I have been debating with an atheist about the possible existence of a god. I wrote this as an explanation but I don’t know if it's a very reasonable explanation. Perhaps someone could read it over and give me some comments.
The question for everyone to ask is, why is there anything? What engendered the existence of the known Universe? Science has yet to provide any kind of answer to this question. Therefore, you must give every possibility an equal probability. An equal probability for every single explanation that has been thought of and for everyone that has not been thought of. As such, the probability that someone stuck their hand in the universal hat full of all possible explanations and pulled out the correct is answer very close to impossible. Interestingly enough, your hypothesis that there is no god, is not an explanation but part of many possible explanations. In the same way, the hypothesis that there is a god is not an explanation but part of many possible explanations.
Therefore, while it is not correct to limit ourselves to a binary choice we can explore this possibility. So the binary options are all the explanations that have a god and all those explanations that do not have a god. I contend that for every explanation you can come up that has no god, I can come up with one that has a god. Therefore, it might seem reasonable to believe that cardinality of the two sets, are equal. If that is the case then each of the binary choices gets a probability of .5. In other words, they would be equally likely.
How can we know if the two sets have the same number of elements? If we can make a one-to-one correspondence then we will have shown this to be true. I contend that for every possible explanation that can be given that has no god, I can simply include a god and therefore make an explanation with a god. And the reverse is also true…..
Therefore, we have a function which effectively maps from one set to another set and we also have that the inverse of the function is also a function. Therefore, the function is one-to-one and thus the two sets have an equal cardinality.
Thus, if we look at the conditional probability of whether or not there is a god given that there are no other possibilities but those two then we have that this probability is .5. So flip a fair coin and call it in the air cause that’s as good as it is going to get.