Author’s note: the title refers to a quote from a 2002 episode of the TV show The Simpsons: Could Jesus microwave a burrito so hot that He Himself could not eat it?
There are multiple definitions of the word “impossible”.
We would like to draw a distinction between the physically impossible and the logically impossible. A distinction between things that are so logistically infeasible as to appear impossible, and things which are not even properly conceivable. This is surprisingly difficult to do rigidly. We suggest a few examples, and note the difficulties:
It is impossible for humans to run a four-minute mile. This was only impossible until it wasn’t. I am not sure how much credence to give to the claims that people felt this was impossible and not merely difficult; the example is useful in any event.
It is impossible for humans to fly to the moon. Well, this assumes they aren’t using a spaceship. It is certainly physically impossible, but is it logically impossible? Surely it is logically consistent that humans could be able to breathe without air, exert propulsion without propellant, and carry snacks for the journey in a backpack. There is a popular comic book, Superman, about a being that can do exactly that.
It is impossible for Adlai Stevenson II to be president of the United States. The historical record says Mr. Stevenson is deceased, and was never elected president during his life. Does that make it impossible? And is it logically impossible or simply physically impossible.
It is impossible for <some math statement> to be false. These are, supposedly, logically impossible, but for many common statements it is less clear. The Pythagorean theorem does not hold on the surface of a sphere. 2+2=11 if you’re writing in base 3. You don’t understand the proof of Fermat’s Last Theorem, why do you think it is true? And who can tell about Zorn’s lemma?
This distinction is not entirely theoretical. Many people believe that השם is omnipotent; while I personally do not, the idea is worth considering. And to be omnipotent, ta can do things that are physically impossible; those things that are logically impossible still cannot be done, it is technically an error of logic to even suggest they might be done.