A suspicious proof of God’s existence

Consider the following argument:

  1. If I will have eternal life if I believe in God, then God must exist.
  2. I do not believe in God.
  3. 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”

  1. (B → E) → G
  2. ~B
  3. Assume ~G
  4. ~(B → E), modus tollens (1,3)
  5. B & ~E, (4)
  6. B, (5)
  7. B & -B, (6,2)
  8. 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?

2 thoughts on “A suspicious proof of God’s existence

  1. This is basically just the drinker paradox. We naively interpret “I will have eternal life if I believe in God” as a counterfactual conditional, but logically interpret it as a material conditional, and therefore it is vacuously true if you do not, in fact, believe in God, regardless of what would be the case if you did believe in God.

    “I will have eternal life if I believe in God” actually means “It is not the case that I believe in God and yet will not have eternal life” in this context. A nonreligious person would not, therefore, grant the premise that this implies the existence of God.

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