Modus tollens
Rule of logical inference / From Wikipedia, the free encyclopedia
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In propositional logic, modus tollens (/ˈmoʊdəs ˈtɒlɛnz/) (MT), also known as modus tollendo tollens (Latin for "method of removing by taking away")[2] and denying the consequent,[3] is a deductive argument form and a rule of inference. 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.
Type | |
---|---|
Field | |
Statement | implies . is false. Therefore, must also be false. |
Symbolic statement | [1] |
The history of the inference rule modus tollens goes back to antiquity.[4] The first to explicitly describe the argument form modus tollens was Theophrastus.[5]
Modus tollens is closely related to modus ponens. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive.