Non-Aristotelian logic
Encyclopedia
The term non-Aristotelian logic, sometimes shortened to null-A, means any non-classical system of logic which rejects one of Aristotle's premises (see term logic
).
since 1910 and Jan Łukasiewicz called their own work non-Aristotelian logic. Alfred Korzybski
carried the term into his system of General Semantics
in 1933 (citing Łukasiewicz), and science fiction writer A. E. van Vogt
later helped popularize it. Korzybski focused on the use of three or more truth values in the new systems of logic, although he connected this to his own rejection of Aristotle's principle of identity. Following Łukasiewicz's early work, Korzybski and later proponents of General Semantics
associate these truth values with probabilities and the use of scientific induction. Łukasiewicz later seemed more cautious about this connection.
While Łukasiewicz seems to have spent more time on three-valued logic than any other system, he said that one could keep increasing the number of truth values indefinitely. Thus, he wrote: "if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details." Richard Threlkeld Cox
later showed in Cox's theorem
that any extension of Aristotelian logic to incorporate truth values between 0 and 1, in order to be consistent, must be equivalent to Bayesian probability
.
Nicolai A. Vasiliev
in 1910 rejected the law of contradiction as well as law of the excluded middle and proposed a logic he called imaginary which is tolerant to contradiction.
Hans Reichenbach
described a system of logic that he explicitly linked with probability theory. He called his probability logic a generalization of two-valued logic. Reichenbach also suggested applying a three-valued logic to quantum mechanics
. His probability logic does not receive much attention from modern logicians.
Aristotle allowed for the possibility of all these logics in De Interpretatione, Chapter 9. He wrote here that when it comes to statements about the future, "it is not necessary that of every affirmation and opposite negation one should be true and the other false." (Revised Oxford translation)
Lotfi Zadeh developed a system of "fuzzy logic
" using a range of truth values from 0 to 1, but distinguished it sharply from probability theory.
Robert Anton Wilson
in The New Inquisition
developed a non-Aristotelian system of classification in which propositions can be assigned one of 7 values: true, false, indeterminate, meaningless, self-referential, game rule, or strange loop
. Wilson did not devise a formal system
for manipulating propositions once classified, but suggested that we can clarify our thinking by not restricting ourselves to simplistic true/false binaries.
Alternative terms for these logics in common academic usage include deviant logic
and multi-valued logic
(see Haack, 'Philosophy of Logic', 1980). Not all non-classical logics fall into this class, e.g. Modal logic
is a non-classical logic which, however, has only two truth values.
as the central theme in his The World of Null-A novels, based on his interest in Alfred Korzybski's
General Semantics
, stories tinged by van Vogt's reflections upon revelations of police state conditions enforced by totalitarian regimes after World War II.
Van Vogt generally shortened non-Aristotelian logic to null-A in his description of logic systems incorporating three or more values, to represent relatively 'subjective' conclusions from inductive logic, rather than relying strictly on the binary, deductive reasoning. The null-A concept as depicted by van Vogt is complementary to Aristotle's system of two-valued, true/false logic, i.e., "A is either B, or it is not B. "
Van Vogt's portrayals of General Semantics in science fiction science fiction
(SF) stories (wherein heroic characters struggled against incrementally stem-winding tactics used by minions of authoritarian entities), was somewhat different from its originator's, as Korzybski developed and described General Semantics not as a 'logic', but as a non-Aristotelian system of evaluation. On the other hand, van Vogt also depicted General Semantics as a method of evaluation used to analyze the reasoning of others. Protagonists in van Vogt's science fiction novels typically used null-A reasoning in almost dream-like settings to outwit villains who relied almost exclusively upon decision-tree, algorithmic reasoning, akin to the use of Aristotelian logic.
Van Vogt was not the only Golden Age
writer of SF that was influenced by Alfred Korzybski.
A major writer of the Golden Age Robert Heinlein explicitly incorporated general semantics formulations and themes. He stated in 1941, regarding Korzybski,
An example of such incorporation by Heinlein is given by Alexei and Cory Panshin from the first few paragraphs of Heinlein’s short novel ‘If This Goes On—’ (1940). The Panshins also illustrate how another major writer of the Golden Age Isaac Asimov
was influenced by General Semantics choosing as an example the Foundation story “The Big and the Little”, stating:
Roger Luckhurst in his volume Science Fiction in the ‘Cultural History of Literature' series shows that General Semantics continued to exert influence on SF beyond the Golden Age, stating that Frank Herbert's
:
Term logic
In philosophy, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century...
).
History
Nicolai A. VasilievNicolai A. Vasiliev
Nicolai Alexandrovich Vasiliev , also Vasil'ev, Vassilieff, Wassilieff was a Russian logician, philosopher, psychologist, poet, the forerunner of paraconsistent and multi-valued logics.-Early years:...
since 1910 and Jan Łukasiewicz called their own work non-Aristotelian logic. Alfred Korzybski
Alfred Korzybski
Alfred Habdank Skarbek Korzybski was a Polish-American philosopher and scientist. He is remembered for developing the theory of general semantics...
carried the term into his system of General Semantics
General Semantics
General semantics is a program begun in the 1920's that seeks to regulate the evaluative operations performed in the human brain. After partial program launches under the trial names "human engineering" and "humanology," Polish-American originator Alfred Korzybski fully launched the program as...
in 1933 (citing Łukasiewicz), and science fiction writer A. E. van Vogt
A. E. van Vogt
Alfred Elton van Vogt was a Canadian-born science fiction author regarded by some as one of the most popular and complex science fiction writers of the mid-twentieth century: the "Golden Age" of the genre....
later helped popularize it. Korzybski focused on the use of three or more truth values in the new systems of logic, although he connected this to his own rejection of Aristotle's principle of identity. Following Łukasiewicz's early work, Korzybski and later proponents of General Semantics
General Semantics
General semantics is a program begun in the 1920's that seeks to regulate the evaluative operations performed in the human brain. After partial program launches under the trial names "human engineering" and "humanology," Polish-American originator Alfred Korzybski fully launched the program as...
associate these truth values with probabilities and the use of scientific induction. Łukasiewicz later seemed more cautious about this connection.
While Łukasiewicz seems to have spent more time on three-valued logic than any other system, he said that one could keep increasing the number of truth values indefinitely. Thus, he wrote: "if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details." Richard Threlkeld Cox
Richard Threlkeld Cox
Richard Threlkeld Cox was a professor of physics at Johns Hopkins University, known for Cox's theorem relating to the foundations of probability....
later showed in Cox's theorem
Cox's theorem
Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This derivation justifies the so-called "logical" interpretation of probability. As the laws of probability derived by Cox's theorem are applicable to...
that any extension of Aristotelian logic to incorporate truth values between 0 and 1, in order to be consistent, must be equivalent to Bayesian probability
Bayesian probability
Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...
.
Nicolai A. Vasiliev
Nicolai A. Vasiliev
Nicolai Alexandrovich Vasiliev , also Vasil'ev, Vassilieff, Wassilieff was a Russian logician, philosopher, psychologist, poet, the forerunner of paraconsistent and multi-valued logics.-Early years:...
in 1910 rejected the law of contradiction as well as law of the excluded middle and proposed a logic he called imaginary which is tolerant to contradiction.
Hans Reichenbach
Hans Reichenbach
Hans Reichenbach was a leading philosopher of science, educator and proponent of logical empiricism...
described a system of logic that he explicitly linked with probability theory. He called his probability logic a generalization of two-valued logic. Reichenbach also suggested applying a three-valued logic to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. His probability logic does not receive much attention from modern logicians.
Aristotle allowed for the possibility of all these logics in De Interpretatione, Chapter 9. He wrote here that when it comes to statements about the future, "it is not necessary that of every affirmation and opposite negation one should be true and the other false." (Revised Oxford translation)
Lotfi Zadeh developed a system of "fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
" using a range of truth values from 0 to 1, but distinguished it sharply from probability theory.
Robert Anton Wilson
Robert Anton Wilson
Robert Anton Wilson , known to friends as "Bob", was an American author and polymath who became at various times a novelist, philosopher, psychologist, essayist, editor, playwright, poet, futurist, civil libertarian and self-described agnostic mystic...
in The New Inquisition
The New Inquisition
The New Inquisition is a book written by Robert Anton Wilson and first published in 1986. The New Inquisition is a book about ontology, science, paranormal events, and epistemology. Wilson identifies what he calls "Fundamentalist Materialism" belief and compares it to religious...
developed a non-Aristotelian system of classification in which propositions can be assigned one of 7 values: true, false, indeterminate, meaningless, self-referential, game rule, or strange loop
Strange loop
A strange loop arises when, by moving up or down through a hierarchical system, one finds oneself back where one started.Strange loops may involve self-reference and paradox...
. Wilson did not devise a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
for manipulating propositions once classified, but suggested that we can clarify our thinking by not restricting ourselves to simplistic true/false binaries.
Alternative terms for these logics in common academic usage include deviant logic
Deviant logic
Philosopher Susan Haack uses the term "deviant logic" to describe certain non-classical systems of logic. In these logics,* the set of well-formed formulas generated equals the set of well-formed formulas generated by classical logic....
and multi-valued logic
Multi-valued logic
In logic, a many-valued logic is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values for any proposition...
(see Haack, 'Philosophy of Logic', 1980). Not all non-classical logics fall into this class, e.g. 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...
is a non-classical logic which, however, has only two truth values.
Use in science fiction
The concept of non-Aristotelian logic was used by A. E. van VogtA. E. van Vogt
Alfred Elton van Vogt was a Canadian-born science fiction author regarded by some as one of the most popular and complex science fiction writers of the mid-twentieth century: the "Golden Age" of the genre....
as the central theme in his The World of Null-A novels, based on his interest in Alfred Korzybski's
Alfred Korzybski
Alfred Habdank Skarbek Korzybski was a Polish-American philosopher and scientist. He is remembered for developing the theory of general semantics...
General Semantics
General Semantics
General semantics is a program begun in the 1920's that seeks to regulate the evaluative operations performed in the human brain. After partial program launches under the trial names "human engineering" and "humanology," Polish-American originator Alfred Korzybski fully launched the program as...
, stories tinged by van Vogt's reflections upon revelations of police state conditions enforced by totalitarian regimes after World War II.
Van Vogt generally shortened non-Aristotelian logic to null-A in his description of logic systems incorporating three or more values, to represent relatively 'subjective' conclusions from inductive logic, rather than relying strictly on the binary, deductive reasoning. The null-A concept as depicted by van Vogt is complementary to Aristotle's system of two-valued, true/false logic, i.e., "A is either B, or it is not B. "
Van Vogt's portrayals of General Semantics in science fiction science fiction
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...
(SF) stories (wherein heroic characters struggled against incrementally stem-winding tactics used by minions of authoritarian entities), was somewhat different from its originator's, as Korzybski developed and described General Semantics not as a 'logic', but as a non-Aristotelian system of evaluation. On the other hand, van Vogt also depicted General Semantics as a method of evaluation used to analyze the reasoning of others. Protagonists in van Vogt's science fiction novels typically used null-A reasoning in almost dream-like settings to outwit villains who relied almost exclusively upon decision-tree, algorithmic reasoning, akin to the use of Aristotelian logic.
Van Vogt was not the only Golden Age
Golden Age of Science Fiction
The first Golden Age of Science Fiction — often recognized as the period from the late 1930s through the 1950s — was an era during which the science fiction genre gained wide public attention and many classic science fiction stories were published...
writer of SF that was influenced by Alfred Korzybski.
- “The tangled relation of general semantics to science fiction began within seven years of the publication of Science and Sanity. John W. Campbell, Jr.John W. CampbellJohn Wood Campbell, Jr. was an influential figure in American science fiction. As editor of Astounding Science Fiction , from late 1937 until his death, he is generally credited with shaping the so-called Golden Age of Science Fiction.Isaac Asimov called Campbell "the most powerful force in...
, the influential editor of Astounding Science Fiction magazine, who regarded general semantics as a prototype 'futurescience,' encouraged several of his most popular writers to familiarize themselves with the general semantics literature. Campbell hoped they would incorporate some general semantics theory or methodology in their stories. Several writers did so …”
A major writer of the Golden Age Robert Heinlein explicitly incorporated general semantics formulations and themes. He stated in 1941, regarding Korzybski,
- “You may not like him personally, but he's at least as great a man as Einstein - at least - because his field is broader. The same kind of work that Einstein did, the same kind of work, using the same methods; but in a much broader field, much more close to human relationships.”
An example of such incorporation by Heinlein is given by Alexei and Cory Panshin from the first few paragraphs of Heinlein’s short novel ‘If This Goes On—’ (1940). The Panshins also illustrate how another major writer of the Golden Age Isaac Asimov
Isaac Asimov
Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...
was influenced by General Semantics choosing as an example the Foundation story “The Big and the Little”, stating:
- “One of the particular strengths of this story was that it presented in dramatic form, a full year before the publication of van Vogt’s The World of Null-A, some of the key ideas associated with Alfred Korzybski.”
Roger Luckhurst in his volume Science Fiction in the ‘
Frank Herbert
Franklin Patrick Herbert, Jr. was a critically acclaimed and commercially successful American science fiction author. Although a short story author, he is best known for his novels, most notably Dune and its five sequels...
:
- “DuneDune (novel)Dune is a science fiction novel written by Frank Herbert, published in 1965. It won the Hugo Award in 1966, and the inaugural Nebula Award for Best Novel...
also evidences the continuing influence on American SF of Alfred Korzybski’s engineering of subjectivity. Herbert, who was ghostwriting a newspaper column on General Semantics whilst completing Dune, details the ‘Bene GesseritBene GesseritThe Bene Gesserit are a key social, religious, and political force in Frank Herbert's science fiction Dune universe. The group is described as an exclusive sisterhood whose members train their bodies and minds through years of physical and mental conditioning to obtain superhuman powers and...
’ mental training method which includes hyper-acute sensitivity, powers of projecting mental will onto others, and even eugenic control of reproduction – ideas not far away from the claims of L Ron Hubbard’sL. Ron HubbardLafayette Ronald Hubbard , better known as L. Ron Hubbard , was an American pulp fiction author and religious leader who founded the Church of Scientology...
DianeticsDianeticsDianetics is a set of ideas and practices regarding the metaphysical relationship between the mind and body that was invented by the science fiction author L. Ron Hubbard and is practiced by followers of Scientology...
. This places Dune, in direct lineal descent from Campbellian SF.”
See also
- Intuitionistic logicIntuitionistic logicIntuitionistic 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...
- Fuzzy logicFuzzy logicFuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
- General SemanticsGeneral SemanticsGeneral semantics is a program begun in the 1920's that seeks to regulate the evaluative operations performed in the human brain. After partial program launches under the trial names "human engineering" and "humanology," Polish-American originator Alfred Korzybski fully launched the program as...
- Meta-systemsMeta-systemsMeta-systems have several definitions. In general, they link the concepts "system" and "meta-". A "meta-system" is a system about other systems, such as describing, generalizing, modelling, or analyzing the other system....
- Multi-valued logicMulti-valued logicIn logic, a many-valued logic is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values for any proposition...
- Paraconsistent logicParaconsistent logicA paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent systems of logic.Inconsistency-tolerant logics have been...
- Quantum logicQuantum logicIn quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account...
- Is logic empirical?Is logic empirical?"Is logic empirical?" is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic...
- Theory of mindTheory of mindTheory of mind is the ability to attribute mental states—beliefs, intents, desires, pretending, knowledge, etc.—to oneself and others and to understand that others have beliefs, desires and intentions that are different from one's own...
Some developers of non-Aristotelian logics
- Giordano BrunoGiordano BrunoGiordano Bruno , born Filippo Bruno, was an Italian Dominican friar, philosopher, mathematician and astronomer. His cosmological theories went beyond the Copernican model in proposing that the Sun was essentially a star, and moreover, that the universe contained an infinite number of inhabited...
- Asger JornAsger JornAsger Oluf Jorn was a Danish painter, sculptor, ceramic artist, and author. He was a founding member of the avant-garde movement COBRA and the Situationist International...
- Nicolai A. VasilievNicolai A. VasilievNicolai Alexandrovich Vasiliev , also Vasil'ev, Vassilieff, Wassilieff was a Russian logician, philosopher, psychologist, poet, the forerunner of paraconsistent and multi-valued logics.-Early years:...
- Jan Łukasiewicz
- Stéphane LupascoStéphane LupascoStéphane Lupasco Stéphane Lupasco Stéphane Lupasco (born Ştefan Lupaşcu; (1900–1988) was a Romanian philosopher who developed Non-Aristotelian logic.-Early years:Stéphane Lupasco was born in Bucharest on 11 August 1900. His family belonged to the old Moldavian aristocracy...
External links
- Lukasiewicz on the Principle of Contradiction from the Journal of Philosophical Research, on the logician and his relation to Aristotle
- Reichenbach's Probability Logic and the Lvov-Warsaw School on attempts to merge logic with probability (also mentions Łukasiewicz)