PLEASE NOTE WELL: This thread is about the logic of arguing that a god does not exist based on the absence of any evidence for that god's existence. This thread is NOT about whether there is or is not evidence for the existence of a god. All posts that attempt to assert evidence for the existence of god will be considered off topic and ruthlessly deleted faster than a seventeen year old virgin can shed his or her pants on prom night.
For the purposes of this thread, please begin by assuming that there is neither sufficient nor conclusive evidence for the existence of a god. The essential question then is whether or not the lack of sufficient and/or conclusive evidence for the existence of a god provides us with sufficient and/or conclusive evidence that a god does not exist?
Or more simply, if there is no evidence for a god, does that mean there is no god?
On the surface, we might quickly answer "no". That is, we might say that the lack of evidence does
not mean there is no god. After all, is not Martin Rees' aphorism correct: "Absence of evidence is not evidence of absence"?
No, it's not correct. As you and others pointed out, an absence of evidence is at least evidence of absence while not being proof of absence.
And it can be elevated to
proof of absence in a couple of special cases:
1. Where the necessary investigation is naturally limited. For instance, if I thoroughly examine a dog carrier and find no dogs, I can conclude that there are no dogs in it. The search domain is small enough that I
can investigate it thoroughly, and the fact that "dog" has an established meaning means I don't have to worry about invisible, incorporeal, or microscopic dogs that would have escaped my notice.
2. Where the evidence is a necessary implication of the existence of the thing. You can think of this like a corollary of the old expression "where there's smoke, there's fire;" the flipside of this is that where there's no smoke, there's no fire: if I look around a room and find no hint of smoke, then I can conclude that there isn't a raging fire in the room, because if there was, the room would be filled with smoke.
But what about cases in which a lack of evidence for something does indeed suggest that something does not exist or is not present? For instance: Suppose your doctor tests you for cancer. No cancer is found. Isn't that evidence that there actually is no cancer?
Or, as the logician Irving Copi once wrote, "In some circumstances it can be safely assumed that if a certain event had occurred, evidence of it could be discovered by qualified investigators. In such circumstances it is perfectly reasonable to take the absence of proof of its occurrence as positive proof of its non-occurrence."
Can we assume that, if a god existed, evidence for that god could be discovered by "qualified investigators"?
If we answer "yes" to that question, then why yes? And if we answer "no" to that question, then why no?
It depends on the god. Some are unfalsifiable. IMO, likely
fabricated to be unfalsifiable, but unfalsifiable nonetheless and therefore can't be disproven.
But really, it's pretty rare for me to care about whether a god can be disproven. It's irrelevant to me virtually all of the time.
When we're talking about that fine line between full-blown disproof and mere lack of evidence, we're really talking about the line between a god that definitely doesn't exist and a god that is indistinguishable in every way we know from a god that doesn't exist.
This irrelevant god isn't the god that any theist believes in. It isn't even a god that is capable of instilling belief in a person. By taking it as given that there is no evidence for gods, we're really saying that every theist ever has been unjustified and unreasonable in assuming that their god(s) exist, even though we can't
absolutely exclude the possibility that they serendipitously stumbled on the right conclusion in an "a stopped clock is right twice a day" kind of way.
We're still taking as given that anything in any religion that would serve as evidence for gods if it was true is necessarily unfounded: no prophets are genuine, no "revealed" scriptures actually came from God, no divine miracles ever actually happened... or at least if they did, there's no valid way to attribute them to any gods.
... so by the time the question of lack of evidence vs. proof of non-existence matters, we've already concluded that every theist anywhere is unjustified in their beliefs and that virtually every theistic religion is at best built on nothing and at worst is completely wrong.