Sneaky little Megaric

Diodorus Cronus is said to have given this argument:

1. That which you have not lost, you still have.
2. You have not lost horns.
3. You still have horns.

The paradox here is that none us have horns, and yet each premise is supposedly true. How can we address this?



We could argue that premise 1 is false, since it does not follow that I have something if I have not lost it. Why? Well, it could have been stolen! Though true, this response is unsatisfactory. We could argue that premise 1 is true, but only under the strict domain of objects attainable by humans, or even things we have, or some other scope of reference excluding horns. That is a far better approach, I think.

What about premise 2? We could say that it is false, though here I would stress that in rendering this proposition false, we should not affirm the proposition "You have lost horns". Instead, we say this: it is not the case that you have not lost horns, or stated simply: it is false that you lost horns. And it is false simply because we, you or I, do not, nor did we ever, have horns. Why? Well, because we cannot lose some thing we never had! If it were otherwise, then, we might also say that I lost a hundred trillion dollars. Of course I didn't lost that much money, since I never had access to or responsibility of that sort of cash!