- If God does not exist, then objective morality does not exist.
- Objective morality does exist.
In a way this article is redundant, since I gave a formal proof for the falsity of both premises being logically impossible in part 2 of my introductory logic series, with part 2 also explaining the basic symbolic logic and various rules of logic needed to understand the proof (thus it isn’t necessary to read introductory logic part 1 to understand the proof, though it wouldn’t hurt either). So what inspired me to write this article to present a more informal proof?
In one Facebook dialogue somebody denied both premises. I said it was logically impossible for both premises to be false, and gave a link that had the proof of this in symbolic logic while noting, “If you’re not well-versed in formal logic, not to worry, because the article gives a crash course of some symbolic logic rules.” His first response to this was to ignore the proof entirely while saying there is “no reason” why one can’t reject both premises. I pressed further to get him to respond to the logical argument against both premises being false, but he seemed to have little motivation to learn the logic and understand the objection (judging from e.g. him saying “I will attempt to go back over this at some point, but I really have very little motivation to do so”). It’s this sort of behavior that temps me to embrace the stereotype of atheists being irrational and giving lip service to logic while in reality having little real interest in learning it (at least when they discover it might be used against them).
But that’s a temptation I’m going to resist. I realize my articles introducing logic require a bigger time investment than reading a 100-word Facebook post, and that not everybody is interested in learning formal logic despite the benefits of doing so (e.g. helping one to think more logically). So in this post I’m going to distill some of the reasons of the logical proof in plain English.
Understanding the First Premise
For brevity’s sake I’ll abbreviate “objective morality” as OM. By morality being objective I mean that moral truths hold independently of human belief and perception of them (this matches closely with how “objective morality” is often defined in the context of the moral argument). Behold the first premise:
- If God does not exist, then OM does not exist.
If it’s hard to see why that would be true here’s another way to look at the first premise. It is important to understand that whether we should believe an if-then statement often depends on the background information we possess, e.g. If it rained heavily in the last five minutes, then Sam’s car is wet depends on factors like whether Sam’s car is in a garage. Similarly, if you believe this equation is true…
God does not exist + background info = OM does not exist…then you believe If God does not exist, then OM does not exist and to think otherwise is to misunderstand the meaning of the first premise. The first premise is not saying it is impossible for OM to exist without God, only that given the facts of the real world we are in OM does not exist if God does not exist.
Let =entails⇒ signify “entails (by the rules of logic).” For example:
I have a hand and I have a leg =entails⇒ I have a legThe above is true thanks to a rule of logic known as simplification (which I explain in introductory logic part 1).
A very important fact in the proof is this: if the following is true….
God does not exist + background info =entails⇒ OM does not exist…then the first premise is true, and to think otherwise is to misunderstand the meaning of the first premise.
Now suppose we know the second premise to be false, i.e. OM does not exist is part of our background info. Then the first premise would be true because we’d get this:
God does not exist + background infoAnd thus the following entailment would be true:
=entails⇒ God does not exist and OM does not exist
=entails⇒ OM does not exist
God does not exist + background info =entails⇒ OM does not existWhich would mean that the first premise is true. Once we accept OM does not exist as part of our background info, it inevitably leads to the above entailment and thus to the first premise. Thus it is logically impossible for both premises to be false, because the falsity of the second premise (OM does not exist) entails the truth of the first premise.
It is also worth noting that God, as traditionally conceived, entails the existence of objective moral values; God is morally good, and is good independently of whether humans believe him to be so, e.g. God was morally good prior to humans existing. Thus, God entails objective morality existing.
Whether we should believe an if-then statement often depends on the background information we possess, e.g. If it rained heavily in the last five minutes, then Sam’s car is wet depends on factors like whether Sam’s car is in a garage. Similarly, when interpreted correctly the first premise is saying that given the facts of the real world we are in, it is not the case that OM exists if God does not exist. Thus if you believe the following entailment to be true…
God does not exist + background info =entails⇒ OM does not exist…then you believe If God does not exist, then OM does not exist is true, and to think otherwise is to misunderstand the meaning of the first premise. So if you’re an atheist who denies moral objectivism (and thus has OM does not exist as part of their background info) you accept the first premise, and to think otherwise is to misunderstand what the first premise means. In contrast, if God (a being who is morally good independently of human opinion) exists, objective morality exists.
Once we accept the falsity of the second premise (OM does not exist) as part of our background info, it inevitably leads to the above entailment and thus to the first premise. It is impossible for both premises to be false because the falsity of the second premise entails the truth of the first premise. All that is a bit rough, so if you want a rigorous formal proof for the logical impossibility of both premises I recommend reading part 2 of my introductory logic series.
 A few examples:
- Adams, Robert M. The Virtue of Faith (New York: Oxford University Press, 1987), p. 105.
- Craig, William Lane. Reasonable Faith, Third Edition (Wheaton, Illinois: Crossway Books, 2008), p. 173.
- Peter Byrne’s article on the moral argument that used to be part of the Stanford Encyclopedia of Philosophy.