Q&A: Logical Fallacy
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Logical Fallacy
Question
Hello,
You once said that if you accept one logical fallacy, you can use it to “prove” any false claim. How?
Answer
No. I said that from a system that contains a contradiction, any conclusion whatsoever can be derived. This follows from the definition of material implication. When the antecedent is intrinsically false, any consequent yields a true implication.
Discussion on Answer
It is worth noting that it’s not actually true that “from a system that contains a contradiction, any conclusion whatsoever can be derived.” That is true in propositional calculus. It is false in paraconsistent logics.
It can be shown through formal calculi. For example, you plug it into the axioms of Hilbert calculus and obtain it as true.