Consider the following argument:
- If I will have eternal life if I believe in God, then God must exist.
- I do not believe in God.
- Therefore, God exists.
Intuitively, it seems possible for (1) and (2) to be true and yet (3) to be false.
But now let’s formalize the argument.
B = “I believe in God”
E = “I will get eternal life”
G = “God exists”
- (B → E) → G
- Assume ~G
- ~(B → E), modus tollens (1,3)
- B & ~E, (4)
- B, (5)
- B & -B, (6,2)
- G, proof by contradiction (2 through 7)
This argument is definitely logically valid, so were our initial intuitions mistaken? And if not, then what’s going on here?