This was in fact a popular view among skeptical philosophers from about 1870 to about 1980, and is still trotted out and dusted off every so often. It's called evidentialism, and philosopher Alvin Plantinga has a great deal of fun dismantling it in his book titled Warranted Christian Belief.
Indeed, since Plantinga's book came out philosophers are much more shy about using this argument against religious believers, but others unfamiliar with the philosophical literature are not so reticent.
Plantinga asks,inter alia, why our beliefs should be considered guilty until proven innocent. Why should beliefs not be counted innocent until proven guilty?
He wonders, too, why a person of sound mind, convinced in her heart that God exists, and who has never been confronted with an antitheistic argument that she found compelling, should be required nevertheless to suspend her belief until she has acquired overwhelming evidence that her belief is true.
Suppose, for instance, that you were accused of a crime. There's substantial evidence against you and little that you can offer to offset it. Even so, you're convinced you're innocent. You know you're innocent. You can't explain the contrary evidence, but it doesn't matter. You just know you didn't commit the crime. Should you, despite this assurance, acknowledge anyway that you're guilty because you can't present an argument to explain why you're certain of your innocence?
Many people believe in God on the basis of a totally subjective experience that they can't document or prove but which leaves them with an assurance that they could not deny even were they so inclined. The experience of former atheist Kirstin Powers, a liberal journalist, provides us with a good example. She writes:
Then one night in 2006, on a trip to Taiwan, I woke up in what felt like a strange cross between a dream and reality. Jesus came to me and said, "Here I am." It felt so real. I didn't know what to make of it. I called my boyfriend, but before I had time to tell him about it, he told me he had been praying the night before and felt we were supposed to break up. So we did. Honestly, while I was upset, I was more traumatized by Jesus visiting me.You can read her full account of her experience at the link.
I tried to write off the experience as misfiring synapses, but I couldn't shake it. When I returned to New York a few days later, I was lost. I suddenly felt God everywhere and it was terrifying. More important, it was unwelcome. It felt like an invasion. I started to fear I was going crazy.
There's a scene in the movie Contact, which was based on a book by atheistic astronomer Carl Sagan, in which the character played by Jodie Foster, a scientist named Ellie Arroway, is part of an experiment in which she's transported to the center of the galaxy. However, upon her return she's unable to offer any evidence that she actually left earth. None of the data collected by her colleagues from her transporter confirm that the experiment worked. Yet she's convinced that she actually experienced all that she claims to have experienced.
Is she justified in holding that belief? If her belief is the product of properly functioning cognitive faculties belonging to an accomplished scientist not given to imaginative flights of hysteria, is what she says in the following exchange with an interrogator discredited by her inability to present empirical evidence?
Michael Kritz: "Wait a minute, let me get this straight. You admit that you have absolutely no physical evidence to back up your story."Ellie Arroway, in Sagan's telling of the tale, had what amounts to a religious experience. Sagan clearly wants us to believe that her experience was veridical and that she's warranted in believing her experience was veridical despite the lack of proof, or even of any objective evidence.
Ellie Arroway: "Yes."
Michael Kitz: "You admit that you very well may have hallucinated this whole thing."
Ellie Arroway: "Yes."
Michael Kitz: "You admit that if you were in our position, you would respond with exactly the same degree of incredulity and skepticism!"
Ellie Arroway: "Yes!"
Michael Kitz: [standing, angrily] "Then why don't you simply withdraw your testimony, and concede that this "journey to the center of the galaxy," in fact, never took place!"
Ellie Arroway: "Because I can't. I... had an experience... I can't prove it, I can't even explain it, but everything that I know as a human being, everything that I am tells me that it was real! I was given something wonderful, something that changed me forever... A vision... of the universe, that tells us, undeniably, how tiny, and insignificant and how... rare, and precious we all are! A vision that tells us that we belong to something that is greater than ourselves, that we are not, that none of us are alone! I wish... I... could share that... I wish, that everyone, if only for one... moment, could feel... that awe, and humility, and hope. But... That continues to be my wish."
But if that's so, why are Christians faulted, by people just like Sagan, for believing in God on the basis of a subjective assurance similar to that possessed by Arroway?
Indeed, far more people have had an experience like Kirstin Powers had than have had an experience like Ellie Arroway. If Arroway is justified in believing that she actually encountered a different world why would people like Powers not be similarly justified?
Just as it would be foolish to expect Ellie Arroway or Kirsten Powers to discount their experiences because they can't empirically prove that they had them, so, too, it's foolish of skeptics to think that the only warrant for belief in God is the ability to provide objective, physical evidence that the belief is true.