Claim

Negation introduction

Overview

logical rule of inference where the conclusion is that a proposition is false

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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1. As when the conclusion is accepted, which it so often is, for proof of the premises. That the premises can not be true if the conclusion is false, is the unexceptionable foundation of the legitimate mode of reasoning called _reductio ad absurdum_. But people continually think and express themselves, as if they also believed that the premises can not be false if the conclusion is true.

   John Stuart Mill, A System of Logic, Ratiocinative and Inductive

   Close in meaning to Negation introduction; the term itself is not named.

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2. But, in this way, an hypothesis can never be established as a demonstrated truth. The modus tollens of reasoning from known inferences to the unknown proposition, is not only a rigorous, but a very easy mode of proof. For, if it can be shown that but one inference from a proposition is false, then the proposition must itself be false. Instead, then, of examining, in an ostensive argument, the whole series of the…

   Immanuel Kant, The Critique of Pure Reason

   Close in meaning to Negation introduction; the term itself is not named.

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3. XXX. However, I will pass over all this. I ask, if those things cannot be explained, and if no means of judging of them is discovered, so that you can answer whether they are true or false, then what has become of that definition,—“That a proposition (_effatum_) is something which is either true or false?” After the facts are assumed I will add, that of them some are to be adopted, others impeached, because they are…

   Marcus Tullius Cicero, The Academic Questions, Treatise De Finibus, and Tusculan Disputations, of M.T. Cicero, With a Sketch of the Greek Philosophers Mentioned by

   Close in meaning to Negation introduction; the term itself is not named.

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Philosophers who discussed Negation introduction

• Stephen Yablo

Related ideas

• Law of noncontradiction
• Propositional logic
• Rule of inference
• Minimal logic
• Frege's theorem
• Currying
• Disjunctive syllogism
• Material implication (rule of inference)

Place in the tradition

Part of Intuitionistic logic.

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