modus ponens and modus tollens
 modus ponens and modus tollens

(
Latin: "method of affirming" and "method of denying") In
logic, two types of inference that can be drawn using a hypothetical proposition
i.
e., from a proposition of the form "If p, then q" (symbolically p ⊃ q). Modus ponens refers to inferences of the form p ⊃ q; p, therefore q. Modus tollens refers to inferences of the form p ⊃ q; ¬q, therefore, ¬p. An example of modus tollens is the following: "If an angle is inscribed in a semicircle, then it is a right angle; this angle is not a right angle; therefore, this angle is not inscribed in a semicircle."
* * *
(
Latin: “method of affirming” and “method of denying”), in propositional logic, two types of inference that can be drawn from a hypothetical proposition—
i.e., from a proposition of the form “If
A, then
B” (
symbolically A ⊃
B, in which ⊃ signifies “If . . . then”).
Modus ponens refers to inferences of the form
A ⊃
B;
A, therefore
B.
Modus tollens refers to inferences of the form
A ⊃
B; ∼
B, therefore, ∼
A (∼ signifies “not”). An example of
modus tollens is the following:
If an angle is inscribed in a semicircle, then it is a right angle; this angle is not a right angle; therefore, this angle is not inscribed in a semicircle.
For disjunctive premises (employing ∨, which signifies “either . . . or”), the
terms modus tollendo ponens and
modus ponendo tollens are used for arguments of the forms
A ∨
B; ∼
A, therefore
B, and
A ∨
B;
A, therefore ∼
B (valid only for exclusive disjunction: “Either
A or
B but not both”). The rule of
modus ponens is incorporated into virtually every formal system of logic.
* * *
Universalium.
2010.
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