6/30/2013

Proving a negative

A. C. Grayling remarks in his short essay 'Proving a Negative' (in Thinking of Answers, pp.32-34) that "[t]he claim that negatives cannot be proved is beloved of theists who resist the assaults of sceptics by asserting that the non-existence of God cannot be proved." (p.32) It is indeed not uncommon for a theist to challenge an atheist with the question 'Can you prove that God doesn't exist?', where the rationale for posing the question is that it is impossible to prove a negative. It is, however, a little strange that Grayling does not mention also the fact that some atheists (and agnostics) like to invoke this very same principle of folk logic when they argue against theism: they would insist that the burden of proof lies with the theist because it is impossible to prove a negative but possible, and sometimes easy, to prove a positive.

In any case, it is puzzling why there are so many people who accept the principle that it is impossible to prove a negative , for the principle seems obviously false. If 'a negative' means simply 'a negative proposition', then anyone who accepts the law of non-contradiction (i.e. '~(p & ~p)') has to accept that there is at least one negative that can be proved: the law of non-contradiction is a negative proposition and it can be proved in classical logic. Relatedly, propositions of the form "'p' is not false" are negatives in this sense. Assuming bivalence, proving that 'p' is not false is equivalent to proving that 'p' is true --- unless propositions of the form "'p' is true" cannot be proved, it is possible to prove a negative.

Perhaps for those who accept the principle in question 'a negative' here means 'a negative existential proposition' (i.e. a proposition of the form 'There is no x' or 'x does not exist'). Grayling does not tackle the question why people accept the principle in question, but he does give a simple counterexample: "consider how you prove the absence of pennies in a piggy-bank. You break it open and look inside: it is empty." (p.34) I think most people would agree that doing so proves the negative 'There are no pennies in the piggy-bank'. So, even when 'a negative' means 'a negative existential proposition', it is still clear that a negative can be proved.

Perhaps the universe of discourse is supposed to be unrestricted when the principle in question is applied. It is easy to prove that there are no pennies in the piggy-bank, but, it may be claimed, it is impossible to prove that there are no unicorns, period (though it can be proved rather easily that there are no unicorns in your closet). There are two problems here. First, if the difficulty of proving that there are no unicorns anywhere in the universe is due to our technological limitations, then those who accept the principle in question have to clarify what they mean by 'impossible' when they claim that it is impossible to prove a negative. It is at least not a metaphysical or logical impossibility. Second, it is not clear that the universe of discourse matters here. It may be easy to prove that there are no unicorns in your closet, but it is difficult to prove that there are no invisible unicorns in your closet. And it seems impossible to prove that there are no unicorns of the following kind in your closet: unicorns that are undetectable unless they allow you to sense their presence.

If it is impossible to prove that God does not exist, it may be because God is undetectable unless God allows us to sense her presence, rather than because 'God does not exist' is an unrestricted negative existential proposition. It remains a puzzle to me why there are so many people who accept that it is impossible to prove a negative.

3 comments:

  1. It seems to me not every philosophical debates accepts "the burden of proof lies with who claiming X exists" rule. For example, in the debate of mathematical entities, anti-Platonists
    often try to use reductio ad absurdum to argue against Platonism who claim inert and abstract mathematical entities exist.

    Actually, i find most philsophical debate of whether or not X (theorotical entities, causality, value etc) exist do not adopt he
    "burden of proof lies with who claiming X exists" rule. So it seems it is inappropriate for atheist to appeal such a rule.

    By the way, is there any philosophical accoount of the burden of proof? And it seems to me the burden of proof is usually assigned on the basis of pragmatic considerations, rather than evidential considerations?

    P.S. Sorry for asking silly question, but i find your passage interesting and i have long been puzzled by the burden of proof as such.

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  2. I'm borrowing some space here to rant:
    I'm annoyed by people saying that one can't prove that God doesn't exist. Let's agree on it. No one can prove it. So what? Now I would say that Gooroo (pun), not God, created the universe. No one can prove that it isn't true or Gooroo doesn't exist either. (Can't disagree on this now after we have the agreement above, too late.) Better yet, I would say that Gooroo created God. Now, prove me wrong. No one can. (Again, too late to disagree on this now.) I can make up thousands of statements like that. Very meaningful statements, or not.
    P.S. It turns out that there are many GooRoos, not just one. The one I talk about above is GooRoo Richard V. Long. He was born just minutes ago and went back via a wormhole to seconds before the Big Bang. He peed and thus he started the Big Bang and created the universe. --zpdrmn

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