Sunday, April 22, 2012

On The Proving of Negatives

Longrider and others both at his place and at Orphans of Liberty have been arguing about the existence of God. They were supposed to be arguing about whether religious people are entitled to proselytize and exactly how much tolerance they should be granted. At least, that’s what the original post was about, and the hosts made a couple of attempts to get it back on track. Inevitably it became an argument, almost a slanging match, about God yes, God no.
I didn’t get involved in the argument. I tried that recently and, as a wise man pointed out at the time, ‘These things never get anywhere, do they?’ So I didn’t intervene. But there are a few points that are worth making about how these arguments are conducted, and why they don’t get anywhere, all of them exemplified in that discussion.

It was asserted several times that, ‘You can’t prove a negative.’ Longrider himself, on the side of the non-believers, said that he could not be expected to demonstrate the non-existence of God, because to prove a negative is impossible. It probably is impossible in practice to demonstrate the non-existence of God, but not for that reason. This is often heard, in this and many other types of argument, and is stated as though it were an iron law of logic. In fact it is complete nonsense. It is folk logic, and it matters here because Longrider, particularly, makes frequent appeals to logic when criticising the arguments of others.

That it is nonsense becomes clear when you consider that any proposition in logic, and most in natural language, can be expressed as a negative. The proposition itself, ‘There does not exist a proof of a negative statement,’ is expressed as a negative, and thus, if it were in fact true, could not be proven. This isn’t just a quibble, and it’s more than an example. It is perfectly simple to state negative propositions which can be proved to be true.

The confusion stems, I think, from the fact that it is often difficult, or impossible, in theory or in practice, to prove the non-existence of some postulated entity. I can prove that there is no albino parrot in my living room by simultaneously observing every subset of space in which such a creature could be. In practice it would involve moving some furniture and fending off men in white coats (it’s quite all right doctor, I’m just looking for a non-existent white parrot), but it can clearly be done. To prove that there is no albino parrot in the world cannot be done by the same means, due to practical limitations, but it is possible in theory. To prove that there is no horse with 21-trisomy in the world is possible, however, through the observation that the same mutation which causes Down’s syndrome inevitably causes spontaneous abortion.

To prove the non-existence of God is certainly possible in theory. If it’s true, of course.


Vincent said...

I cannot imagine the circumstance in which I would want to prove or disprove the existence or non-existence of anything.

I will stop short of saying that such an activity is a misuse of the brain, because I cannot speak for others and how they spend their time.

CIngram said...

I used to be a mathematician and, like philosophers, we spend our lives trying to prove the existence or non-existence of abstract entities that few other people care about.

That aside, for normal people it's probably when challenged to do so in debate that we try to find ways to strengthen our positions with intellectual rigour. Which was the case here.

Mark Wadsworth said...

"To prove the non-existence of God is certainly possible in theory."

How? Can you think of a fair and simple* test where even the Pope or the Ayatollah would throw up their hands and say "Oops, it's a fair cop, there isn't a God, certainly not in the sense we've been describing him"?

Or indeed any such test where people like Longrider or me would be forced to admit "Yup, you were right, X has happened therefore there must be a God. Please remind us, which religion does he favour most as we wouldn't want to back the wrong team."

* Whereby 'simple' does not exclude 'laborious', i.e. searching the whole of the surface of Earth for an albino parrot is laborious but simple.

CIngram said...


In practice, no. And I haven't thought much about how such a test/search might work because people have been trying to prove both existence and non-existence for two thousand years and if they haven't done it yet I don't suppose I'll have any more luck.

Also, there is the fact that God seems to take delight in sliding out any of any and all attempts to detect His existence by the sensorial and intellectual means available to us. His existence is almost by definition unprovable.

Despite the apparent assumptions of both sides whenever I write about things like this, I have no position to defend. From time to time I idle away a few minutes looking for a way to approach an answer to these questions, and to analyse the arguments used, but the sudden appearance of definitive proof either way wouldn't cause me any deep psychological trauma. (Actually, I think definitive proof of the existence of God would come as a terrible shock to most people, including the majority of 'believers'. If I were certain that heaven and hell were waiting I'd have to change my behaviour quite a bit.)