Is the following argument valid?
- If A is to be good, they must be just
- If B is to be good, they must be just
- Therefore, if C is to be good, they must be just
- Therefore, if C is just, they become good
(1) to (3) looks valid to me, but I'm not sure on what grounds I can make this inference.
(3) to (4) also looks valid to me, and I think it has something to do with necessary and sufficient conditions, but I'm not sure how to make the reasoning explicit.
Edit (7/24/21): Thanks all for the helpful comments, and my intuition above was clearly wrong. If I may, I'd like to turn that into a more specific argument. (Originally, I thought putting the argument in simplified terms would be enough for my purpose and make it easier to get feedback. I apologize for the confusion.)
Folks have rightly pointed out that (1) to (3) are invalid because, basically, there is nothing tying A, B, and C together. Would my following substitution change this judgement?
Let A = adult men and adult women, B = children and old people, and C = all humans.
- If adult men and adult women are to be good, they must be just
- If children and old people are to be good, they must be just
- Therefore, if all humans are to be good, they must be just
For the sake of the argument, let's assume that adult men and women, and children and old people, constitute all humans. So now, there seems to be something tying A, B, and C together. But my question is: Is this enough to make the argument valid? If not, why?
One more uncertainty: Would adding this implicit premise (also pointed by folks) help, something like, "One who is good must be just"? Or would the argument end up being circular, since this is akin to what (3) tries to establish?