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Can Modus Ponens Be Invalid?

Maya Lin-Takahashi • • 7 min read
Can Modus Ponens Be Invalid?

30] In cases that the first premise is the probabilistic or abductive conditional, he suggests, modus ponens is deduc- tively invalid. But he also admits that modus ponens is valid in the case of an absolute conditional. Third, denying the antecedent (DA) and affirming the consequent

affirming the consequent
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dark,") and invalidly inferring its converse ("The room is dark, so the lamp ...
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(AC) are regarded as invalid forms.

Can a modus tollens argument have false premises and a true conclusion?

A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion. ... Since a sound argument is valid, it is such that if all the premises are true then the conclusion must be true.

How do you prove modus ponens?

Conjunction If both hypotheses are true, then the conjunction of them is true. Modus ponens If both hypotheses are true, then the conclusion is true. Modus tollens If a hypothesis is not true and an implication is true, then the other proposition cannot be true.

Maya Lin-Takahashi
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Maya Lin-Takahashi

Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.