mjhjmtu

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.

My answer was it is not valid because the conclusion don't follow from the premises.

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 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).

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




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

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

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