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?

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