Recently in correspondence with non believer I have repeatedly meet with the following argument. This is usually touted as a kind of self evident mantra.
 There is no proof that God exists  Its irrational to believe something unless you have proof . Therefore:  belief in the existence of God is irrational.
Now we need to elaborate what is meant by proof here; in Philosophical Theology the word is historically used for the various philosophical arguments that purport to show God exists. Such, things as the Cosmological, ontological, teleological, and moral arguments for Gods existence as well as the 2 dozen or so other arguments that have been proposed. I take it then that claim then that there is no proof means that these arguments all fail.
I think this argument is a bad one. I’ll elaborate why below.
First note there is an interesting relationship between  and  , in that if  is true then a person should not believe in  unless they have some arguments for the truth of  merely asserting  is not enough. If I believe  in the absence of a reason for doing so I am, according to  irrational, and hence in the very same epistemic situation the proponent of this argument claims a theist is in. Consequently, the first thing, that needs to be asked is: what’s the basis for asserting ?. In order to rationally accept this premise, the objector would need take me through the most sophisticated versions of the cosmological, teleological, moral and ontological arguments being proposed in the literature today and demonstrate that they all fail. Now few atheists I know can do this, most in fact have never even read these arguments and have next to zilch familiarity with the literature on these arguments. It seems to me then that these people hold to an incoherent irrational position. They maintain  without any proof or reason at all and then assert in  that one should not maintain things without proof or reason.
However, to be fair, some atheists have studied this literature and believe they have rebuttals of the arguments in question. So to advance the argument let us assume they are correct, this takes us to , but here I think several problems arise.
First,  leads to a regress problem, suppose I believe P, to be rational I need proof, therefore I need an argument and I need to be able to rationally believe the premises of this argument. But then by  I need proof for these premises. But then I have to believe further premises and I will need proof for this and so on. Unless we stop at some point and believe something without proof, we will be irrational in believing everything.
Second,  leads to scepticism, since at least the time of Hume it has been fairly clear that some of the most important beliefs we hold cannot be proved. Consider the belief in a physical world that exists independently of our senses. It has proven difficult if not impossible to find any argument for the existence of this world which does not assume the external world’s existence as an implicit premise. Familiar Sci Fi scenarios where a person is plugged into a virtual reality machine show its logically possible for the world to not exist and us think it does and have all the current experiences we do and hence deductive arguments from the way things appear are unsound. Inductive arguments appear also to fail. For an inductive argument to work one need’s to assume that the future will resemble the past, that there is uniformity in the world. But the existence of the world is what one is trying to prove. William Alston has argued, cogently I believe that the existence of the external world cannot be proven, neither can for that matter the existence of other peoples thoughts and feelings, the existence of moral rightness, the existence of a past and numerous other things. So if  is true we are in serious epistemological trouble.
Third  is incoherent, suppose  is true, then it follows I should not believe anything without proof. But then I should not believe  without proof. Until I become aware of some compelling argument for  its irrational to accept it and if the skeptic has no argument to offer me, he is irrational accepting it as well. I think the points above show that such an argument is impossible. Any such argument will employ premises which will need to be justified by other premises, which will need other premises and so on and seeing even things such as the existence of the physical world cannot be proven its doubtful such an argument can get off the ground.
The claim that one is never rational in believing in something without proof “on examination consists of a mass of incoherence. The objector contends that the theist is irrational why? Well because according to a claim for which he has no proof, one should not accept things without proof, oh and according to another claim he has not proved, theism has not been proved. Hardly compelling stuff if the premises are true we should reject them, and if they are not true then the argument is unsound.
When I began studying Theology and Philosophy I discovered that some important Christian traditions claim that not all beliefs require proof to be rational in order to know anything at all, some things need to be taken for granted unproven. On this they are clearly correct. Second, and interesting they maintained that certain theological beliefs about God should be accepted this way.
Now this does not mean that there is no place for rational argument in assessing theological claims, or in thinking about this issues. If one starts assuming belief in God is true, one still need to reason *from* this and see if it can provide coherent answers to various, metaphysical, moral and existential questions. One still needs to ask whether various arguments against belief in God is sound. One still needs to show the implications of what one believes are not contrary to obvious facts. And one needs to be able to examine whether theism is able to cohere with and be consistent with other things we know. One requires arguments to do all these things and if a one cannot do these things reason may provide us grounds for rejecting theism.
But the claim that one cannot prove theism from the outset does not. The traditions I mention deny one needs to be able to do this, one does not rebut them by simply asserting their claims are false one needs to provide them with an argument, and the incoherent nonsense which is often provided is not a very good argument.