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I have to take issue with the point about negative statements, surely it's no more fruitful to say "Prove there IS an invisible ball of undetectable mass swirling in my hand."

Wouldn't it be more accurate to say that it's fruitless to place the burden of proof on a statement which is syllogistically isolated from any statement known to be true?

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No, it is more fruiful to say, "Prove there is..." because that's the basis of scientific/mathematical rigor. If you can prove it exists, it does. If you can't prove it exists, it doesn't, for all intents and purposes. You then act as though it doesn't, because until you can find evidence for it, it might as well be nonexistent, and you should act that way to be logical.

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