A Quick Digression About Proving Negatives

Posted on July 9, 2010. Filed under: Uncategorized |

Today I spent all day lurking on other sites and have seen a common thread running through most of them. Jerry Coyne has a post about what proof you would require to question your atheism. Signal In The Noise took this post and ran with a rebuttal. Greta Christina has a couple posts on whether you care about the truth of your beliefs. Even the mental clusterfuck that has become the debate over Rand Paul’s personal beliefs about the age of the Earth are getting in on the action.

Proof seems so easy on the face of it. In response to a essay Signal has in his post, I responded thusly:

The essay you point to about proving negatives makes some glaring errors in logic. I’m not saying you can’t prove a negative, but rather that the degree to which you can prove it will never satisfy a skeptic. For the author of that paper to conflate the existence of Unicorns to the rising of the sun every day is disingenuous at best.
In fact I will take the next logical step.

1. If unicorns had existed, then there is evidence in the fossil record.
2. There is no evidence of unicorns in the fossil record.
3. Therefore, unicorns never existed.

By this logic:

1. If Homo habilis had existed, then there is evidence in the fossil record.
2. There was no evidence of H. habilis in the fossil record until 1960
3.Therefore, H. habilis never existed before 1960.

The problem here isn’t that inductive arguments won’t give us certainty about negative claims (like the nonexistence of Bigfoot), but that inductive arguments won’t give us certainty about anything at all, positive or negative.

If there is another way of proving a negative other than induction, I’d like to hear it.
He then goes on to conflate my belief that the sun will rise tomorrow as a similar inductive process.
It is by degrees not the case. The inductive process of proving a negative always requires one faulty step in induction. In the case of our unicorn analogy, it is that there does not appear to be evidence for unicorns in an incomplete fossil record. I don’t deduce the sun will rise tomorrow just because it has always done so. I deduce the sun will rise tomorrow because the earth completes a full revolution once per day and the sun rises and sets over my horizon as a result. If the sun does not rise tomorrow, that should be the least of my worries; I would hazard a guess none of us would be capable of worry at all.
What the author should be claiming is that you can trust a conclusion derived from the process of induction if the premises that you use are practical.
That seems far too cautious to be called a truth.

If Signal, you believe the arguments that Hale makes are correct; it should follow that we have enough evidence to say Jesus didn’t exist:
1. If Jesus had existed, then there is evidence in the records of the Romans.
2. There is no evidence of Jesus in the record of the Romans.
3. Therefore, Jesus never existed.