Concept
Deviant logic
Overview
Deviant logic is a type of logic incompatible with classical 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.
the set of theorems generated is different from the set of theorems generated by classical logic.
The set of theorems of a deviant logic can differ in any possible way from classical logic's set of theorems: as a proper subset, superset, or fully exclusive set. A notable example of this is the trivalent logic developed by Polish logician and mathematician Jan Łukasiewicz. Under this system, any theorem necessarily dependent on classical logic's principle of bivalence would fail to be valid. The term deviant logic first appears in Chapter 6 of Willard Van Orman Quine's Philosophy of Logic, New Jersey: Prentice Hall (1970), which is cited by Haack on p. 15 of her book.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Deviant logic is.
The chief business of the logician is to classify arguments; for all testing clearly depends on classification. The classes of the logicians are defined by certain typical forms called syllogisms. For example, the syllogism called _Barbara_ is as follows: S is M; M is P: Hence, S is P. Or, to put words for letters— Enoch and Elijah were men; all men die: Hence, Enoch and Elijah must have died.
Charles S. Peirce, Chance, Love, and Logic
States what Deviant logic is.
This complete quantity of the extent in relation to such a condition is called universality (universalitas). To this corresponds totality (universitas) of conditions in the synthesis of intuitions. The transcendental conception of reason is therefore nothing else than the conception of the totality of the conditions of a given conditioned. Now as the unconditioned alone renders possible totality of conditions, and…
Immanuel Kant, The Critique of Pure Reason
States what Deviant logic is.
Related ideas
- Mathematician
- Philosophy of logic
- Principle of bivalence
- Set (mathematics)
- Subset
- Jan Łukasiewicz
- Theorem
- Susan Haack
- Vagueness
- Modal logic
- Willard Van Orman Quine
- Well-formed formula
- Paraconsistent logic
- The Philosophical Review
- Logic
- Fuzzy logic
- Classical logic
- Linear logic
- Achille Varzi (philosopher)
Place in the tradition
Part of Non-classical logic.