Ivan Orlov
Encyclopedia
Orlov, Ivan Efimovich was a philosopher, a forerunner of relevant and other substructural logic
s, and an industrial chemist. The date of his death is unknown but is believed to have occurred no earlier than 1936.
and the notion of inductive proof. 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
and logic
, specifically on the so-called dialectical logic, Marxist in nature. He wrote on the theory of probability, psychology
, theory of music, and on chemical engineering
.
and contradiction
. (When Orlov wrote this, the invention of natural deduction
, the sequent calculus
, and the semantic tableaux all lay in the future.) We must seek the semantic relation between antecedent
and consequent
. 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 in nature.
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
. It is only with the post-WWII rise of what have come to be known as substructural logic
s (Restall 2000) that Orlov's pioneering role has gradually emerged. Substructural logic
s, a category including intuitionistic
, relevant, linear logic
s, etc., can be obtained by restricting the natural deduction
("structural") rules for classical logic
. For example, relevant logic does not employ the structural rule of weakening (also called the rule of monotonicity), 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
of Georg Cantor
, the theory of relativity
(he believed in the existence of aether
), and the heliobiology of A. Chizhevsky.
, specifically the production of bromine
and iodine
, and in translating German works on chemistry into Russian.
Substructural logic
In logic, a substructural logic is a logic lacking one of the usual structural rules , such as weakening, contraction or associativity...
s, and an industrial chemist. The date of his death is unknown but is believed to have occurred no earlier than 1936.
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 reasoningInductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
and the notion of inductive proof. 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
Communist Academy
The Communist Academy was founded in Moscow on June 25, 1918, as the Socialist Academy; it was renamed in 1924...
, 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
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
and logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, specifically on the so-called dialectical logic, Marxist in nature. He wrote on the theory of probability, psychology
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
, theory of music, and on chemical engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...
.
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 identityIdentity (mathematics)
In mathematics, the term identity has several different important meanings:*An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of...
and contradiction
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...
. (When Orlov wrote this, the invention of natural deduction
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...
, the sequent calculus
Sequent calculus
In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi, systems LK and LJ, were introduced by Gerhard Gentzen in 1934 as a tool for studying natural deduction in...
, and the semantic tableaux all lay in the future.) We must seek the semantic relation between antecedent
Antecedent
An antecedent is a preceding event, condition, cause, phrase, or word. It may refer to:* Antecedent moisture, a hydrologic term describing the relative wetness condition of a sewershed.* Antecedent , the first half of a hypothetical proposition....
and consequent
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".Examples:* If P, then Q.Q is the consequent of this hypothetical proposition....
. 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
Non-Aristotelian logic
The term non-Aristotelian logic, sometimes shortened to null-A, means any non-classical system of logic which rejects one of Aristotle's premises .-History:...
, dialectical in nature.
The Logic of Compatibilty 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 implicationImplication
Implication may refer to:In logic:* Logical implication, entailment, or consequence, a relation between statements* Material implication, or conditional implication, a binary truth functionIn linguistics, specifically in pragmatics:...
procedure. He also foresaw the translation of systems with intuitionistic negation
Intuitionistic logic
Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well-formed statements are assumed to be either true or false, even if we do not have a proof of either...
into S4 modal logic
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
with classical negation
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...
.
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
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
. It is only with the post-WWII rise of what have come to be known as substructural logic
Substructural logic
In logic, a substructural logic is a logic lacking one of the usual structural rules , such as weakening, contraction or associativity...
s (Restall 2000) that Orlov's pioneering role has gradually emerged. Substructural logic
Substructural logic
In logic, a substructural logic is a logic lacking one of the usual structural rules , such as weakening, contraction or associativity...
s, a category including intuitionistic
Intuitionistic logic
Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well-formed statements are assumed to be either true or false, even if we do not have a proof of either...
, relevant, linear logic
Linear logic
Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter...
s, etc., can be obtained by restricting the natural deduction
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...
("structural") rules for classical logic
Classical logic
Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...
. For example, relevant logic does not employ the structural rule of weakening (also called the rule of monotonicity), 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
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
of Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
, the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
(he believed in the existence of aether
Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
), and the heliobiology of A. Chizhevsky.
Industrial Chemistry
Around 1928, Orlov ceased publishing logical and philosophical work, turning to industrial chemistryChemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, specifically the production of bromine
Bromine
Bromine ") is a chemical element with the symbol Br, an atomic number of 35, and an atomic mass of 79.904. It is in the halogen element group. The element was isolated independently by two chemists, Carl Jacob Löwig and Antoine Jerome Balard, in 1825–1826...
and iodine
Iodine
Iodine is a chemical element with the symbol I and atomic number 53. The name is pronounced , , or . The name is from the , meaning violet or purple, due to the color of elemental iodine vapor....
, and in translating German works on chemistry into Russian.
Further readings
- Orlov, I. E., 1925. The Logic of the Natural Sciences. Moscow-Leningrad. (in Russian).
- ------, 1928, "The Logic of Compatibility of Propositions" in Matematicheskii Sbornik 35 (3-4): 263-86 (in Russian).
- Bazhanov, V. A., 2003, "The Scholar and the 'Wolfhound Era': The Fate of Ivan E. Orlov's Ideas in Logic, Philosophy, and Science," Science in Context 16 (4): 535-50.
- Došen, K., 1992, "The First Axiomatization of Relevant Logic," Journal of Philosophical Logic 21: 339-56.
- Došen, K., 1993, "A Historical Introduction to Substructural Logics" in Substructural Logics, eds. Schroeder-Heister P., and Došen K. Oxford Univ. Press: 1-36.
- Restall, Greg, 2000. Substructural Logics. Routledge.
- Stelzner, Werner, 2002. Compatibility and relevance: Bolzano and Orlov, Logic and Logical Philosophy 10: 137-171.