What logic should not make sense but does anyway?

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Rules of inference and symbolic logic.

Take, for example, the following argument with 1 as the original premise, and 2 through 5 as rules of inference:

  1. A
  2. A or ~B · addition
  3. ~B or A · commutative
  4. ~(~B) → A · material implication
  5. Therefore, B → A · double negation

Now replace A and B with the following statements: A = apples taste delicious, and B = Batman exists. Let’s translate the above argument:

  1. Apples taste delicious
  2. Either apples taste delicious, or it’s not the case that Batman exists
  3. Either it’s not the case that Batman exists, or apples taste delicious
  4. If it’s not not the case that Batman exists, then apples taste delicious
  5. Therefore, if Batman exists, then apples taste delicious

It makes no sense. But it follows the rules of logic.