Is there a good definition of magic which does not rule out the existence of magic, but also does not imply that actually magic exists? Magic cannot be "the ability to do impossible things", since this is a contradiction. I wonder if we could define magic as "the ability to violate the laws of physics". The problem is that if we discovered, for instance, that uttering "abracadabra" was a good way to make rabbits appear inside hats, he would have found a new law of physics, wouldn't we? And is it possible to argue that there is no magic without implying that most religions are false? My feeling is that the concept of magic has a reasonable sense only if we accept some religion: magic would be something like the wrong use of entities posited by such religion.
It's an interesting question, and I think it's best considered the context of times and settings in which the idea of magic was taken seriously. I also doubt that there's a lot to be gained by looking for a full-blown definition, but we can learn something by looking at broad commonalities. First on the bit about magic words and rabbits. If it turned out that saying the right words in the right way could make rabbits appear in hats, then we would have discovered a new regularity in the world, though whether we had discovered a new law of physics is a lot more doubtful. After all, the regularities of the special sciences aren't usually classed as laws of physics, even though physics has to be consistent with them.* We might want to say that this regularity is "natural" because all the events take place in nature (saying the words, the rabbit appearing...) but it wouldn't follow that it wasn't magical. Older notions of magic explicitly included a concept of natural magic. What counted as ...
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