To prove a negative actually means someting different. It is possible to prove that something does not have this or that attribute, (e.g. a number system does not have completelness, for example) but not possible to prove something does not exist. Personally, I am not convinced this is true. Take jimt's example: If I postulate the existence of gnorixes, for example, who control the rate of corrosion on pennies, can you prove they don't exist?
They can, in fact, be pretty easily disproved, because the nature of the corrosion of pennies is well understood, and we know exactly how that rate is determined. Occam's razor precludes another redundant cause for the same thing, however wonderully imagined it is.
This was my point about definitions. Most of the things that one supposedly cannot disprove are only difficult to disprove because what they are supposed to be is left vague. As soon as a postulated existent is actually defined, it is usually fairly easy to determine if it assumed attributes are possible.
I am surprised by those who argue against God that this argument is never made. In every day life, the theists attribute everything from the country's economy to the health of their dog to the action of God. Most of these things, however, already have complete explanations, just as the corrosion of pennies do. Attributing an additional cause, like the action of God, to events the cause of which is already fully understood is a violation of Occam's Razor.
The cause of the house burning down cannot be both the act of the arsonist and the act of God, unless God is the arsonist, of course.
Hank
Just so we're clear, you're claiming that proofs of negative statements do not exist. You'll need to prove that statement before I believe it -- a rather pretty paradox, no?
But at a deeper level, please note that you've completely excluded the use of attributes in the realm of negative proofs -- which is both artificial, and absurd. It's difficult to see how one can prove that "something" doesn't exist without having access to the attributes that make it "something."
I think what you're really doing, BTW, is butting up against the limits of axiomatic thinking, and masking the problem by arguing about attributes.
They can, in fact, be pretty easily disproved, because the nature of the corrosion of pennies is well understood, and we know exactly how that rate is determined. Occam's razor precludes another redundant cause for the same thing, however wonderully imagined it is.
However, Occam's razor is nothing but an assumption that the simplest explanation is the correct explanation -- and also that we have a full understanding of what the "simplest" explanation really is. That's not necessarily true, however -- I think all of us have seen cases where the "simplest" explanation is incorrect, for any number of reasons.