized. At the same time, the systematization is based on the strength of modality, as well as its positivity or negativity. There are three basic modal concepts, although some scholars insist on the view that there are four of them. The three main modal concepts are characterized by the fact that the first of them is strong and positive, the second is a weak characteristic, and the third, in contrast to the first, is a strong negative characteristic. The fourth modal concept is intended in some cases to replace a strong positive concept and a weak characteristic. Modalities can be logical and ontological, diontic, epistemic, axiological and temporal. Logical modalities together with ontological ones form alethic modalities. Speaking about the modality of judgments, it was mentioned more than once about modal operators. They show the necessity of a judgment or its chance, possibility or impossibility. However, the process did not define either truth or falsity or other terms from this series. Meanwhile, knowing the exact meaning of the above categories is important. So, the necessity of a judgment means that this judgment is based on a law discovered within the framework of any science, including logic. In this case, all justified consequences derived from these laws are also recognized as necessary. The determining factor in this case is the factor of objectivity. In other words, the law must be real, not virtual, that is, it must correctly reflect the real state of affairs. Random judgments are defined as statements, although not based directly on the laws known to science, but not contradicting them. The same applies to the consequences of these laws. In the case of impossible judgments, everything is obvious. Such judgments are those that contradict scientifically confirmed laws or their consequences. Possible judgments are based on common sense and do not contradict scientific laws and their consequences. The above categories study alethic modalities. 2. Truth of judgments Turning to the question of the truth of judgments, it should immediately be said that often the definition of this factor becomes a difficult task. This may be due to the ambiguity of the words used in statements, or to the incorrect construction of the judgment from the point of view of logic. The reason may be the complexity of the structure of the judgment itself or the impossibility of determining the falsity or truth at the moment due to the unknown or unavailability of the necessary information. Determining the truth of judgments is directly related to comparability and incomparability. Comparable judgments are divided into compatible and incompatible. Incompatible judgments can be in a relationship of contradiction and opposition. The concepts included in the relation of contradiction are characterized by the fact that they cannot be simultaneously true or false. If one of the contradictory propositions is true, then the other is false, and vice versa. If one of the opposite propositions is true, the other is necessarily false, since they completely exclude each other. At the same time, the falsity of one of the opposite judgments does not mean the falsity or truth of the other. Indeed, the opposite of judgments does not yet mean that one of them is always true, and the other is false. For example: "There is no life on Mars" and "There is life on Mars". These concepts are indefinite, that is, it is not known whether they are true or false. Both of them may be false. But only one of them can be true. Compatible judgments enter into a logical relationship subordination, equivalence and overlap (intersection). Subordinate compatible judgments. They bear such a name due to the fact that one of these judgments is included in the scope of the other, is subordinate to it. Such judgments have a common predicate. The definition of the truth of judgments that are in relation to subordination is associated with a certain specificity, since one of the judgments is included in the scope of the second. In this regard, the truth of the general judgment entails the truth of the particular, while the truth of the particular does not determine with certainty the truth of the general. The falsity of the general leaves the particular judgment indefinite, and the falsity of the particular does not mean that the general is also false. Let's give an example: "Ferrari is a good car" and "All cars are good". The second proposition is false. It is subordinate. At the same time, the private judgment subordinated to it is true. Relatively speaking, compatible equivalent judgments reflect the same phenomenon or object of the surrounding world, but they do it differently. So, if we take for consideration two different judgments about one object or phenomenon, that is, two compatible judgments, then we will notice a pattern: in one case, both of these statements will have one subject, but differently expressed (although having the same meaning) predicates . In another case the opposite situation arises. However, in this case we are talking only about equivalent, but in no case about all compatible judgments. It goes without saying that when two judgments are equivalent, identical in meaning, if one of them is false, the second is false, and vice versa. Examples of equivalent compatible propositions are the following statements: "The moon is a natural satellite of the Earth" and "The moon is a satellite of the Earth that arose as a result of natural causes." When determining the truth of compatible judgments that are not equivalent, it is necessary each time to proceed from the real state of things: since compatible concepts often reflect the same subject only partially, each of them in this case can be both true and false. The intersection relation is characterized by the fact that if one such judgment is false, the other is necessarily true. This is due to the fact that such judgments have the same subject and predicate, which nevertheless differ in quality. Moreover, if one of these judgments is true, then with respect to the other it is not clear whether it is true or false. Author: Shadrin D.A. << Back: Complex judgments. Formation of complex judgments (The concept of complex judgments. Expressing statements. Denial of complex judgments) >> Forward: logical laws (The concept of logical laws. The law of identity. The law of non-contradiction. The law of excluded middle. Sufficient reason)
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