# Logic

**Logic**. A branch of philosophy dealing with the forms of valid reasoning. Formal logic, which was first systematized by Aristotle, deals with the nature of concepts, propositions, and syllogistic arguments. Mathematical or symbolic logic, which is a formal logic more powerful than the traditional Aristotelian logic, was developed in the 19th century. Dialectical logic is the branch of dialectical materialism dealing with the categories and the three laws of thought.

In Ukraine the earliest knowledge about logic was derived from Church Slavonic translations of Byzantine sources. The *Izbornik* of Sviatoslav (1073) contains Saint Maximus the Confessor's and Theodore of Rhaithu's discussion of concepts, definitions, and categories based on Aristotle's *Organon* and Porphyry's *Isagoge*. A late 13th- to early 14th-century Slavonic translation of Saint John of Damascus's *Dialectica* reached Kyivan Rus’ in the first half of the 15th century. Toward the end of the 15th century two important additions were made to the literature on logic: *Lohika Aviasafa* (Aviasaf's Logic, 1483), a compilation based on al-Ghazali's *Aims of the Philosophers*, and *Knyha, hlaholemaia lohika* (The Book Called Logic), a compilation based on M. Maimonides' *Logical Terms*. Both of these works were translated most probably in Kyiv and were based on Hebrew, not Byzantine, sources. Their treatment of logic was much fuller than that in the *Izbornik* and *Dialectica*: it covered not only concepts, definitions, and categories, but also propositions, inferences, and syllogisms. Instead of adopting the Old Church Slavonic technical vocabulary of the earlier works, they introduced a terminology based on the Ukrainian vernacular.

With the introduction of European forms of higher education in the 17th century, logic became an important and permanent part of the curriculum. At the Kyivan Mohyla Academy one year of the three-year philosophy program was devoted to logic, which was valued primarily for its usefulness in rhetoric. The short introductory course, called dialectic or minor logic, was taught often at the end of the rhetoric course. The full course, called major logic, discussed the nature of terms, categories, predicables, universals, propositions, inference, and syllogisms, as well as the concept of science and logic. Although the courses differed from each other because each lecturer prepared his own course, they were patterned more or less on Peter of Spain's textbook. The core of Aristotle's logic was supplemented with new ideas and techniques worked out by scholastic and neoscholastic thinkers. Occasionally the Kyivan professors raised objections to Aristotle and offered their own solutions to problems. Over 30 logic manuals prepared in Kyiv have survived, including the courses of Yosyf Kononovych-Horbatsky (1639–40), Innokentii Gizel (1645–6), Stefan Yavorsky (1691), Y. Turoboisky (1702), Teofan Prokopovych (1708), Y. Volchansky (1717), S. Kalynovsky (1729), Mykhail Kozachynsky (1743), Heorhii Konysky (1749), and Heorhii Shcherbatsky (1751). Only a few of them have been translated, wholly or partly, from Latin into Ukrainian. Ya. Kozelsky, a graduate of the academy, devoted a section of his *Filosoficheskie predlozheniia ...* (Philosophical Propositions ... , 1768) to logic. In the mid-18th century Wolffian philosophy was adopted by the academy, and C. Baumeister's logic textbook became the basic source for its courses in logic. The Wolffian tradition was continued into the 19th century by Pero Lodii, whose *Logicheskie nastavleniia ...* (Logical Principles ..., 1815) was the best textbook in the Russian Empire at the time.

In the 19th century, logic studies were strongly emphasized at Kharkiv University. Its first rector, Ivan Rizhsky, had taught logic in Moscow and had written a textbook (1790) based on C. Baumeister. Teoktyst Mochulsky (1811), L. Jacob (1811, 1815), I. Liubachynsky (1817), and Petro Liubovsky prepared logic textbooks in Russian; Johann Baptist Schad explored the nature of formal logic in contrast to transcendental logic in his *Institutiones philosophiae universae ...* (1812). The mathematics professor Timofei Osipovsky translated E.B. de Condillac's (1805) *La Logique* into Russian. At Kyiv University Orest Novytsky published a large textbook on logic and scientific methodology (1841) and a short version of it (1846, 1848). A section of the third volume of Sylvestr Hohotsky's philosophical lexicon (1866) was devoted to logic. In Odesa Osyp Mykhnevych wrote an elementary logic textbook for the students of the Richelieu Lyceum (1848; 2nd edn 1874). Toward the end of the 19th century Odesa University became a leading center of logic studies. There Nikolai Lange wrote a textbook (1891; repr 1894, 1898, 1903, 1910) that was accepted as the standard in the field. His colleagues Ivan Sleshynsky (1893), Ye. Bunytsky (1896), and Samuil Shatunovsky (1917) followed the development of mathematical logic in the West and made their own contributions to it. P. Poretsky, a graduate of Kharkiv University and professor of astronomy at Kazan University, made some important discoveries in mathematical logic (1881, 1884, 1902). The leading logicians at Kyiv University were F. Kozlovsky, whose logic textbook went through 4 editions (1894–1907), and G. Chelpanov, whose textbook went through 10 editions (1906–18). At Kharkiv University F. Leikfeld worked on the nature of hypothetical judgment (1906), and S. Glagolev pointed out the shortcomings of traditional syllogistic logic (1907, 1910).

In the Soviet period formal logic continued to be taught according to pre-Soviet textbooks written by G. Chelpanov (repr 1918, 1924) and Nikolai Lange (repr 1918). Research in mathematical logic was continued at Odesa University and Kharkiv University, but the attention of philosophers was concentrated increasingly upon dialectical logic. To define the place of the dialectic in the general system of knowledge, Marxist thinkers had to show how it was related to traditional (formal) logic. For over a decade this relation was the main subject of discussion. V. Asmus in his book on dialectical materialism and logic (1924) and O. Bervytsky in his book on logic and dialectic (1929) conceded that formal logic, being static and discrete, cannot reflect, as dialectical logic does, constantly changing and interconnected reality, and yet they defended the usefulness of formal logic for systematizing knowledge and even for expanding it.

By the early 1930s opinion had turned against this conciliatory position: if formal logic did not correspond to reality, then it was false and could not be useful. This conclusion was stated clearly in a collection of articles published in Kharkiv on dialectical materialism (1932). Mathematical logic was associated with formal logic and denounced as mechanistic (Volodymyr Yurynets), abstract, and useless (Ya. Kaufman). As these logics were dismissed from the schools and research institutes, the development of dialectical logic was encouraged. Following Vladimir Lenin's instructions, published in his *Philosophical Notebooks* (1929), to work out a materialist interpretation of Georg F. W. Hegel's dialectic and give a materialist treatment of the categories, philosophers such as O. Bervytsky, T. Stepovy, O. Vasileva, Ya. Bludov, R. Levik, N. Milhevsky, and Semen Semkovsky wrote many articles on Hegel's logic, and Petro Demchuk, T. Stepovy, V. Hadzinsky, and V. Boiko analyzed various logical categories.

After the Second World War the discussion of the relationship between formal and dialectical logic was reopened by the 1946 CC CPSU decision to reintroduce formal logic into the educational program. Old Russian textbooks by G. Chelpanov (1945, 1946) and S. Vinogradov and A. Kuzmin (1949, 1952, 1953, 1954) were republished (sometimes in translation), and new ones were prepared by V. Asmus (1947, 1954) and M. Strogovich (1949). Some of them were translated into Ukrainian. Joseph Stalin's new position on language as a realm outside the economically determined superstructure gave the defenders of formal logic an additional argument in its favor. The theoretical debate over formal logic dragged on for many years, while the subject spread quickly in the schools and institutes. In Kyiv one of the chief defenders of mathematical logic was V. Beliaev, a historian of Aristotelian logic. The rapid development of cybernetics and the philosophy of science in Kyiv stimulated interest in mathematical logic. Pavel Kopnin, the director of the Institute of Philosophy of the Academy of Sciences of the Ukrainian SSR (1962–8), wrote a number of influential books on dialectics as logic (1961, 1973) and on logic and science (1968, 1973). His colleague Myroslav Popovych discussed the basic methods of modern logic and its cognitive status and relation to the dialectic (1971). F. Moskalenko explored the relationship between inductive and deductive logic and wrote a history of inductive logic in the Russian Empire (1955); V. Melnikov (1959), Valeriia Nichyk (1960), and M. Bulatov (1981) studied the nature of the categories; S. Krymsky speculated on the evolutionary emergence of logical forms and laws (1962); and M. Popovych examined the role of cultural context in the history of logic (1979). The development of logic in Ukraine has been investigated by V. Nichyk, S. Krymsky, and I. Paslavsky.

In interwar Western Ukraine the psychologist Stepan Balei taught logic at the Lviv (Underground) Ukrainian University and wrote an elementary textbook (1923). As a member of the Polish Lviv Philosophical Association he was acquainted with the new work done by Polish logicians in Lviv. Rev V. Maksymets taught logic at the Greek Catholic Theological Academy in Lviv (1931–9).

Outside Ukraine logic has been taught at Ukrainian postsecondary schools in interwar Prague and postwar Munich. Dmytro Chyzhevsky wrote an outline (1924) of his logic course at the Ukrainian Higher Pedagogical Institute in Prague.

BIBLIOGRAPHY

Nichyk, V. ‘Lohika,’ in *Rozvytok filosofiï v Ukraïns'kii RSR*, ed V. Ievdokymenko; et al (Kyiv 1968)

Paslavs'kyi, I. ‘Rozvytok lohichnykh idei u vitchyznianii filosofiï druhoï polovyny XV st.,’ *Filosofs'ka dumka*, 1986, no. 6

Taras Zakydalsky

[This article originally appeared in the *Encyclopedia of Ukraine*, vol. 3 (1993).]