By a strange bit of synchronicity, this topic popped up twice in my various feeds in the same day. The first came from magician Eric Mead in a Facebook post.
The original comment that sparked the Facebook exchange was a comment made early in this video. The trick he performs is beside the point, although it is well worth watching through to the end for.
This second longer video is from Matt Dillahunty. Matt also know a fair amount of magic, though he works primarily in the freethought community. This video is part of the "Atheist Debates" project
Spoiler alert for those who don't want to sit through the full in-depth discussion: we are epistemologically blocked from actually inferring supernatural causation.
The discomforting corollary to this is that the entire field of magic is rooted in a logical fallacy. I'm not sure if that's a bad thing or not.
There is a correct line of deductive reasoning that looks something like this:
- A or B
- Not A
- Therefore B
The problem arises when you try to use this line of reasoning to explain something. Because when you're trying to explain things in the real world, the first premise is false. It should be:
- A or B or X Where X is some explanation I haven't thought up yet.
- Not A
- Therefore B or X
- If (not X) then B
The validity of B depends entirely on your ability to exclude X; to demonstrate that there couldn't be any other explanation you haven't considered. (Depending whether it's Eric or Matt talking, B is either magic or god respectively.)
But your "not X" will always be tentative. The defences of "not X" typically take the form of "arguments from insufficient imagination"  or "arguments from incredulity" . Which is essentially the argument that "I'm so smart, I couldn't possibly be wrong."
We have good historical support for this. Every paradigm shifting discovery in the history of the species has taken the form of things that not only no one had thought of, but no one before could have imagined them. Think of evolution (all of the complexity of life on the planet without a designer), relativity (the word "now" doesn't mean anything), quantum mechanics (sure you can be in two places at once given the right conditions), the germ theory of disease, even heliocentrism (you mean, the sun doesn't orbit the earth?).
Magic is the same way. There is no deductive argument that can possibly end with the conclusion "It was magic." That conclusion is simply a state of abandonment; I was more persistent in trying to deceive you than you were in trying to see through the deception.
I'm not sure if that's a good thing or not. I'm really not.
 Thank you Richard Dawkins for naming that one.
 I'm crediting this one to the Backstreet Boys unless anyone has a better citation.