Formal logic is the science of the rules for transforming statements that preserve their true meaning, regardless of the content of concepts included in these statements, as well as the construction of these rules. As the founder of formal logic as a science, Aristotle called it “ analytics, ” while the term “ logic ” came into common use after his death in the 3rd century BC [1] .
Formal logic, in contrast to informal , is organized as a formal system with a high level of abstraction and well-defined rules [2] . Formal logic deals with the derivation of new knowledge on the basis of previously known knowledge without resorting to experience in each particular case, but with the application of laws and rules of thinking. The initial stage of formal logic can be considered traditional logic. [ unknown term ] , and its next step is mathematical logic , using a formalization similar to mathematical, a symbolic apparatus and logical calculi [3] .
Content
- 1 History
- 2 "Logistics" program
- 3 Subject and method of formal logic
- 4 Loss of specificity
- 5 Disputes around formal logic in the Soviet Union
- 6 Applications
- 7 notes
- 8 Literature
- 8.1 History of Logic
- 8.2 The fate of formal logic in the USSR
History
The author of the first system of formal logic is Aristotle , who introduced the concept of syllogism and the variables by which he denoted the terms of syllogism [4] .
According to Kant, formal logic (in the Critique of Pure Reason it is called “general”) is abstracted from the content of concepts and deals only with their form:
The boundaries of logic are precisely determined by the fact that it is a science that spells out and rigorously proves only the formal rules of all thinking (it doesn’t matter whether it is a priori or empirical, it doesn’t matter what its origin and subject matter ...) [5] .
Kant himself contrasted formal logic (to which he attributed primarily syllogistics , based on Aristotle 's Analysts) to substantial, transcendental logic , the development of which is the main subject of the Critique of Pure Reason:
But since there are pure and empirical contemplations ... one can expect that things can be thought of differently ... In this case, there should be logic that does not abstract from any content of knowledge [6] ...
Logistics Program
Formalists (representatives of the so-called “logistics”, which was formed at the Geneva Congress of 1904 by L. Couture , A. Laland, and others) of the late XIX - early XX centuries, the formality of logic was associated with the allocation of the truth values of statements when transferring them from a natural language in symbolic notation . Logistics sought to substantiate mathematical knowledge (in the future, natural science) within the framework of formal logic alone. Significant efforts in this direction were made by D. Hilbert , Couture, B. Russell .
By a form in general we mean an expression in which at least one variable enters in such a way that this expression turns into a true or false statement due to the fact that we substitute something in the place of this variable [7] .
The focus on truth value distinguished formal logic from other disciplines dealing with form, such as linguistics and mathematical disciplines such as arithmetic , geometry , algebra , and mathematical analysis . Accordingly, they included formal logic in all those sections of logic that could be formalized in symbolic forms developed by mathematicians and logicians O. de Morgan , J. Boulle , J. Peano , G. Frege , Russell and others, developed in the 19th and early 20th centuries.
Such logic disciplines as dialectics (in its medieval version and various modern versions), inductive logic ( J. S. Mill ) and other variants of the logic of science remained “behind” the formal logic.
The so-understood formal logic ceased to be a science of thinking, and many formalists [8] [9] completely disavowed it as a “ psychological ” concept that has nothing to do with logic as such, which should focus on the study and improvement of language , on structural rather than procedural properties of speech structures. This point of view was developed in the views of the Vienna Circle , the Lviv-Warsaw School and, further, Anglo-Saxon analytical philosophy . However, it was not shared by other formalists.
At the same time, in the 1910–20s. the claims of the logisticians to justify the exact knowledge were convincingly criticized by A. Poincare [10] and, later, by Hilbert, who joined him in this criticism, after which the logistic movement came to naught.
The subject and method of formal logic
The subject of formal logic was specially reconstructed and criticized in the works of the Moscow Logical Circle [11] and then the Moscow Methodological Circle [12] . The criticism concerned the inappropriateness of the development of formal logic as such or its usefulness, and the completeness of its exhaustion of logical problems and its claims to the role of the theory of thinking.
According to the reconstruction carried out at MMK, logic deals with “ language thinking ” (or, “language taken as a function of thinking”), in which groups of signs in a certain way interconnected according to certain laws replace real objects and each other with respect to actions :
- objective content ────────────── signs of the language
- value relationship
- objective content ────────────── signs of the language
Formal logic is possible when the substitute content is not directly the objects of action, but, in turn, the signs that form closed operating systems. The method of formal logic consistently holds the principle of parallelism of form and content of thinking .
The development of symbolization in formal logic and its transformation into one of the mathematical disciplines are regular, natural and inevitable.
The claims of formal logic on the role of the theory of thinking are untenable, because:
- its concepts do not describe thinking in general, but only its symbolic form, and even that is incomplete;
- its concepts do not take into account the dependence of the structure and transformation rules of this form on the content;
- its concepts do not reflect the difference between thinking and its products, ( knowledge );
- its concepts cannot explain the formation of complex knowledge;
- her method is incompatible with the historical approach to the study of thinking [13] .
Loss of specificity
The spread of the ideas of multi-valued logic in its various variants (including symbolized ones), and then the ideas of abstract data types in theoretical programming, problematized the “specificity” of truth from the inside as a range of values of logical functions that include only two possible values. Thus, the apparatus of infinite-valued logic of Lukasevich – Tarski [14] is practically indistinguishable from the apparatus of probability theory , and in the theory of data types the logical (Boolean) type does not differ anything special from the others either from the operator point of view or from the point of view of machine implementation.
On the other hand, new sections and versions of symbolic logic (for example, intuitionistic logic , intentional logic , deontic logic ) went far beyond the boundaries of syllogistics and truth research in the narrow sense and encompassed many other sections of logic .
At present, the term “formal logic” has lost its specific meaning and is used (outside the context of the history of science ) as a synonym for symbolic or mathematical logic. The “traditional” (as opposed to the “modern”) formal logic can be called the same sections of logic that are stated without using a mathematical apparatus.
Disputes around formal logic in the Soviet Union
In the 1930s and 1940s, formal logic was pushed by official philosophical instances as the “theoretical basis of the bourgeois worldview” [15] , something incompatible with Marxism and communist ideals. There was no active work in the relevant areas, traditions were lost, the few surviving specialists were forced to engage in other disciplines or were deprived of the conditions for normal scientific communication.
The situation changed somewhat in 1946-1947 , when (according to some information [16] [17] , by personal order of I. V. Stalin ) logic was introduced into the school curriculum [18] (a number of textbooks were written ( V. F. Asmus , K. S. Bakradze , M. S. Strogovich ) and even in abridged or revised form the “bourgeois” textbooks of S. N. Vinogradov and G. I. Chelpanov were reprinted). This was followed by the creation of the Department of Logic at the Philosophical Faculty of Moscow University ( A.F. Losev was considered as one of the candidates for the department, although P.S. ] and some other events [17] .
However, the struggle between the “dialecticians" and the "formalists" continued with varying success around this topic. In the 1950s and 1960s, formal logic (having already left school) settled in universities and research institutes. An outstanding role in the restoration of logical research and the teaching of logic in the country was played by such representatives of the formalistic direction as S. A. Yanovskaya , A. S. Yesenin-Volpin , Yu. A. Gastev, A. A. Markov and others.
The flip side of the process was the counter-reaction of the "formalists" with respect to logicians who sought to develop logic outside the program of its formalization. Already in the 1960s and 1970s, logics such as A. A. Zinoviev (forced to change his language and switch to “mathematical” symbols), E. V. Ilyenkov (who left the Philosophical Encyclopedia collective in protest) experienced difficulties with publications. against the substitution of a logical mathematical problem), etc.
To some extent, this reaction continues even in the post-Soviet years [20] .
Applications
- Relational data model
Notes
- ↑ Logic as a science
- ↑ Nat, 2010 , p. 2.
- ↑ Kondakov, 1971 .
- ↑ Kondakov, 1971 , p. 576.
- ↑ Kant I. Criticism of Pure Reason . - M .: 1994. - S. 14.
- ↑ Kant I. Cit. Op. - S. 72-73.
- ↑ Scholz H. Concise History of Logic . - New York , 1961 .
- ↑ Carnap R. Induktive Logik und Wahrscheinlichkeit. - Wien, 1958.- S. 31.
- ↑ Lukasevich Ya. Aristolevskaya syllogistics from the point of view of modern formal logic. - M. , 1959. - S. 48-49.
- ↑ Poincare A. On science. - M .: Nauka, 1983 .-- S. 475-518, 580-616. - 736 p.
- ↑ Zinoviev A. A. Ascent from the abstract to the concrete (based on the material of Capital by K. Marx). - M. , 2002 .-- 321 p. ; Shchedrovitsky G. P. “Linguistic Thinking” and its Analysis // Questions of Linguistics . - 1957. - No. 1 . - S. 56-68 . ; Alekseev N.G. , Shchedrovitsky G.P. On possible ways to study thinking as an activity // Doklady APS RSFSR. - 1957. - No. 3 . ; Shchedrovitsky G.P. On some aspects in the development of concepts // Questions of Philosophy . - 1958. - No. 6 . - S. 55-64 . ; Ladenko I.S. On the relation of equivalence and its role in some processes of thinking // Doklady APS RSFSR. - 1958. - No. 1 . ; Ladenko, I. S., On Some Thinking Processes Associated with Establishing an Equivalence Relationship // Doklady APS RSFSR. - 1958. - No. 2 . Shvyrev V. S. On the question of the ways of logical research of thinking // Doklady APS RSFSR. - 1960. - No. 2 . and etc.
- ↑ Shchedrovitsky G.P. On the structure of attributive knowledge // Reports of the APS of the RSFSR. - 1958-60. ; Shchedrovitsky G.P., Ladenko I.S. On some principles of the genetic study of thinking // Abstracts of reports at the 1st Congress of the Society of Psychologists June 29 - July 4, 1959. Issue. 1: Sat - M. , 1959. - S. 100—? . ; Shchedrovitsky G. P., Alekseev N. G., Kostelovsky V. A. The principle of “parallelism of the form and content of thinking” and its significance for traditional logical and psychological research // Doklady APS RSFSR. - 1960–61. ; Shchedrovitsky G. P. On the relationship of formal logic and the neopositivist “logic of science” // Dialectical materialism and modern positivism: Sat. - M. , 1961 .; Shchedrovitsky G. P. On the difference between the initial concepts of “formal” and “substantial” logics // Methodology and Logic of Sciences: Sat. - Tomsk, 1962 .-- T. 41 . - S. 81-92 .
- ↑ Shchedrovitsky G.P. On the method of researching thinking. - M. , 2006 .-- S. 110-183. - 600 s. . See also Schedrovitsky G.P. Processes and structures in thinking (lecture course) / From the archive of G.P.Shchedrovitsky. T. 6 . - M. , 2003 .-- 320 s. and Shchedrovitsky G. P. Problems of the logic of scientific research and analysis of the structure of science / From the archive of G. P. Shchedrovitsky. T. 7. - M. , 2004 .-- 400 p.
- ↑ Łukasiewicz J., Tarski A. Untersuchungen über den Aussagenkalkül // Sprawozdania z posiedzec Towarzystwa Naukowego Warszawskiego. Wydział II. R. XXIII. - Warszawa, 1930.
- ↑ Formal logic // Rosenthal M., Yudin P. (eds.). Brief philosophical dictionary . - M .: 1940 .
- ↑ Ladenko I. S. Formation and development of the ideas of genetic logic // Questions of methodology , 1991, No. 3.
- ↑ 1 2 Lahuti D.G. Stalin and Logic // Questions of Philosophy. - 2004. - No. 4 . - S. 164-169 .
- ↑ Resolution of the Central Committee of the All-Union Communist Party of Bolsheviks from 03.12.46 “On the teaching of logic and psychology in high school”.
- ↑ “Fundamentals of Theoretical Logic” by Hilbert and V. Akkerman (1947), “An Experience in the Study of the Meaning of Logic” by S. Serryus ( 1948 ), “Introduction to the Logic and Methodology of the Deductive Sciences” by A. Tarski (1948) and others.
- ↑ See, for example, the article “ Ilyenkov Evald Vasilyevich ” defaming Ilyenkov as a scientist in the Philosophical Encyclopedic Dictionary (M., 2004, edited by A. A. Ivin).
Literature
- Kondakov N.I. Logical Dictionary / Gorsky D.P. - M .: Nauka, 1971. - 656 p.
- Arnold vander Nat. Simple formal logic: with common-sense symbolic techniques. - Routledge, 2010 .-- 360 p. - ISBN 978-0415997454 .
- Chupakhin I. Ya., Brodsky I. N. Formal logic. - L .: LSU, 1977 .-- 357 p.
History of Logic
- Makovelsky A.O. History of logic . - M., 1967 .
- N. I. Kondakov, Logical Dictionary-Reference , M.: “Science”, 1975 , p. 285. on the website of Runivers
- Popov P. S. History of the logic of the new time . - M., 1960 .
- Logic, history of: Precursors of modern logic // Encyclopedia of philosophy / Donald M. Borchert, editor in chief. - 2nd ed. - N. Y .: Thomson Gale, 2006 .-- V. 5 .-- S. 440-446. - 742 s. - ISBN 0-02-865785-3 .
- Logic, history of: Modern logic // Encyclopedia of philosophy / Donald M. Borchert, editor in chief. - 2nd ed. - N. Y .: Thomson Gale, 2006 .-- T. 5 .-- S. 447-484. - 742 s. - ISBN 0-02-865785-3 .
The Fate of Formal Logic in the USSR
- Alekseev M.N. Discussion of questions of logic at Moscow State University // Questions of Philosophy , 1951 , No. 2;
- Alekseev M.N. Discussion on the relationship of formal logic and dialectics // Moscow State University Bulletin , Series I. Social Sciences , 1951, No. 4.
- Biryukov B.V. Struggle around logic in Moscow State University // Logical Studies , T. X, 2003 .
- N. I. Kondakov, Logical Dictionary-Reference , M.: “Science”, 1975, p. 290 on Runivers website
- Shchedrovitsky G.P. I have always been an idealist .... - M. , 2001 .-- 323 p. - ISBN 5-93733-010-2 .
- Formal logic. - Leningrad: Publishing House of the Leningrad University, 1977.— 357 p. on the Runivers website
- Philosophical questions of modern formal logic. - M.: Publishing House of the Academy of Sciences of the USSR, 1962.— 365 p. on the Runivers website