Is this argument valid?

  1. No one under 18 is permitted to vote.
  2. No faculty member is under 18.
  3. The philosophy chairperson is a faculty member.
  4. Conclusion: The philosophy chairperson is permitted to vote.

Was my answer not valid because the conclusion doesn't follow from the premises?

  • Wait. Philosophy chairperson is a faculty member -> philosophy chairperson is 18 years old or older -> philosophy chairperson is permitted to vote. The argument is sound. And "the conclusion don't follow from the premises." is not what validity means.
    – rus9384
    Oct 22, 2018 at 22:58
  • I'm sorry, to avoid gamesmanship here on the forum... are you asking about the argument ending in "Then the philosophy chairperson..." ? or the one ending in "My answer was it is not..."? Oct 22, 2018 at 22:59
  • I'm asking if my answer was correct or not Oct 22, 2018 at 23:09
  • What you might need to add is why the conclusion does not follow from the premises, not just assert that it doesn't follow from the premises. What were your reasons? Welcome to this SE! Oct 23, 2018 at 3:12
  • This is the recurrent question type (RQT) “Is X valid?”. I invite anyone to discuss or analyze how such questions may be improved at the link provided. Mar 24 at 14:53

3 Answers 3


The argument is invalid. In fact, it's an instance of the fallacy of denying the antecedent.

To see this, we can formalize the argument as follows:

  1. Under-18 → not Permitted
  2. Faculty → not Under-18
  3. Chair is Faculty

From 2 and 3 we can deduce that Chair is not under 18. But we cannot then deduce from this and 1 that Chair is permitted to vote: that would commit the fallacy of denying the antecedent.

Another way to see that the argument is invalid is to imagine a scenario where the premises are true and the conclusion is false. For example, the chairperson might not be permitted to vote because they are not a citizen (which isn't ruled out by the premises). If it's possible for the premises to be true and the conclusion false, then the argument is invalid.

  • I used the star test by Harry j. Gensler and that's why my answer was invalid. Oct 22, 2018 at 23:34

I arrived at the same conclusion (invalidity) as Eliran H, but for a different reason. The premises are insufficient to show, affirmatively, that persons 18 years old and older are permitted to vote. Missing that information, the reasoning fails.

Here are my notes on my attempt to reason it through:

  1. If Person is Underage, then they are not permitted to Vote.

1.1 If Person is permitted to Vote, then they are not Underage. Contrapositive of #1 (looking for an affirmative statement about voting).

  1. If Person is Faculty, then they are not Underage.

  2. If Person is Chairperson, then they are Faculty.

Partial (valid) Conclusion: If Person is Chairperson, then they are not Underage. (#2 + #3)

  1. Final (failed) Conclusion: If Person is Chairperson, then they are permitted to Vote.

I don't see it as valid but I believe it WOULD be valid if you said EVERYONE over 18 is permitted to vote.

For instance, you could say the chairperson already voted once and is not allowed to vote again. In that case the first 3 premises are satisfied but the conclusion is not. But if everyone over 18 was permitted, he could vote again even though he already voted once. Unless you added another axiom saying someone could vote only once.

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