Well, in what way do you think the truth of the premises does *not* guarantee the truth of the conclusion? In which situations is the promise "If the premises are true, the conclusion will be true" broken?

The definition of validity is:

For all interpretations it holds that if all premises are true under that interpretation, then the conclusion is true under that interpretation as well.

The negation of this is

Not for all interpretations it holds that if all premises are true under that interpretation, then the conclusion is true under that interpretation as well.

which is equivalent to

There is an interpretation for which it does not hold that if all premises are true under that interpretation, then the conclusion is true under that interpretation as well.

which is in turn equivalent to

There is an interpretation such that all premises are true but the conclusion is false under that interpretation.

That is, an argument being invalid amounts to saying that there is a concrete counter interpretation which makes all premises true but the conclusion false. If there is no interpretation which can make all premises true to begin with, then in particular there can be no such counter interpretation. **If there arises no situation in which the condition on the truth preservance guarantee (the truth of the premises) takes effect, then there is no situation in which this promise can be broken.**

So yes, the argument is valid, precisely for the reason cited by your teacher. An argument that is valid because the premises are contradictory is called **vacuously valid**.

You may be interested in the notion of a **sound argument**: A sound argument is one which is valid and where in addition the premises are true in the real world. Premises which are contradictory can obviously not be true in the real world, so the above argument is **unsound**. This may be closer to your intuition of a "correct" argument than the notion of validity.

Is this not a counter interpretation? "Grass is green. Grass is not green. Therefore cows do not bark". I used the same premises, but reached a different conclusion. Shouldn't that not happen for valid arguments? – Cell – 2020-08-07T22:02:33.597

Actually to be more precise I reached the opposite or contradictory conclusion, but I can no longer edit my comment. – Cell – 2020-08-07T22:30:21.220

@Cell An interpretation is an assignment of truth values to sentences. A counter interpretation to an invalid argument is an interpretation that makes all premises true but the conclusion false. There can be no interpretation that satisfies both "Grass is green" and "Grass is not green", hence there can be no counter interpretation. Your argument is valid for the same reason as stated in the answer. – lemontree – 2020-08-07T22:45:43.860

And no, reaching different conclusions from the same premises is perfectly possible. For instance, from the premises

if p then q and r; pwe can conclude both the conclusionsqandr. The scenario where we can draw two conclusions that are contradictory (e.g.Cows barkandCows do not bark) happens precisely when the premises are contradictory. This doesn't make the argument invalid, however, it just shows that we must reject at least one of the premises. – lemontree – 2020-08-07T22:48:47.023... And it also shows that the arguments can not be sound: At least one of the premises must be false in the real world if we can draw contradictory conclusions from them. – lemontree – 2020-08-07T22:56:09.120