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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).
Nicolai A. Vasiliev 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.
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)
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.
The concept of non-Aristotelian logic was used by A. E. van Vogt as the central theme in his The World of Null-A novels, based on his interest in general semantics. The stories were tinged by van Vogt's reaction to real-life news reports of police state conditions in the 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 highlights the aspect of general semantics in his science fiction (SF) stories, that portrays the general semantics as a speech evaluation tool. It occurs where heroic characters use general semantics to struggle against the rousing orations used as an incremental tactic by the minions of authoritarian entities. Alfred Korzybski's development and description the general semantics was not as a 'logic', but as a non-Aristotelian system of evaluation. Van Vogt depicted the general semantics as a method of evaluation used to analyze the reasoning of others. Protagonists in van Vogt's science fiction novels typically use a dream-like, null-A reasoning to outwit villains who rely upon decision-tree, or algorithmic, reasoning, akin to Aristotelian logic.
Van Vogt was not the only Golden Age writer of SF 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: