This connection is especially convincing in our time.
In the formulas that express the structure of thoughts, some symbols are replaced by the names of specific objects taken from certain subject areas, others – are contained (not replaced) in all specific in content thoughts that have this structure. The first symbols (signs) are called logical variables, the second – logical constants (constants). The latter retain their properties for any subject areas. In the formula “All S are. P” logical variables – “S” and “P” and logical constants – “all” and “are”.
When constructing a strict logical theory, symbols denote not only logical variables but also logical constants. This not only achieves an abbreviated record, but also eliminates the ambiguity of words that express logical connections, constant.
Thus, in the above judgments, the connection “is” expresses various logical connections:
Subject and meaning of logic All rectangular rhombuses are squares. The atom is divisible. The rod is a river.
In the first judgment, the word “is” expresses the relationship of equivalence of concepts, in the second – the inclusion of a subset in the set, in the third – the relationship of the element of the set to the set. The relationship between the subject and the predicate (logical subject and logical predicate) in such judgments are denoted by different symbols.
Logical variables, which are replaced by a variety of judgments that are characterized only in terms of their truth or falsity, will be denoted by the letters a, b, c, and so on. Logical variables, which are replaced by words that fix properties and relations – the letters S, P, R. Logical variables, which are replaced by names that mean individual objects, will be denoted by the symbols x, y, z and so on. Note that the concepts that reflect the properties and relations of objects, in logic called predicates.
The value of logic
Certain categories of people (including prominent thinkers) tend to underestimate or even ignore the importance of formal logic. Some of them believed that people’s reasoning could be perfect even without knowledge of logic, so its study is superfluous or at least ineffective. The nihilistic attitude to the logic of others is explained by their antipathy to the impersonal attitude of the subject of strictly logical reasoning to the problems that are solved with the help of these considerations. Such views, of course, have some, though insufficient, basis.
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In fact, everyone has a more or less perfect spontaneously formed, intuitive logic. Without it, she would not be able to think properly, communicate with people and so on. But spontaneously formed logic can never replace consciously acquired knowledge of laws and forms of thinking. First, it is not always able to solve the problems that people face. And secondly, only a small percentage of people who have not studied logic have a more or less satisfactory level of spontaneously formed logical culture.
The need to study the course of logic is evidenced by the fact that many people can not distinguish right reasoning from wrong. Thus, only four to five percent of students who are just beginning to study logic are able to detect a logical error in the following reasoning: “In all cities beyond the Arctic Circle, white nights are observed, and St. Petersburg does not lie beyond the Arctic Circle; there are no white nights in this city. “However, they claim that this reasoning is wrong, because this is not about cities that do not lie beyond the Arctic Circle. This is the correct answer, typical of people with a perfect spontaneously formed logical culture.
The vast majority of students see the logical inaccuracy of this reasoning in the fact that in St. Petersburg, in fact, there are white nights. However, this true position is not directly related to the correctness or incorrectness of reasoning. The inaccuracy of conclusions can follow not only from the incorrect reasoning, but also from the inaccuracy of the foundations.
Revealing the problem of the importance of logic, we find out, firstly, what role it plays as a science, and secondly, what is the importance of knowledge of logic as a science. Clarifying the first aspect, it should be noted that the level of development of logic was constantly manifested in all areas of scientific knowledge, and ultimately – in practice. History shows the inseparable (though far from ambiguous) connection of logic with other sciences, the progress of technology and engineering.
This connection is especially convincing in our time. One of the famous founders of cybernetics, the American mathematician N. Wiener, believed that the emergence of cybernetics would be impossible without modern logic. Automation and computer technology used in cybernetics are known to use the algebra of logic, and in the control systems of cybernetics play an important role relay-contact circuits that simulate logical operations.
Modern logic penetrates into new fields of science and technology. The achievements of logic are used in all areas of knowledge, because it explores the general principles of correct reasoning, the relationship between the basics and conclusions, regardless of the field of knowledge from which these principles are taken. It is important to take into account that different logical systems (classical and non-classical) and even different sections of these systems, especially non-classical, perform their specific functions.
Clarifying the importance of knowledge of logic as a science, it should first be noted that it enhances the overall intellectual culture of man, contributes to the formation of logically correct thinking, the main features of which are clear definition, consistency, consistency and provability.
Mastering logical science makes it possible to consciously build correct reasoning, distinguish them from wrong, avoid logical errors, skillfully and effectively substantiate the truthfully opinions, defend their views and convincingly refute erroneous thoughts and wrong reasoning of their opponents, improves spontaneously formed logic. Thanks to logic, especially modern, a person joins the latest results of logical research.
The need for knowledge of logic is explained by the fact that it explores the universal laws of thought that apply in all branches of science. The high logical culture of the country’s citizens contributes to its progress in all spheres of life.
21.10.2011
Logic: reasoning and judgment. Abstract
Right and wrong reasoning. Simple and complex judgments. The structure of simple judgments. Formulas
Right and wrong reasoning
The term “reasoning” is used in a double sense. By “reasoning” is meant both the mental process of deriving new knowledge from judgments, and the new judgment itself, as a consequence of a mental operation.
Reasoning (inference) is a form of thinking by which a new judgment is derived from one or more judgments, which contains new knowledge.
Reasoning is a logical means of acquiring new knowledge. In the process of inference there is a transition from the known to the unknown. The objective basis of inference is the connection and interdependence of objects and phenomena of reality. If the world around us consisted of accumulated unrelated random objects and phenomena, it would not be possible to move from the knowledge of some objects to the knowledge of others, and therefore inference as a form of thinking would be impossible. But since the objects and phenomena of objective reality are interconnected, subject to a certain law, there is not only the possibility but also the need to know some objects on the basis of knowledge of others.
Reasoning is not any combination, but only one in which there is a logical connection between the judgments, which reflects the relationship of objects and phenomena of reality itself. If the objects of reality are not connected with each other, then the judgments that reflect these objects will logically be unrelated, and therefore it is impossible to derive any new meaning from them, that is, to draw an inference.
The conclusion will be true if there are two necessary conditions:
If the parcels are true in content. If the inference is correct in its structure.
Example:
Conclusion 1 – All artists are sensitive to nature. Foundation 2 – Levitan – artist. Conclusion – Levitan subtly felt nature.
In this conclusion, both premises are true, and therefore it is built correctly and is completely true. This follows from the following scheme:
A – Levitan
In – artists
C – those who subtly feel nature
On the contrary, the conclusion may be erroneous if:
At least one of the parcels is wrong; The inference is wrong.
Example:
Parcel – All witnesses are true. Parcel – Zakharov – witness. The conclusion – Zakharov – is true.
In this conclusion, one of the basics-parcels (the first) is wrong. The conclusion, accordingly, will not be true.
As to how important it is to construct an inference correctly, a humorous example known in logic shows that the conclusion from two true premises is meaningless.
Example:
Parcel – All birds carry feathers. Parcel – Savages sometimes wear it too. Conclusion – Sometimes savages are birds.
C – those who wear feathers.
B – birds.
A – savages.
Just as it is impossible to build a house without sound material, it is impossible to build a correct inference without correct judgments, which are built according to the correct scheme.
From the four basic logical laws come three signs of correct thinking. With these objective qualitative features, we can trace or realize how much people’s thinking (and, above all, our own) can be called true.
1. Clarity – clarity of meaning, clarity and unambiguity of terms, concepts, phrases that are expressed. The importance here is that people take into account that not only the words they address us should be clear, but also our own language addressed to people – this aspect is extremely important, say, in the professional activities of managers, lawyers, sociologists.
2. Consistency – a person must be able to build a “logical chain” – be aware of the consequences of their own thoughts, the results of the consequences and so on – then his thinking will be multi-step and he will be able to take into account events and predict them.
3. Proof – a person should strive not for unsubstantiated phrases, but proven arguments. If proof is not currently needed, the person must at least prepare it, keep in mind.