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When can I say “I know”?

February 28, 2010

As a mathematician I’m used to being able to say when something is known and when something isn’t. I know there are an infinite number of primes, just as the ancient Greeks knew this, and just as mathematicians in the future will know. The mathematical standard of proof allows me, for the most part, to make sure and certain statements. However, I’ve often gotten into arguments with people about our ability to make similar statements in more day-to-day situations. How can I justify making statements of certain knowledge about things that don’t have the epistemological framework of maths?

Reading A C Grayling’s ‘To Set Prometheus Free’ has given me the seed of an argument that starts to address this question. A Bayesian approach to answering a question about the existence of, say, god, would take into account the prior probability of such existence. Thus I might look around at the complexity and beauty of the world around me and wonder how it could possibly exist without a creator; in a Bayesian world-view I could then be justified in making the statement “I think it is likely that god exists”. I may on the other hand look at the large and ever-growing body of knowledge that science has given us regarding the creation of the universe, the laws of nature and the evolution of humans. I might look at the historicity of the bible and other religious texts and beliefs, and the lack of evidence underpinning the basic tenets of religious faith. These things could justify my making the statement “It is highly unlikely that a god exists”.

At this point it is not obvious how this line of reasoning will allow me to make a sure statement of knowledge about the existence or nonexistence of god. If I made the statement “God does not exist”, I may be asked to provide proof of this, something I certainly cannot do. Whilst I am sure that it is 99.9999% certain that god doesn’t exist, a religious arguer could use the tiny non-zero probability of the existence of god to slot their beliefs into the realm of possible arguments and attempt to justify my need to accept their belief. What is needed is to examine how the Bayesian style of making knowledge statements works in a rational world.

Suppose we are having an argument about the existence of fairies (to use A C Grayling’s favourite example). If I made the statement “It is highly unlikely that fairies exist”, how would this be viewed? In a rational world I would (or should) be considered an idiot. We know that fairies don’t exist. There are of course circumstances where I may have to use a Bayesian style statement, circumstances where, compared to the fairy example, there is much more room for doubt. However, when the probability of the existence or nonexistence of fairies is such a one sided affair it is nonsense to resort to a Bayesian argument. In a rational world it is an all or nothing affair. I know that fairies do not exist.

So we come to the statement “I know god doesn’t exist”. Can I justify this? There is no evidence of the existence of a god or gods (and indeed, faith is by definition belief in the absence of evidence). Modern religious beliefs are the remnants of ancient myths handed down from generation to generation before being recorded in religious texts that are, by-and-large, of poor historicity and subject to editing for social and political reasons. Science and reasoning are giving us the knowledge of the universe that religion once gave. I am 99.9999& certain that god does not exist. It is not a 50/50 argument. So, in a rational world, I know god does not exist.

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