In logic, you start with premises that lead to a conclusion. Can you start a logical argument with premises that are not true?

  • No. This is an opportunity to put in place a simple, canonical question and answer. Commented Feb 6 at 23:08
  • 1
    Yes, you can... Commented Feb 7 at 6:45

1 Answer 1


Premises need not be true, but if you start with untrue premises, you get untrustworthy conclusions. The conclusion need not be false, but there's no way to know, from the argument and the premises, whether the conclusion is true if the premise is false.

  1. Harry Potter exists.
  2. Harry Potter is a wizard.
  3. Therefore a wizard exists.

False premise, valid argument, false conclusion.

  1. Harry Potter exists.
  2. Harry Potter is a boy who needs glasses.
  3. Therefore a boy who needs glasses exists.

False premise, identical valid argument, true conclusion.

Try inputting a probability of 0 into a premise with my answer to your similar question here, which is in fact this question generalized for probabilities other than 0 or 1.

  • Probabilities of the truth of statements is a meaningless concept in any sort of mind independent sense Commented Feb 7 at 13:25

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