- p → q (means, if p then q)
- ¬ q
- ¬ q → ¬ p (contrapositive of 1)
- ∴ ¬ p
Let p denote the proposition "God exists"
Let q denote the proposition "I believe in God"
- If God exists, then I believe in God. (means, "God exists" implies "I believe in God")
- I do not believe in God.
- If I do not believe in God, then God does not exist. (contrapositive of 1)
- Therefore, God does not exist.
|p → q||p implies q |
meaning, if p is true, then q is true.
if p is false, the truth of q is unknown.
|¬ p||not p |
negative of p
meaning, p is false.
in other words, the negative of p is true.
Update: For anyone who may misunderstand what I'm trying to show you here, let me give you an explanation.
When I say that "If God exists, then I believe in God." I am talking about myself. It is true that if I happen to have irrefutable proof that God exists, then I would happily believe in God. Currently, it is also true that I do not believe in God. By contrapositive in propositional logic, you (as a logic mathematician, not a linguistic scholar*) can derive that if I don't believe in God, then God doesn't exist. And since it is true that I don't believe in God, it implies that it is also true that God does not exist.
* Alas, propositional logic often creates confusion when it is attempted to be expressed in the language I'm trying to explain (which is English). Hence you may misunderstand.By the way, the above argument is a thought I had since I studied propositional logic and read "Irreligion" by John Allen Paulos, in which he uses propositional logic as well.
A religious person can easily rewrite it this way (conforming to propositional logic rules):
- q → p --- If I believe in God, then God exists.
- q --- I believe in God.
- ∴ p --- Therefore, God exists.
* Belief is after all a personal thing, isn't it?Supernatural beings' existence depends on your belief in them. A believer has no doubt that the supernatural entity (including imaginary friends) exists. But the moment he doubts, the existence of the supernatural entity is undermined. The more he doubts, the more it ceases to exist. Basically, God exists to and only to those who believe in him.
This is unlike natural entities and scientific concepts. Take the example of evolution. Not one scientist has claimed that you have to believe in evolution. Even Darwin did not. What scientists do is to prove or disprove theories. Evolution maybe a theory, but there's a substantial amount of proof supporting this theory, with more being discovered. However, the existence of evolution is not jeopardized by creationists not believing in it. This is because evolution depends on proofs and discoveries (such as fossils), not on the scientists' belief in it.*
In fact, a scientist can believe very religiously in a theory he has created, but unless he can show proof, the theory remains a unproven theory. And if he discovers or someone else shows him something that contradicts his theory, it becomes a disproven theory. In other words, no matter how much a scientist believes in the theory he formulated, it will not become true by virtue of his belief.
* The same can be said of natural entities such as celestial bodies, human beings, supercomputers, to name a few. No matter how strongly you believe a human being exists in the empty corner of your room, one doesn't suddenly begin to exist there. And I am yet to know of a murder case where a man killed another simply by disbelieving in his existence.