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In propositional logic, tautology is either of two commonly used rules of replacement. [1] [2] [3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs.
Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. [2] A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (equiv ...
Starting from these eight tautologies and a tacit use of the "rule" of substitution, PM then derives over a hundred different formulas, among which are the Law of Excluded Middle 1.71, and the Law of Contradiction 3.24 (this latter requiring a definition of logical AND symbolized by the modern ⋀: (p ⋀ q) = def ~(~p ⋁ ~q).
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias . Illustrating a general tendency in applied logic, Aristotle 's law of noncontradiction states that "It is impossible that the same thing can at the same time both ...
However, the term tautology is also commonly used to refer to what could more specifically be called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it ...
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 ∧ ¬A) are not tautologies in Ł3. However, using the operator I defined above, it is possible to state tautologies that are their analogues: A ∨ IA ∨ ¬A (law of excluded fourth)
Indeed, the contradictions of conservative masculinity are key to its appeal. Christopher Ewing is an assistant professor of history at Purdue University. His research examines sexuality, race ...
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