I'm still waiting on anything that might count as evidence of any "reality" other than the physical world and its contents. I thought a theist might have presented some such thing in this thread by now, but no luck there.
From post #7:
1. The cosmological fine-tuning arguments. This one appears to me to be a recent (last few decades) eruption of the traditional design argument in new ostensibly scientific guise. But I'm put off by how it's dependent on what I consider highly speculative theories of mathematical physics, incomprehensible to laymen and hence a matter for religious-style faith.
https://en.wikipedia.org/wiki/Fine-tuned_Universe
https://plato.stanford.edu/entries/fine-tuning/
2. The class of more traditional cosmological arguments, derived from Aristotle by way of Aquinas.
https://en.wikipedia.org/wiki/Cosmological_argument
https://plato.stanford.edu/entries/cosmological-argument/
This class of arguments seems to me to revolve around a whole class of unanswered metaphysical questions. (How did reality originate? What is the source of its order?) It doesn't really point to a theistic-style deity unless one introduces the deity as an additional premise which would seemingly render the arguments circular.
3. Religious experience. This class of evidences has the advantage of being exceedingly empirical, assuming that we allow 'empirical' to range over all experience and not just sensory experience.
https://en.wikipedia.org/wiki/Religious_experience
https://plato.stanford.edu/entries/religious-experience/
This class of evidence faces serious epistemological difficulties in my opinion. (But so does mathematics, and atheists love mathematics.)
4. Miracles. A great deal depends on what we interpret this word to mean. Strong Humean violation of the natural order interpretations make the reality of miracles hard to demonstrate (certainly by science, whose methodological naturalism always assumes the existence of natural explanations), while weak interpretations weaken the inference between the miracle and a deity, unless that premise is initially added, once again rendering the argument circular. (The young couple who think of their new baby as a miraculous answer to their prayers aren't committed to believing that the baby is a violation of the laws of nature, nor does their thinking of their baby as a miraculous answer to their prayers logically imply the existence of a deity.)
https://en.wikipedia.org/wiki/Miracle
https://plato.stanford.edu/entries/miracles/
If you are saying the natural/supernatural distinction is a false dichotomy, you are destroying the meanings of the words. Something can't be both natural and supernatural at the same time. If, on the other hand, you are complaining that God is not really "supernatural" after all, then you ought to be able to provide some recognisable evidence for God from "nature".
I'm inclined to give "natural" a physicalist spin, applying it to the realm in which physics and physical explanations hold true. Or perhaps to the realm accessible (at least indirectly) by sensory experience, the realm of space-time-matter. (Which may or may not be identical with the idea preceding.) The reality with which we can (at least in principle) physically interact. (Lots of questions and problems implicit in all that.)
That leaves us with problem cases like mathematics and the laws of physics themselves. It still isn't clear what kind of reality those have or precisely how human beings know about them. Which suggests that the natural/supernatural boundary might be a fuzzy distinction.
Regarding evidence of God from nature, the goal of the cosmological arguments seems to be to point to unanswered metaphysical questions whose answers don't seem to lie within the natural realm (as defined above): The reason why anything exists at all, the source of cosmic order and so on. In other words, the physical world doesn't seem to be a closed system so much as an unanswered question. Throw in an implicit assumption that everything has an explanation, define 'God' as the missing explanation, and there you are.
Something "transcendent" is outside the limits of usual human experience or understanding. God is supernatural by description, so transcendent in the secondary sense of being outside the limits of natural law.
So the common atheist demand that God present "himself" for inspection by mankind's physical senses (that he be visible in the sky or something, like the flying saucers in
Independence Day) would seem to contradict that sort of transcendence. (Which many religious traditions insist upon.) The cosmological arguments avoid that difficulty by arguing that physical reality (the realm of the senses in principle including all the possible instrumental extensions) requires an explanation beyond itself, an explanation of a different sort.
Not that I am aware of. There are threads like this one where scientists are open-minded as to the possibility of evidence of non-natural phenomena, for example.
What about the purported objects of religious experience? Practitioners of yoga, Muslim sufis and Christian religious contemplatives sometimes claim to have tapped into some kind of higher reality. It's usually something ineffable, something that can't be described in words or conventional concepts. They take those kind of experiences as evidence for their various religious beliefs.
That's exceedingly empirical in its way, assuming that we allow the word 'empirical' to range over all experience and not just sensory experience. One of the things that struck me about early Buddhism was exactly that, how empirical it is. Don't believe just because a teacher tells you or because you read it in a "scripture" somewhere, or because you concocted it as a result of a chain of reasoning. (The famous Kalama sutta.) Withhold final judgment until you actually experience it for yourself.
While at first glance that seems to be entirely subjective, the yogin might argue that if you devote years to yoga practice then you can experience it too, that confirming evidence is available to anyone who puts in the effort. Which isn't unlike science really. Scientific evidence is exceedingly arcane, perceptible only to a chosen few. But scientists argue that anyone who pursues years of university education and then gets access to the right research group, can have these confirming experiences as well. Or at least access to the data sets that confirm hypotheses after elaborate chains of inference are applied to them.
So problems of circularity start to leak in and the public/private distinction gets fuzzy too.
Atheism just holds that there's (probably) no God.
That might indeed be the minimum qualification for being an atheist, atheism's defining characteristic.
But atheists typically go well beyond that in real life. Atheists will typically insist that atheists have good justification for their belief that there is no God. Many of them will omit your 'probably'. They will typically insist that conversely, there is no good justification for belief in the existence of God. Or divine beings or transcendent realities, or something.
One of the profound problems with atheism is that it's typically blurred together with anti-Christianity. Divine realities are conceived in very Biblical ways. You haven't lived until a room full of atheists start spouting Bible quotations at you as if they were protestant fundamentalists, which many of them probably were until they lost their faith. (I'm not and never was a Christian, so Bible quotations don't move me. The Quran is just as dim.)
I'm most emphatically not an atheist in that image. I consider myself an agnostic in Thomas Huxley's original sense. I feel that I'm constantly surrounded by mysteries that not only do I not have the answers to, I strongly suspect that no one does. I'm fascinated by the philosophy of religion, not because it offers me something to smash and feel superior about, but because it presents no end of interesting problem cases on the epistemological and metaphysical margins.