Concept
Infinite-valued logic
Overview
In logic, an infinite-valued logic (or real-valued logic or infinitely-many-valued logic) is a many-valued logic in which truth values comprise a continuous range. Traditionally, in Aristotle's logic, logic other than bivalent logic was abnormal, as the law of the excluded middle precluded more than two possible values (i.e., "true" and "false") for any proposition. Modern three-valued logic (trivalent logic) allows for an additional possible truth value (i.e., "undecided") and is an example of finite-valued logic in which truth values are discrete, rather than continuous. Infinite-valued logic comprises continuous fuzzy logic, though fuzzy logic in some of its forms can further encompass finite-valued logic. For example, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification of fuzzy logic.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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That gives rise to these eternal, and usually mistaken, contentions on necessity and contingency, on the possible and the impossible. But provided that it is understood that necessity and possibility, taken metaphysically and strictly, depend solely upon this question, whether the object in itself or that which is opposed to it implies contradiction or not; and that one takes into account that contingency is…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
States what Infinite-valued logic is; the author is tied to Infinite-valued logic in the knowledge graph.
The logical basis of the theory alone belongs to philosophy, and alone will occupy us to-night. The way the problem of continuity enters into philosophy is, broadly speaking, the following: Space and time are treated by mathematicians as consisting of points and instants, but they also have a property, easier to feel than to define, which is called continuity, and is thought by many philosophers to be destroyed when…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Infinite-valued logic is.
Hence, in the conclusion of a syllogism we restrict a predicate to a certain object, after having thought it in the major in its whole extent under a certain condition. 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…
Immanuel Kant, The Critique of Pure Reason
States what Infinite-valued logic is.
Related ideas
- First-order logic
- Felix Hausdorff
- Gottfried Wilhelm Leibniz
- Bas van Fraassen
- Imaginary number
- Isaac Newton
- Truth value
- Kurt Gödel
- Intuitionistic logic
- Synthese
- Law of excluded middle
- Mathematics
- Rational number
- Infinity
- Real number
- Natural language
- Sorites paradox
- Richard Dedekind
- Principle of bivalence
- Paradox
- Trial and error
- Three-valued logic
- Stephen Cole Kleene
- Jan Łukasiewicz
Place in the tradition
Part of Intuitionistic logic.