Looking back at the philosophy of religion in the 20th century, I cannot help but be intrigued by the large amount of literature published on verificationism and positivism. It seems to me that the philosophy of language was a powerful and prevalent factor that permeated most of the discourse on religious epistemology and theistic proofs/demonstrations. The reasons for this are interesting, but far beyond my scope here. Presently, my attention has been channeled on the verificationist principle(s) such as elucidated by A.J. Ayer and the logical positivists. What can or cannot be spoken about and how was a major topic for decades.
From the Davies anthology, this excerpt is taken from Ayer's Language, Truth and Logic (is it a form of British humor that no Oxford comma is in the book title?):
"...there can be no way of proving that the existence of a god, such as the God of Christianity, is even probable...For if the existence of such a god were probable, then the proposition that he existed would be an empirical hypothesis."
One thing I find compelling about this claim is that it still, nearly 90 years later, captures the core basis of why many people deny the existence of God. It is a good reminder that the ideas we encounter today are, in most cases, not really new or novel. Ayer notably wrote for many years on the subject after Language, Truth and Logic, but the core of the claim seemed to remain intact.
What I believe Ayer so nicely summarizes in his verificationist ideal is the standard scientistic/reductionist view of the world. This position holds everything that exists or has meaning is, in principle, ultimately expressible or can be investigated and either proved or disproved by the physical sciences (physics, chemistry, biology). Essentially, all that exists is matter in motion; nothing can be that is not eventually quantifiable or accessible to the senses in some way (or reduced to intelligibility by mathematical description). Certainly, there are many open questions, but the scientistic view affirms nothing in the grand scheme can be outside the purview of empirical investigation.
Scientism is the default view so often that Christian thinkers and other theists often spend a meaningful deal of time taking it apart before proceeding to arguments for the existence of God or the attending preliminary metaphysics. For example, Edward Feser's writings in Scholastic Metaphysics and Aristotle's Revenge and David Bentley Hard in The Experience of God.
It is very difficult to see how Ayer's way of framing the conversation does not beg the question against theists. The theistic argues God exists and means by 'God' that which is not a locatable object in the world. The verificationist denies the 'term' God (or 'Creator' or whatever) has any meaning because it is not a physical object. So, the verificationist effectively says "God cannot exist, therefore God does not exist." Before any theistic argument can be made it is dismissed out of hand as improper use of language or the expression of a psychological state (emotive).
Certainly, God is not the only object in the verificationist's gunsight. Any metaphysical utterance is purportedly nonsense on the same idea. Yet, I wonder why it would not be open to the theist (or other non-reductionist metaphysicians) to simply state the same thing back to the verificationist. For what the verificationist seems to be offering is a blunt assertion or presupposition. To argue in favor it would be to borrow premises from ideas or propositions outside the verificationist scope. For instance, one could say "verificationism is true because ___". And filling in the blank seems to be either circular or not verifiable.
Sometimes the verificationist will say something like "we can prove that physical things are real by simply reaching out and touching them. We cannot prove God or angels or demons are real. So, we are justified in thinking that physical things are real and the theist must show us how in some way non-physical things are real." In one sense, there is a certain very basic intuition captured here. Surely this seems straightforward to the man on the street. But a closer look shows this way of thinking is the very same problem as above dressed in different clothes. A major issue is that it oddly asks the theist to show that non-physical things are real in the same way physical things are. So, it begs the same question. This is like saying "walk with both feet in the air." The interlocutor in this case simply dismisses a priori that any non-physical thing can exist. He cannot even hear the theists (or non-metaphysical reductionist) case. And, like Ayer's claim, it imports a very dubious notion of 'proof' that is laden with reductionist assumptions. It would be incumbent on the one asserting this to demonstrate its veracity.
I sometimes wonder how far 'Ayer-esque' verificationism (along with Carnap and others), and its scientistic offspring, moved the dialogue on religion onto unfruitful ground. There is not much gameplay when the rules are constantly being changed and the goalposts moved. To my mind, this was the primary outcome of the verificationist movement. The influence of this thought is still felt in contemporary debates. Hopefully, the verificationist ideal will eventually fade into the oblivion it so vehemently denies.