Ivan Efimovich Orlov (Russian: Иван Ефимович Орлов; Galich,

Kostroma Oblast Kostroma Oblast (russian: Костромска́я о́бласть, ''Kostromskaya oblast'') is a federal subject of Russia (an oblast). Its administrative center is the city of Kostroma and its population as of the 2021 Census is 580,97 ...

, –

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...

after After may refer to: Literature * ''After'' (Elgar), an 1895 poem by Philip Bourke Marston set to music by Edward Elgar * ''After'' (Prose novel), a 2003 novel by Francine Prose * ''After'' (book), a 2005 book by Canadian writer Francis Chalifour ...

1936 ОРЛОВ
''iphlib.ru'') was a Russian philosopher, a forerunner of

relevant Relevant is something directly related, connected or pertinent to a topic; it may also mean something that is current. Relevant may also refer to: * Relevant operator, a concept in physics, see renormalization group * Relevant, Ain, a commune ...

and other

substructural logic In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are r ...

s, and an industrial chemist. The date of his death is unknown, but is most likely between 1936 and 1937.

Education and Scientific Career

Orlov studied at the Natural Sciences Faculty of Moscow University. His academic career began in 1916, when he published several papers related to the method of inductive reasoning and the notion of

inductive proof Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help ...

. For 7 years beginning 1916, he published no scientific work, presumably because of the political turmoil of the era. In the 1920s, he taught in the newly established Communist Academy, and was an officer at the Chemical Institute. In 1923 Orlov resumed his academic activity, becoming very productive. Most of his papers were published in leading Soviet ideological journals, where he waxed polemical in the manner typical of that place and time. Orlov's work bore on the

philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in peop ...

and

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 ...

, specifically on the so-called

dialectical logic 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. The precise nature of the relation between dialectical and formal logic was ho ...

, Marxist in nature. He wrote on the

theory of probability Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

psychology Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between ...

theory of music Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "Elements of music, rudiments", that are needed to understand ...

, and on

chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials int ...

Logic

Analyzing the development of the natural sciences, he sought to uncover their specific "logic." According to Orlov, the laws of thought should be treated as formal rules, bounded by the laws of

identity Identity may refer to: * Identity document * Identity (philosophy) * Identity (social science) * Identity (mathematics) Arts and entertainment Film and television * ''Identity'' (1987 film), an Iranian film * ''Identity'' (2003 film), ...

and

contradiction In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's ...

. (When Orlov wrote this, the invention of

natural deduction In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use ax ...

, the

sequent calculus In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology i ...

, and the

semantic tableau In proof theory, the semantic tableau (; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure comput ...

x all lay in the future.) We must seek the semantic relation between antecedent and

consequent A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if ''P'' implies ''Q'', then ''P'' is called the antecedent and ''Q'' is called ...

. The main "contradiction of logic" manifests itself in the linkage of premise and corollary, and requires a logic different from the traditional one. If we insist that a corollary be a necessary condition of the premises then, according to Orlov, we necessarily arrive at a non-Aristotelian logic,

dialectical 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 ...

in nature.

The Logic of Compatibility Propositions

Orlov proposed a logic of just this type in his work "The Logic of Compatibility of Propositions" published in 1928 in a Soviet mathematical journal. This paper analysed the problem of compatibility (noncompatibility) of propositions through the interpretative prism of an implication procedure. He also foresaw the translation of systems with intuitionistic negation into S4 modal logic with classical negation. Orlov's work was very little known for a long time, because his publications, all in Russian, were almost totally unknown outside of the

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

. It is only with the post-World War II rise of what have come to be known as

s (Restall 2000) that Orlov's pioneering role has gradually emerged.

Substructural logic In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are r ...

s, a category including

intuitionistic In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of f ...

, relevant, linear logics, etc., can be obtained by restricting the

("structural") rules for classical logic. For example,

relevant logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...

does not employ the structural rule of weakening (also called the rule of

monotonicity In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of orde ...

), and this rule is unlike the other structural rules (Dosen). Orlov believed in a mechanistic reduction of the laws of nature. He castigated the

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

Georg Cantor Georg Ferdinand Ludwig Philipp Cantor ( , ; – January 6, 1918) was a German mathematician. He played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of ...

, the

theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

(he believed in the existence of aether), and the heliobiology of A. Chizhevsky.

Industrial Chemistry

Around 1928, Orlov ceased publishing logical and philosophical work, turning to industrial chemistry, specifically the production of

bromine Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table ( halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simi ...

and iodine, and in translating German works on chemistry into Russian.

Education and Scientific Career

Logic

The Logic of Compatibility Propositions

Industrial Chemistry

References

Further reading