In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is...
38 KB (5,693 words) - 21:00, 11 July 2024
ambiguous expressions: the law of identity (ID), the law of contradiction (or non-contradiction; NC), and the law of excluded middle (EM). Sometimes, these...
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one of the so called three laws of thought, along with its complement, the law of excluded middle, and the law of identity. However, no system of logic...
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Brouwer–Hilbert controversy (category History of mathematics)
objected to the use of the law of excluded middle over infinite sets. Hilbert responded: "Taking the Principle of the Excluded Middle from the mathematician...
30 KB (4,442 words) - 15:34, 24 September 2024
noncontradiction, and the law of excluded middle. However, few systems of logic are built on just these laws. The earliest recorded use of the law appears in Plato's...
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propositional logic. It can be thought of as the law of excluded middle written in a form that involves only one sort of connective, namely implication. In...
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principle of bivalence is related to the law of excluded middle though the latter is a syntactic expression of the language of a logic of the form "P...
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Proof by contradiction (category Methods of proof)
to derive it from the law of the excluded middle, as follows. We assume ¬¬P and seek to prove P. By the law of excluded middle P either holds or it does...
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Thought (redirect from Nature of human thought)
the topic of thought. The term "law of thought" refers to three fundamental laws of logic: the law of contradiction, the law of excluded middle, and the...
120 KB (13,687 words) - 03:47, 27 September 2024
Cantor's diagonal argument (category Theorems in the foundations of mathematics)
the law of excluded middle is not taken as axiom), it is consistent to adopt non-classical axioms that contradict consequences of the law of excluded middle...
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Definite description (redirect from Present King of France)
Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content. As France is currently...
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Calculus (redirect from Degree of smallness)
in terms of discrete entities. One aspect of this formulation is that the law of excluded middle does not hold. The law of excluded middle is also rejected...
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early formulation of the law of trichotomy Dichotomy Law of noncontradiction Law of excluded middle Three-way comparison Trichotomy Law at MathWorld Jerrold...
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Intuitionistic logic (redirect from Semantics of intuitionistic logic)
constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and double negation elimination, which are...
51 KB (7,743 words) - 01:40, 20 September 2024
Type theory (redirect from Elementary Theory of the Category of Sets)
by their rules of inference. Classical set theory and logic have the law of excluded middle. When a type theory encodes the concepts of "and" and "or"...
59 KB (7,869 words) - 19:35, 13 September 2024
False dilemma (redirect from Fallacy of the excluded middle)
Contradictories follow the law of the excluded middle but contraries do not. For example, the sentence "the exact number of marbles in the urn is either...
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Impossible world (category Articles with Internet Encyclopedia of Philosophy links)
For the sake of argument, assume that either (or both) of the following are the case: 1. Intuitionism is false. 2. The law of excluded middle is true. Presumably...
10 KB (1,364 words) - 23:03, 6 November 2023
TND (TV station), in Darwin, Australia Tertium non datur, the law of excluded middle, a law in logic The National Desk, an American television news program...
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Pre-intuitionism (category Theories of deduction)
still used principium tertii exclusi (the "law of excluded middle"). The principle of the excluded middle does lead to some strange situations. For instance...
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Since p ⇒ q and ~q ⇒ ~p are equivalent by the principle of transposition (see law of excluded middle), p ⇒ q is indirectly proved. Proof methods that are...
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Constructive proof (redirect from Proof of Existence)
existence of objects that are not explicitly built. This excludes, in particular, the use of the law of the excluded middle, the axiom of infinity, and...
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Philosophical logic (redirect from Classification of logic)
intuitions shared by many, like the law of excluded middle, the double negation elimination, and the bivalence of truth. Extended logics are logical systems...
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definition of dichotomy at Wiktionary Binary opposition Bipartite (disambiguation) Class (set theory) Dichotomy paradox Dilemma Law of excluded middle, which...
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formula when applied to an appropriate number of terms. In set theory with the law of excluded middle, predicates are understood to be characteristic...
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Many-valued logic (redirect from Applications of many-valued logic)
fact, Aristotle did not contest the universality of the law of excluded middle, but the universality of the bivalence principle: he admitted that this principle...
30 KB (3,346 words) - 23:05, 6 November 2023
(intuitionistic) truth of some instance of the law of excluded middle, p ∨ ¬ p {\displaystyle p\lor \neg p} . weak excluded middle A principle in intuitionistic...
270 KB (30,189 words) - 22:16, 28 September 2024
consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the law of excluded middle is true, then all instances of the formula (A...
46 KB (5,764 words) - 12:56, 17 July 2024
Three-valued logic (redirect from Law of excluded fourth)
logic. Not all tautologies of classical logic lift to Ł3 "as is". For example, the law of excluded middle, A ∨ ¬A, and the law of non-contradiction, ¬(A ∧...
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and not be.' The law of excluded middle: 'Everything must either be or not be.' In accordance with the law of excluded middle or excluded third, for every...
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non-constructive foundational material such as the axiom of infinity, the axiom of choice or the law of excluded middle. Such theorems provide no indication as to how...
6 KB (631 words) - 20:12, 16 July 2024