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Modal logic. Ignoratio elenchi. Ignoratio elenchi, also known as irrelevant conclusion,[1] is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question.

Ignoratio elenchi

Ignoratio elenchi falls into the broad class of relevance fallacies.[2] It is one of the fallacies identified by Aristotle in his Organon. In a broader sense he asserted that all fallacies are a form of ignoratio elenchi.[3][4] Ignoratio Elenchi, according to Aristotle, is a fallacy which arises from “ignorance of the nature of refutation.” The phrase ignoratio elenchi is Latin meaning "an ignoring of a refutation". Here elenchi is the genitive singular of the Latin noun elenchus, which is from the Greek ἔλεγχος elenchos, meaning an argument of disproof or refutation.[6] The translation in English of the Latin expression has varied somewhat. An example might be a situation where A and B are debating whether the law permits A to do something. See also[edit] References[edit] Lack of belief in gods.

Principle of explosion. The principle of explosion, (Latin: ex falso quodlibet, "from a falsehood, anything follows", or ex contradictione sequitur quodlibet, "from a contradiction, anything follows") or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction.[1] That is, once a contradiction has been asserted, any proposition (or its negation) can be inferred from it.

Principle of explosion

As a demonstration of the principle, consider two contradictory statements - “All lemons are yellow” and "Not all lemons are yellow", and suppose (for the sake of argument) that both are simultaneously true. If that is the case, anything can be proven, e.g. "Santa Claus exists", by using the following argument: Symbolic representation[edit] The principle of explosion can be expressed in the following way (where " " symbolizes the relation of logical consequence): or This can be read as, "If one claims something is both true ( . Gödel's incompleteness theorems. Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic.

Gödel's incompleteness theorems


Fuzzy logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact.

Fuzzy logic


Irrationality can be described in terms of what is known as the fuzzjective. [citation needed] The term "fuzzy logic" was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Three-valued logic. In logic, a three-valued logic (also trivalent, ternary, trinary logic, or trilean,[citation needed] sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.

Three-valued logic

This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false. Conceptual form and basic ideas were initially created by Jan Łukasiewicz and C. I. Lewis. These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.