Proving the Negative
Often, you get into the position where the claim is made ‘well, you can’t prove X doesn’t exist’. This might be used with reference to some god, a secret society, the power of the stars to affect lives or some other thing someone believes is true. Here you are in danger of getting sucked into the realm of trying to ‘prove the negative’ — which is generally impossible.
This switches the burden of proof from the one making the claim to the one refuting the claim. But sometimes this is a challenge worth taking!
A classic story of this was to do with swans. Since Roman times it was thought ‘all swans are white’. There was a common saying for hundreds if years along the lines of ‘as rare as a black swan’ to mean something that did not exist. That is until black swans were discovered in Australia!
From a logical perspective, your inability to ‘disprove’ something has no bearing whatsoever on the truth of their claim. It is often advised to avoid falling for this trick, stick to your guns regarding your lack of belief and insist on the fact that they have to provide evidence for you to believe it, not the other way around.
Taking on the Challenge
Of course, if the claim contains logical contradictions, then it is possible to make the case that it does not exist; for instance consider ‘the barber pardox’. This is about a barber who lives in a town and who ‘shaves everyone who does not shave themselves’. So, who shaves the barber? If he shaves himself, he is not the barber; if someone else shaves him he is not the barber. Therefore he cannot exist. Other examples can be given, such as an omniscient god and the existence of free-will. If god already knows everything that will happen, how can free-will exist? If free-will exists, how can god be omniscient?
Of course, they might not be making such a logically inconsistent claim and still insist that your inability to prove ‘X does not exist’ in some way provides evidence that in fact ‘X does exist’. If I had a penny for every time I have heard ‘no one has ever proven god does not exist’ I would be a rich man.
Taking a Street Epistemology approach, we can see this as an opportunity for education. Moreover, it is not necessary to prove ‘X does not exist’ it is only necessary to assign it to the same level of belief as all the other things that are generally accepted, in a pragmatic sense, to not exist.
For example, take Thor, the ‘god of thunder’. Now, it is true that I cannot prove Thor does not exist. Perhaps he used to be active, going round making thunderous noises, but has been on a short break for the last hundred years or so. Likewise, you can’t prove the intangible, invisible dragon that lives in my garage, and only reveals himself to me, doesn’t exist.
The point is that it is not necessary to prove that ‘X does not exist’ in a strictly logical sense, it is only necessary to push it into the same bucket of degree of belief as all the many thousands of other things that you are happy to accept as ‘not existing’ in any pragmatic sense.
