I adamantly disagree, as would most philosophers since the 1930s. What you are espousing here is a variety of logical positivism, which is self-refuting. Consider the statement "Empirical evidence is required to affirm the existence of anything." Okay, just empirically affirm the existence of empiricism. More importantly, empirically justify empiricism as a philosophical standard. The problem with logical positivism is that it requires an evidentiary standard that it cannot, itself, fulfill. And that's why its adherents were run out of the academy in the first half of the 20th Century. Its really only New Atheists who make such demands of people, much to the chagrin of more learned atheists. When Richard Dawkins says stuff like this, the loudest criticisms come from atheistic philosophers simply because they're embarrassed.
This statement is obviously wrong. Science is a fairly narrow enterprise concerned with observable aspects of the material universe. A few things science cannot even evaluate, much less "prove": mathematics, logic, science, itself. In fact, science must take all these things for granted, before one can do science. Godel's theorems of incompleteness suggest that the more exact a mechanism is, the less complete it is, and this is why there are no logical justifications of logic, no mathematical justifications of math. Science, itself, rests on a fairly thin inductive assumption that natural laws are uniform across space and time, which cannot be proved scientifically--ever. Science will never be in a position to observe enough to make a deductive argument about the conditions of the universe; it must always make some problematic inductive argument. You see, the biggest casualty for your empirical philosophical requirements is, in fact, science. This was Hume's greatest problem, and he never found a solution, nor did anyone else. If we had to sit around and wait for empirical evidence of the conditions surrounding every physical phenomenon in the universe, science couldn't operate: no reasonable statement could be made about anything. The variety of empiricism you espouse is known to be one of the most crippling world views in all of history, most specifically as it relates to science.
Additionally, lack of scientific “proof” doesn’t render something illogical. I wonder whether you understand what a “proof” is, as it’s a strictly formal arrangement of necessarily concluding statements most often relegated to the realm of mathematics. For instance, there’s no formal proof of evolution or gravity. Moreover, science isn’t the arbiter of what’s logical; logic, itself, is. Scientists don’t sit around trying to render judgments about the rationality of statements, but rather test hypotheses according to criteria of observation. Just because science, for structural reasons, can never attempt to prove the irrationality of the square root of two doesn’t mean that the statement, itself, is illogical.
Also, you make the mistake of conflating irrationality with being delusional. When someone makes a mistake of logic, we do not then commit them to an insane asylum.
Your notion that theistic belief can only be grounded in gut feelings and "psychological conditions" is plainly false. In fact, the vast majority of rational discourse in human history has hinged in some manner on the belief. Cosmological and ontological arguments for God are hardly "gut feelings." You do understand that, for instance, Descartes's work culminated with an ontological argument for God. The truth is the theistic worldview is more defensible--by a long shot--than what you're espousing as a worldview, which currently looks a lot like logical positivism. Though that's not saying much since, your worldview refutes itself. The interesting thing is that you're not even aware of this.



