The ancient Greeks had a neat
myth dealing once and for all with the irritating semantic
paradoxes this type of question presents:
After raping Europa, Zeus left her with a keepsake: the magical hound Laelaps, who was able to catch anything he was set on. Laelaps passed to Europa's son king Minos, and thence to Procris and her husband Cephalus, who lent it to Hercules' stepfather Amphitryon, who proceeded to do something exceedingly stupid.
He set the dog on the trail of the Teumessian Vixen which was at that time plaguing the vicinity of Thebes. The funny thing about this fox is that Hera had decreed that it could never be caught. Cephalus thought that he had located a loophole.
However, the gods will go to exorbitant measures to avoid mere mortals messing with their poorly-conceived absolute and contradictory creations. Before the argument was solved, Zeus stepped in just as Laelaps was about to bite down on the fox's neck and got Hephaestus to turn them both to stone. One myth has this explaining the presence of the unusually life-like statue of a dog found in the Parthenon at Athens' Acropolis, but more traditionally Zeus, out of some sense of responsibility for the creation of the innocent mutt, brought him into heaven and placed him among the skies as Canis Major, the big dog.