Checking the validity of an argument

Question

Is the following argument valid?

1. If A is to be good, they must be just
2. If B is to be good, they must be just
3. Therefore, if C is to be good, they must be just
4. 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.

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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.

1. If adult men and adult women are to be good, they must be just
2. If children and old people are to be good, they must be just
3. 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?

Answer 1

No.

A good -> A just

B good -> B just

C good -> C just ? Non sequitur. C was not mentioned before

C just -> C good ? Another non sequitur. This would be the converse of line 3, but an implication does not entail its converse.

Answer 2

No, it is not.

1. and 2) are premises. In a vacuum i cannot evaluate them, so i assume them to be true and correct.

2. is a first conclusion; which does not follow.

3. would be valid if "all that are good must be just" would be a (true) premise, which was not mentioned. Even if A and B are the only existing cases of whatever they are, the fact that both of them are good and just might be a coincidence

4. simply does not follow from 1) and 2). With 3) not being valid in this argument, 4) cannot be valid either, since it depends on 3) The step from 3) to 4) is valid by itself, but if 3) isn't valid, 4) cannot be.

A more accurate argument would be: P1) all that are good must be just P2) C becomes "good" Q1) C will automatically become "just"

(Note that neither A nor B are included, since they are examples of P1, and therefore irrelevant to the basic argument)

Answer 3

Concerning the first argument:

1. If A is to be good, they must be just
2. If B is to be good, they must be just
3. Therefore, if C is to be good, they must be just

This is not valid essentially because there is nothing in the argument making necessary that whatever applies to A or B also applies to C.

Concerning the second argument (without the "all" in the conclusion):

1. If adult men and adult women are to be good, they must be just
2. If children and old people are to be good, they must be just
3. Therefore, if humans are to be good, they must be just

This second argument is not formally valid. The reason is that to try and see it as valid, you need to interpret the words "human", "children" etc. In a formally valid argument, there is no need for interpretation.

The argument is also not clearly informally valid.

Essentially, informal validity depends on what we means by "humans", "children" etc. Informal validity requires that we give the argument a "charitable interpretation". However, this interpretation should be uncontroversial, and here we have a problem with babies. Are babies children? Are they not humans?

Suppose we say babies are human but not children, so the premises don't apply to them but the conclusion does, so you infer a conclusion (about babies) that does not follow from the premises (that are not about babies). This makes the argument invalid, not only formally invalid, but informally invalid.