p1. If an omni-god exists, then evil cannot exist

p2. evil exists

c. an omni-god does not exist

I'm pretty sure its modus tollens and is represented as follows,

p -> q



But my friend is representing it as,

p -> ¬q



which one is correct? are they both?

  • 1
    I agree with your friend. That version makes “can do evil” an affirmative statement, then negates it. I see this as cleaner, and easier to think about, than assuming a negative. Commented Sep 18, 2019 at 23:21
  • 4
    First note that the negation of "cannot" is "can" so the negation of "evil cannot exist" is "evil can exist" rather than "p2. evil exists". Having said that, I think that your choice of the form modus tolens is the more natural choice considering the context.
    – nwr
    Commented Sep 18, 2019 at 23:29
  • I agree with what you're saying, Nick R, I think my friend is getting confused by the 'cannot' in the conditional statement, thinking that it must mean a negation.
    – Jonah Pate
    Commented Sep 19, 2019 at 1:37
  • 1
    @NickR, you should expand this into a real answer. Anyone else answering the question will look like they are copying from you even if they did think of it independently. Commented Sep 19, 2019 at 13:56
  • 1
    Both arguments are fine, but the premises are weak so the conclusion will unlikely convince anyone who does not already believe it. See the logical problem of evil: iep.utm.edu/evil-log for what people have tried in the past. In particular look at Plantinga's objections. Commented Sep 19, 2019 at 18:04

1 Answer 1


The one is ((p → q) & ~q) → ~p and other is ((p → ~q) & q) → ~p. Replace q by ~q. The first is the second or the second is the first. Because of this, they are the same. Neither is better than the other. (And the "p → q" is false according to the Gospel, cause "~p" is invalid. So they are also the same, but both are in error.)

The "an omni-god exists" is God shall be Godself by His own Will to Life; "evil cannot exist" is God forbids every evil in the world; and, "evil exists" is evil is allowed to come in the world (as Satan was allowed to tempt Job to show Job's faith). So the whole proof has the logic ((O(p) → O(~q)) & ~O(~q)) → ~O(p)). [The (O(p) → O(~q) is also false according to the Bible. God, to be Godself, need not clean every evil from the world until the last day.]

  • The question is not about whether p1 is true. The question is about how best to represent the logic of this reasoning. Commented Sep 19, 2019 at 13:56
  • I made an edit for clarity. You may roll this back or continue editing. Best wishes. Commented Sep 20, 2019 at 16:39

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .