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 de-
nying”),
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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