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Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
This diagram shows the contradictory relationships between categorical propositions in the square of opposition of Aristotelian logic. 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.
David Dunning Some researchers include a metacognitive component in their definition. In this view, the Dunning–Kruger effect is the thesis that those who are incompetent in a given area tend to be ignorant of their incompetence, i.e., they lack the metacognitive ability to become aware of their incompetence. This definition lends itself to a simple explanation of the effect: incompetence ...
Affirming the consequent is the action of taking a true statement and invalidly concluding its converse . The name affirming the consequent derives from using the consequent, Q, of , to conclude the antecedent P. This fallacy can be summarized formally as or, alternatively, . [5]
Description. The simplest and most common form of mathematical induction infers that a statement involving a natural number n (that is, an integer n ≥ 0 or 1) holds for all values of n. The proof consists of two steps: The base case (or initial case): prove that the statement holds for 0, or 1. The induction step (or inductive step, or step ...
Law of effect. The law of effect, or Thorndike's law, is a psychology principle advanced by Edward Thorndike in 1898 on the matter of behavioral conditioning (not then formulated as such) which states that "responses that produce a satisfying effect in a particular situation become more likely to occur again in that situation, and responses ...
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 ...