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What happens if we choose premises that aren’t just wrong (i.e., they don’t correctly describe the world)? What happens if they actually contradict each other? It turns out that, if we do that, in even one case, we’ll be able to prove any conclusion we can come up with.
24 wrz 1996 · A standard contemporary logical view has it that, from contradictory premises, anything follows. A logical consequence relation is explosive if according to it any arbitrary conclusion \ (B\) is entailed by any arbitrary contradiction \ (A\), \ (\neg A\) (ex contradictione quodlibet (ECQ)).
9 maj 2023 · For example, if one statement claims that the sky is blue and another statement claims that the sky is not blue, then these two statements are contradictory. In argumentation, a contradiction can be used to undermine the validity of a claim by demonstrating that it is logically inconsistent.
8 kwi 2015 · An argument would be valid when "it would be impossible (in the sense of contradictory) for all the premises to be true and the conclusion to be false. For example: P1.
10 mar 2021 · Here is a very simple example. We test '(3x)(Bx & -Bx)' to see whether it is a contradiction: J1 (3x)(Bx & -Bx) S (The sentence being tested) 42 (Ba & -Ba) 1, 3, New name 3 Ba 2, 4 - Ba 2, X. The sentence is a contradiction. The idea of a logical truth carries over from sentence logic in exactly the same way.
To demonstrate that a finite collection of sentences is inconsistent, demonstrate their conjunction to be a contradiction. Equivalently, provide a derivation with all of the sentences in the collection as premises and a contradiction as the final conclusion.
