Originally posted by twhitehead
Yes - assuming that you have no other information available.
Given any real number - and no other information about it, the probability that it is an integer is nearly zero because there are infinitely more real numbers than integers. If I recall correctly, it is also infinitely more likely to be irrational than rational.
While this is a nice example, it's of course problematic:
You say
Given any real number - and no other information about it. Now keep in mind that in this comparison "God" is equated to "an integer". You do have additional information about integers though, namely that there are less integers than real numbers.
Because of this additional information - which your are using - you can make a probability claim about whether the number is an integer. Such information is not available about god. Therefore probabilities about god cannot be calculated. Later you say
Probability is all about information. I agree. And because there is no measurable information available about god, calculating the probability of his existence is not possible.
(Mind you, certain types of god I think can be called "impossible" to exist. For instance when contradictory statements about this god are being made. An omnipotent god creating a rock he cannot lift would be the most famous example.)
If I'd continue with this comparison, it would have to be something like "because there is an infinite amount of numbers, the chance of a particular number existing is infinitely small" which I think is nonsense.
If anything, if an infinite amount of numbers exist, than a particular number
must exist. Which I think is similar to what Divegeester said.