One Man’s Modus Ponens is Another Man’s Modus Tollens

Consider the following pair of arguments:

(1) If there is no God, then everything is permitted.
(2) There is no God.
(3) Therefore, everything is permitted.


(1) If there is no God, then everything is permitted.
(2′) It is not true that everything is permitted.
(3′) Therefore, it is not true that there is no God.

Note that (2) is the same as the denial of the conclusion of the second argument, and that (2′) is the denial of the conclusion of the first argument.

Call (1) the Dostoyevsky Premise (his character Ivan Karamazov famously claimed it in Brothers Karamozov). I suppose that if naturalism (i.e., atheism) is true, morality would merely amount to some sort of set of inclinations that had survival value and was thus selected for in our evolutionary past. The set wouldn’t have any sort of authority. It might be useful relative to the goal of survival, but that’s not authority.

Then again, a naturalist could just say that moral truths are brute truths, primitives, that are not based in anything more basic. Math/logic seems to be that way. Why not ethics? It’s less arbitrary to say this than to base morality in God’s commands, naturalists might claim.

Atheists certainly aren’t in agreement regarding (1). Some agree. Jean Paul Sartre is one of the best examples. Some deny (1), thinking that morality can be naturalized. Sam Harris is an example. (For another example of an atheist realist regarding morality, see this blog).

But suppose it’s true. The two above competing arguments come to my mind. One could argue that there is no God, so everything is permitted. Or one could argue that not everything is permitted, and conclude that God exists. The first argument is in the form of Modus Ponens:

(1) If A, then B,
(2) A,
(3) Therefore, B.

The second is in the form of Modus Tollens:

(1) If A, then B,
(2′) Not-B,
(3′) Therefore Not-A.

Both are deductively valid forms. So something’s got to give. If (1) is true, then there is a competition between (2) and (2′). Which has more behind it?

I’d definitely say (2′), given pretty near universal intuitions about basic moral values (we must not harm people unless there is justification; we must take care of our children).* The case against God’s existence is much more shaky (atheists usually don’t try to prove that God doesn’t exist anyway; they put the burden of proof on theists).

Or put it this way, there’s an argument for atheists taking on a burden of proof (given (1)) if there is a burden of proof on those who deny objective morality. For accepting (1) and (2′) implies God’s existence, and if we should default to believing in (2′), then we should default to believing in (3′).

*Psychopaths are excluded. Just because some people are blind doesn’t mean there’s nothing to see.