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In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") [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 ...
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens. The history of modus ponens goes back to antiquity. [4]
Much like modus ponens and modus tollens, hypothetical syllogism (sometimes abbreviated as HS) contains two premises and a conclusion. It is, however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well.
A valid mixed hypothetical syllogism either affirms the antecedent (modus ponens) or denies the consequent (modus tollens). An invalid hypothetical syllogism either affirms the consequent (fallacy of the converse) or denies the antecedent (fallacy of the inverse). A pure hypothetical syllogism is a syllogism in which both premises and the ...
In classical logic, disjunctive syllogism [1] [2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. [5] [6] An example in English: I will choose soup or I will choose salad. I will not choose ...
Modus ponendo tollens (MPT; [1] Latin: "mode that denies by affirming") [2] is a valid rule of inference for propositional logic. It is closely related to modus ponens and modus tollendo ponens . Overview
This is the modus ponens rule of propositional logic. Rules of inference are often formulated as schemata employing metavariables . [ 2 ] In the rule (schema) above, the metavariables A and B can be instantiated to any element of the universe (or sometimes, by convention, a restricted subset such as propositions ) to form an infinite set of ...
Of the possible forms of "mixed hypothetical syllogisms," two are valid and two are invalid. Affirming the antecedent (modus ponens) and denying the consequent (modus tollens) are valid. Affirming the consequent and denying the antecedent are invalid. [7]