The 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. By this they hope to persuade themselves and others that at least the possibility remains open that a supernatural agency exists; from there they make the inflationary move from alleged mere possibility to not eating meat on Fridays. They are, however, wrong both about not being able to prove a negative, and about not being able to prove supernatural agencies exist and are active in the universe. Seeing why requires a brief refresher on the nature of proof.
Proof in a formal deductive system consists in deriving a conclusion from premises by rules. Formal derivations are literally explications, in the sense that all the information that constitutes the conclusion is already in the premises, so a derivation is in fact merely a rearrangement. There is no logical novelty in the conclusion, though there might be and often is psychological novelty, in the sense that the conclusion can seem unobvious or even surprising because the information constituting it was so dispersed among the premises.
Demonstrative proof, as just explained, is watertight and conclusive. It is a mechanical matter; computers do it best. Change the rules or axioms of a formal system, and you change the results. Such proof is only to be found in mathematics and logic.
Proof in all other spheres of reasoning consists in adducing evidence of the kind and in the quantity that makes it irrational, absurd, irresponsible or even lunatic to reject the conclusion thus being supported. This is proof in the scientific and common-sense meaning. The definitive illustration of what this means, especially for the use that theists would like to make of the myth that you cannot prove a negative, is Carl Sagan's "dragon in the garage" story, which involves the teller claiming that he has a dragon in his garage—except that it's invisible, incorporeal and undetectable. In response to which one can only ask— if there's no way to disprove a contention, and no conceivable experiment that would count against it, what does it mean to say that something exists?
No self-respecting theist would go so far as to claim that "you cannot prove the non-existence of God" entails "God exists." As mentioned, their point is merely to leave open the possibility that such a being might exist. But Sagan's dragon dashes even this hope. For one can show that it is absurd, irrational, intellectually irresponsible or even lunatic to believe that fairies, goblins, the Norse gods, the Hindu gods, the gods of early Judaism (yes, there were several: go check), and so endlessly on, "might exist." It would compound the felony a millionfold to grant this and yet insist that one's own (Christian or Muslim, say) deity "nevertheless" exists or might exist.
For a simple case of proving a negative, by the way, consider how you prove the absence of pennies in a piggy-bank.
Sent in by Ben Marks, north London
Send your philosophical queries and dilemmas to AC Grayling at question@prospect-magazine.co.uk
