Paulos playfully takes on 12 alleged 'proofs' of the existence of a deity - proofs that range from the subtly fallacious to the downright silly. The thing I liked most about the book was that Paulos summarized most of the proofs in syllogistic form, to help expose the flaws in the proofs. He cites an example from Woody Allen :
All men are mortal.
Socrates is a man.
Therefore, all men are Socrates.
It has never seemed to me that the proofs of god's existence are very difficult to refute, but Paulos at least brings good humor to the task - humor without rancor or condescension.
My question is : what would constitute a 'proof', or even evidence, of the existence of a deity. I think that it would be of the same nature as evidence for, say, dark matter. That is, there would need to be some phenomenon that is not accounted for by our physical theories, that in fact contradicts our physical theories, and that is explainable by the existence of a deity with well-defined properties. Moreover, the deity explanation would have to be such that specific additional predictions could be formed from that explanation, and those predictions could be empirically tested.
But there are two problems here: first, religious believers are unable to ascribe any well-defined properties to their deities. Most of their deities were invented by primitive people who imagined god as a kind of really big and powerful person. So contemporary believers either stick with that story, or replace it with a sort of fuzzy 'god is everywhere as a kind of spirit' concept, which inherently has no explanatory value whatsoever.
Second, a 'deity hypothesis' that actually predicts and explains natural phenomenon is no longer in the realm of the supernatural, and therefore does not refer to a deity at all. Unless, of course, you want to think of natural laws as a deity.
So evidence or 'proof' of god of an empirical nature is doomed from the outset: scientific evidence can only ever be evidence of natural processes, not super-natural entities.
Creationists and other fundamentalists seem to have an intuitive idea that this is so - hence the many 'god of the gaps' arguments for creationism and the formation of the universe.
On the other hand, purely analytical proofs can tell us nothing about the world. By definition, any statement about the world, in particular any statement about what does or does not exist, is an empirical statement, not an analytic statement. For example, Euclidean geometry tells us nothing about the actual geometry of the universe that we inhabit. Neither do any of the non-Euclidean geometries. The question of whether the fifth postulate holds in the real world is one that can only be decided by observation of the real world.
So an analytic proof of god's existence is likewise impossible.
This leaves us with Wittgenstein's observation that "a nothing is as good as a something about which nothing can be said". It is often asserted by religious believers that atheists are just like them, in the sense that atheists have a fundamental belief in something that can't be proven but must be taken 'on faith': namely, the non-existence of a deity. But I would argue that most atheists in fact don't feel much need to deny the existence of a deity, but simply see no reason to believe in something for which there is absolutely no evidence and which explains nothing.
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