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Validity and soundness (of deductive arguments)

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There are some surprising ways an argument can be made valid, for instance:

• If the premises imply a contradiction (so that it is impossible for all of the premises to be true):
  1. P (premise)
  2. Not-P (premise)
  3. P or Q (valid inference from 1)
  C. So Q (valid inference from 2 and 3)

• If the conclusion is a tautology (so that it is impossible for the conclusion to be false):
  1. Q (premise)
  C. P or not-P (valid inference from 1)

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