If there was one phrase that I feel gets overly abused in discussions between theists and atheists, it is the phrase “…it is logically possible that…”.
What does it mean for something to be “logically possible”? Is “logic” a function of ontology, or a function of epistemology?
I'm leaning on the latter. Since I am no philologist, I'll have to resort to my rudimentary undergrad philosophy courses.
When I think of logic, I think of modes of inference, deduction, induction, necessary conclusions, etc. So for instance, this following syllogism is an instance of “logic”:
1. All fish live in the ocean
2. Dolphins live in the ocean
C. Dolphins are fish
This syllogism is valid, but not sound. That is, if the premises and conclusion were [ontologically] true, then this would help us understand something about our world. It would add to our epistemic framework. If we didn't know that dolphins, by definition, are not fish this would establish that dolphins being fish is “logically possible”. But notice all of the words that I used to describe logic: “modes of inference”, “necessary conclusions”. These are not categories of ontology. They are epistemic qualifiers. They are traffic signals on the road to learning.
Now, what we are learning completely depends on our initial premises, or our initial axioms. It is logically possible that in the next Superman comic I read, Superman can get his ass kicked by a powered up Lex Luthor after Lex kidnaps Lois Lane. What does this have to do with the ontological status of Superman, Lex Luthor, or Lois Lane? They don't “exist” in the real world; this is only a mental exercise. Thus the “logic” in logically possible.
If something is logical, it only means that we can follow the deductive (or inductive) steps that lead to a given conclusion. Jesus' virgin birth is just as “logically possible” as Spiderman's radioactive spider bite. Jesus' resurrection from the dead is just as “logically possible” as Superman's resurrection from the dead. That is, given some initial axioms that we accept, we can follow the logical steps that lead to those conclusions. According to the logic of the Wonder Woman universe, Wonder Woman can fly around in an invisible plane. Just like according to the logic of the Christian universe, Jesus can walk on water. Neither of these, though, make any ontological statement about our world.
Logic is just a guide for comprehension and understanding. I can encounter something that is incomprehensible or something that doesn't make sense to me, but this does not preclude its ontological status. A lot of quantum physics is “logically impossible”, but quantum physics is still “real”. I think when people speak about “logical possibility” they really should be saying “ontological possibility”.