It is a basic rule of logic that burden of proof always lies on the affirmative, that whoever asserts something will be the one who has to prove it. Ei incombit probatio qui dicit, non qui negat – “the burden of proof lies upon him who affirms, not him who denies” – and so whoever tries to shift the burden of proof to the opponent by insisting that a claim is true simply because it has not been shown to be false is committing a logical fallacy.
Burden lies on the affirmative. But now the question is, What is an affirmative? Does it simply mean a ‘positive’ claim, hence statements in the negative carry no such burden?
Let us see how Webster defines the word affirmative:
We see in No. 3 that affirmative also means ‘positive’. Now let’s see what positive means:
It appears that affirmative and positive are about confident assertion instead of statements that are merely positively worded (take a look at the above example, “her answer was a positive no“). As such, the statements “There are no fairies” and “Fairies don’t exist” are therefore actually affirmative statements and so they are also laden with the burden of proof. (By the way, asserting that “there are no fairies” is not the same as saying “I don’t believe in fairies”, because the latter is not affirming their non-existence but simply disbelieving their existence.)
Now some might say that it is impossible to prove a negative. I beg to disagree. One can prove certain negatives, like proving that there are no “supercontinents” ten times the size of Asia (one can easily accomplish that with Google Earth). Other negatives may be harder – but still not impossible – to prove, like the statement that “There is no oil in Davao City”, because one would then have to dig up every square inch of the entire city to prove that.
I read this article about proving a negative that states that “a person is justified in believing that X does not exist if all of these conditions are met:
1. the area where evidence would appear, if there were any, has been comprehensively examined, and
2. all of the available evidence that X exists is inadequate, and
3. X is the sort of entity that, if X exists, then it would show.”
I totally agree. In the case of the “supercontinents”, all three conditions are easily met, especially #3.
But as for fairies, it would be virtually impossible to prove their non-existence because even if we had simultaneous 24-hour video coverage on every garden and forest on Earth showing no fairies (satisfying conditions #1 and #2), believers would simply say that fairies are normally invisible but can choose to show themselves to certain people at certain times, failing condition #3.
However, the inability to prove there are no fairies doesn’t automatically allow for the conclusion that fairies do exist, because that would also be an affirmative statement requiring proof. And so we are left with a technical stalemate as far as proof goes. But not probability.
Fairies are simply way too improbable that although it is impossible to prove their non-existence, one can reasonably live his/her life on the assumption that they don’t exist. And so when planting a garden, it would be a good idea to till it and water it and fertilize it – instead of just lying down waiting for fairies to magically make it bloom.