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In case of the difficulty in trying to derive a contradiction, one should proceed as follows. From the negation of the corresponding conditional derive a theorem in conjunctive normal form in the methodical fashions described in text books. If, and only if, the original argument was valid will the theorem in conjunctive normal form be a ...
Chainstore paradox: Even those who know better play the so-called chain store game in an irrational manner. Decision-making paradox: Selecting the best decision-making method is a decision problem in itself. Ellsberg paradox: People exhibit ambiguity aversion (as distinct from risk aversion), in contradiction with expected utility theory.
Of its five connectives, {∧, ∨, →, ¬, ⊥}, only negation "¬" can be reduced to other connectives (see False (logic) § False, negation and contradiction for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical connectives.
The law of identity can be expressed as (=), where x is a variable ranging over the domain of all individuals. In logic, there are various different ways identity can be handled. In first-order logic with identity, identity is treated as a logical constant and its axioms are part of the logic itself. Under this convention, the law of identity ...
In classical logic, Aristotle's three laws, namely, the excluded middle (p or ¬p), non-contradiction ¬ (p ∧ ¬p) and identity (p iff p), are regarded as the same, due to the inter-definition of the connectives. Moreover, traditionally contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality ...
Contradiction: Spot the Liar!, also known as Contradiction: The All-Video Murder Mystery Adventure or just Contradiction is an FMV game developed by video game music composer Tim Follin through Kickstarter crowdfunding with production company Baggy Cat and released through Apple Inc.'s iOS App Store and Mac App Store on January 14, 2015 and Steam on July 10, 2015.
The material conditional (also known as material implication) is an operation commonly used in logic.When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false.
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...