Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?

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Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?

user14373

Posted 2015-04-21T00:45:01.037

Reputation: 63

The truth table would be pretty trivial, no? – James Kingsbery – 2015-04-21T18:39:11.147

Answers

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No. If the conclusion is a tautology, that means it is always true, and it is impossible for it to be false. An argument is truth-functionally valid if it is impossible for the premises to be true and the conclusion to be false. If it's impossible for the conclusion to be false, then the argument is automatically valid for that reason.

ChristopherE

Posted 2015-04-21T00:45:01.037

Reputation: 5 348

I've deleted all of the comments. If you want to write a competing answer to the question, please feel free to do so. There's no need to bicker in the comments for this type of question. – virmaior – 2015-04-21T05:47:54.850