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Is it true that anything can be concluded from a contradiction? Can you explain? It's seems like its a tautology if taken figuratively because we can indeed conclude anything if we suspend the rules of reasoning, but there is nothing especially interesting in that fact in my humble opinion.

@William Rapaport: Unless disjunctive syllogism or one of the other two rules used in the derivation fails, the "irrelevance" of the conclusion to the premise is irrelevant to whether the conclusion follows from the premise. Relevance logic has to give up at least one of those rules, none of which is easy to give up.

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The topic is controversial (as I indicate below), but the inference rules of standard logic do allow you to derive any conclusion at all from any (formally) contradictory premise. Here's one way (let P and Q be any propositions at all): 1. P & Not-P [Premise: formal contradiction] 2. Therefore: P [From 1, by conjunction elimination] 3. Therefore: P or Q [From 2, by disjunction introduction] 4. Therefore: Not-P [From 1, by conjunction elimination] 5. Therefore: Q [From 3, 4, by disjunctive syllogism] Those who object to such derivations usually call themselves "paraconsistent" logicians; more at this SEP entry . They typically reject step 5 on the grounds that disjunctive syllogism "breaks down" in the presence of contradictions. I confess I've never found their line persuasive.

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