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Concept
Modus ponens
Summary
In propositional logic, modus ponens (ˈmoʊdəs_ˈpoʊnɛnz; MP), also known as modus ponendo ponens (Latin for "method of putting by placing"), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q. P is true. Therefore Q must also be true."
Modus ponens is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of modus ponens. Hypothetical syllogism is closely related to modus ponens and sometimes thought of as "double modus ponens."
The history of modus ponens goes back to antiquity. The first to explicitly describe the argument form modus ponens was Theophrastus. It, along with modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal.
The form of a modus ponens argument resembles a syllogism, with two premises and a conclusion:
If P, then Q.
P.
Therefore, Q.
The first premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is the case. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be the case as well.
An example of an argument that fits the form modus ponens:
If today is Tuesday, then John will go to work.
Today is Tuesday.
Therefore, John will go to work.
This argument is valid, but this has no bearing on whether any of the statements in the argument are actually true; for modus ponens to be a sound argument, the premises must be true for any true instances of the conclusion. An argument can be valid but nonetheless unsound if one or more premises are false; if an argument is valid and all the premises are true, then the argument is sound. For example, John might be going to work on Wednesday.
Official source
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