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In first order logic, can an argument that has a conclusion that is necessarily false (e.g. It is raining and it is not) possibly still be valid?

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An argument is formally valid just in case it can never have true premises and a false conclusion. Validity certifies truth preservation. There are two trivial cases of validity --when the premises are necessarily false or when the conclusion is necessarily true.

In this case, the conclusion cannot be true, but in the case the premises are necessarily false, the argument will be still be valid, because truth is "preserved" (there is no truth in the premises, so none is certified for the conclusion).

  • That's what I asserted elsewhere once (and what I think is generally what anyone asking it would be seeking), but it turns out that Tarski's definition of validity is such that an argument is valid only in the case where it can be modelled. – virmaior Nov 12 '15 at 8:36

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