Antilogisms

Antilogisms are a form of argument that take a syllogism and negate the conclusion. So whereas a syllogism might say:

1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.

Its corresponding antilogism would be:

4. All men are mortal.
5. Socrates is a man.
6. Socrates is not mortal.

The interesting thing about this is that you can now accept any two premises, but not all three. You can accept that Socrates is a man and is not mortal if you deny that all men or mortal. Or you can accept that all men are mortal and Socrates is not mortal if you deny that Socrates is a man. So any two premises in a genuine antilogism can be made into a valid syllogism by negating the remaining premise.

There are a lot of interesting antilogisms and pseudo-antilogisms in philosophy. One of the most famous goes back to the ancient Greeks, and was re-emphasized by David Hume.

7. God is omnipotent (all powerful).
8. God is omnibenevolent (perfectly good and loving).
9. Evil exists.

This really captures the intuitive sense behind the problem of evil, which asks how a perfectly good and omnipotent God could allow evil to take place. Unfortunately, premise 9 is not the negation of the valid conclusion of a syllogism:

10. God is omnipotent.
11. God is omnibenevolent.
12. Therefore, there is at least one omnipotent, omnibenevolent being.

I think what the antilogism is trying to say is something like this:

13. God is omnipotent.
14. God is omnibenevolent.
15. An omnipotent and omnibenevolent being would not allow evil to take place.
16. Evil does take place.
17. Therefore, God is either not omnipotent, not omnibenevolent, or neither -- perhaps by not existing.

(You could also throw omniscience in there to emphasize that God must be aware of the evil that takes place.) The problem here is defending premise 15. The history of philosophy (and theology) is filled with attempts to explain how God could allow evil to take place, called theodicies, which is not to say that any of them are successful. But if we negate 15 we get:

18. An omnipotent and omnibenevolent being could allow evil to take place.

Premises 7, 8, 9, and 18 are a consistent set. So 7, 8, and 9 is not a true antilogism. Naturally, we all want a reason to accept premise 18 -- a common claim is that God only allows evil when he is able to bring about a counterbalancing good from it -- but it's not necessary in the structure of the argument. As long as 18 is logically possible then premises 7, 8, and 9 do not form an antilogism.

To see an antilogism in action, let's apply it to this scene from "Gandhi."


This presents us with the following antilogism:

19. Gandhi is a "colored attorney."
20. Gandhi is in South Africa.
21. "There are no colored attorneys in South Africa."

Granted, premise 20 is never actually stated, but I think we can infer it with confidence. Once again, we can accept any two premises but not all three. So Gandhi reverses premise 21 to form a genuine syllogism:

22. Gandhi is a "colored attorney."
23. Gandhi is in South Africa.
24. "There is at least one colored attorney in South Africa."

And the rest of the scene shows how dangerous logic can be.