Dialectical logic is the system of laws of thought, developed within the Hegelian and Marxist traditions, which seeks to supplement or replace the laws of

formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

. The precise nature of the relation between

dialectic Dialectic ( grc-gre, διαλεκτική, ''dialektikḗ''; related to dialogue; german: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing to ...

al and formal logic was hotly debated within the Soviet Union and China. Contrasting with the abstract formalism of traditional logic, dialectical logic in the Marxist sense was developed as the logic of motion and change and used to examine concrete forms. Its proponents claim it is a materialist approach to logic, drawing on the objective, material world. Stalin argued in his " Marxism and Problems of Linguistics" that there was no class content to formal logic and that it was an acceptable neutral science. This led to the insistence that there were not two logics, but only formal logic. The analogy used was the relationship between elementary and higher mathematics. Dialectical logic was hence concerned with a different area of study from that of formal logic. The main consensus among dialecticians is that dialectics do not violate the law of contradiction of formal logic, although attempts have been made to create a

paraconsistent logic A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" syst ...

. Some Soviet philosophers argued that the materialist dialectic could be seen in the mathematical logic of

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...

; however, this was criticized by Deborin and the Deborinists as panlogicism.

Evald Ilyenkov Evald Vassilievich Ilyenkov (russian: link=no, Э́вальд Васи́льевич Илье́нков; 18 February 1924 – 21 March 1979) was a Marxist author and Soviet philosopher. Biography Evald Ilyenkov did original work on the mater ...

held that logic was not a formal science but a reflection of scientific

praxis Praxis may refer to: Philosophy and religion * Praxis (process), the process by which a theory, lesson, or skill is enacted, practised, embodied, or realised *Praxis model, a way of doing theology * Praxis (Byzantine Rite), the practice of fai ...

and that the rules of logic are not independent of the content. He followed Hegel in insisting that formal logic had been sublated, arguing that logic needed to be a unity of form and content and to state actual truths about the objective world. Ilyenkov used ''

Das Kapital ''Das Kapital'', also known as ''Capital: A Critique of Political Economy'' or sometimes simply ''Capital'' (german: Das Kapital. Kritik der politischen Ökonomie, link=no, ; 1867–1883), is a foundational theoretical text in materialist phi ...

'' to illustrate the constant flux of

A

and

B

and the vanity of holding strictly to either

A

\neg A

, due to the inherent logical contradiction of self-development. During the Sino-Soviet split, dialectical logic was used in China as a symbol of Marxism–Leninism against the Soviet rehabilitation of formal logic. Recently, research on the formalization of dialectics also attracted scholars by applying formal non-classical logic such as

References

{{Reflist, 30em Marxist theory Philosophical methodology