Note that there are two main topics at play: my initial argument (which considers consensus in itself), and the question of whether and why some particular consensus can lack rational weight given considerations posterior to the facts of consensus and global reliability (i.e. posterior to my initial argument).
Yes, we are talking about local reliability because, when it comes to the specific questions we are concerned with, the consensus achieved by polling the entire human race does not matter if the majority of its members are not reliable in that domain. In other words, when considering specific matters, we are necessarily talking about what you call "local reliability," even if we are polling the entire human species or a random sample of its members. We are asking whether they (in this case, the entire species) are reliable on that particular question or in that particular domain ("local reliability"). As I noted previously, and to which you agreed, even if human beings are generally reliable, there may be particular domains in which their conclusions are notoriously unreliable. Whether you are sampling the entire set or a particular subset, the question is the same: is this set of individuals reliable in this domain?
It seems that you are conflating the consensus view of the complete set with what you call "global reliability." But if we are talking about a consensus view on a particular matter, then we must be talking about "local reliability," regardless of whether the consensus was achieved by the complete set or only a subset.
I think this represents the main point of your post.
First, I grant that global reliability does not mean the same thing as the complete set, and local reliability does not mean the same thing as a subset. Yet global reliability is related to the complete set in the same way that local reliability is related to the subset. Further, given your domain emphasis, let us think of local reliability only in terms of expertise (even though it is true that a reliable subset could be reliable on the basis of expertise or the basis of random sampling).
Why is global reliability related to the complete set? Because global reliability is the antithesis of global skepticism, and the object of global skepticism is the human being (rather than some particular sort of qualified human being). That is, there is no human being that does not escape the judgment of global skepticism. Global reliability, as the opposite of global skepticism, also takes the human being (considered as human) as its object. So global reliability says that human beings are reliable. It doesn't say that scientists, archaeologists, or psychics are reliable. Insofar as they are human, they are reliable, but global reliability passes no judgment on particular varieties of humans.
It is related to the complete set because we are talking about consensus. The argument I gave rests on a consensus of reliable instruments--indeed, of all existing reliable instruments of the human kind.
But if we are talking about a consensus view on a particular matter, then we must be talking about "local reliability," regardless of whether the consensus was achieved by the complete set or only a subset.
I disagree. Every matter is a particular matter. Therefore if what you say is true, we could never talk about global reliability.
Yes, we are talking about local reliability because, when it comes to the specific questions we are concerned with, the consensus achieved by polling the entire human race does not matter if the majority of its members are not reliable in that domain.
Again, all questions are specific questions. Global reliability extends to all "domains," just as global skepticism extends to all "domains." Human beings are not inherently reliable when it comes to counting to five, and inherently unreliable when it comes to astronomy.
Let's revisit your example of 10 psychics at this point. The problem I already pointed out has to do with the nature of consensus, sets, and subsets. If there are 5,999,999,990 humans who do not believe the future can be known by tarot cards, and 10 psychics who disagree, it is misleading to talk about a consensus. If we hold to global reliability (and therefore prescind from expertise) then this answer I already gave is quite relevant to your scenario of 10 psychics.
But you want something stronger. You want to suppose that there is a true consensus among all humans in favor of psychic activity, and that their belief is simultaneously known to be false. Does this create a problem for my argument? If so, I would be curious as to what premise it falsifies. I don't think it does.
- I don't think there actually exists a true consensus among all humans in favor of psychic activity.
- If at some point in the past such a consensus did exist (e.g. geocentrism), then it carried the relevant rational weight of a burden of proof given the state of knowledge at the time. If everyone then knew what we know now, no such consensus would have existed.
If there is a bias in the consensus population that is known to you and not to them, and this biases them in favor of their belief, then this would be a reason to ignore the consensus. At this point the discussion could branch in many directions. I would contend that this bias is a secondary consideration that follows after the burden of proof.
My main argument is based on reliability and testimony. Let me spell out a scenario. You are living a few millenia ago and you poll the human race, asking what celestial model is thought to be true. You yourself are undecided on the matter. The overwhelming answer is geocentrism. All you have is the answer. You don't have explanations, methods, or rational argumentation. You have testimony. Will this incline you to believe or disbelieve in geocentrism? The answer has to do with whether you are a proponent of global skepticism or global reliability.
This is why I specified "religionists," a subset of humans.
If the group is religionists rather than all humans, then the conclusion may have no more weight than the case of the 10 psychics.
If the consensus was achieved by means of indoctrination and conquest, rather than by satisfying the burden of proof for Islam, then nonbelievers need only point to these facts to argue that the consensus, however large, has no merit.
Again, I take this to be a secondary consideration that does not bear on my argument.
The question is this: does consensus
qua consensus have merit, or not? Without introducing extraneous factors, this question must be answered. My argument has nothing to do with methods or means, it has to do with consensus and reliability.
You seem to be introducing an accidental consideration, similar to this:
Person A: Taller people have a better chance of dunking than shorter people.
Person B: But there are some short people who can jump much higher than tall people!
This is why I have often inquired into precisely what premise you wish to oppose.
Essentially, every aspect of it. I feel that I have already articulated the main reasons, so I'll try to summarise them concisely here. Regarding P1, even if human beings are generally reliable, there may be particular domains in which their conclusions are notoriously unreliable. You agreed on this point. Regarding P2, you have introduced religion into the argument, thereby raising the question of whether man is inherently reliable in that domain. (What you call "local reliability" thus enters the picture.) Related to this, I have argued that the way in which the consensus is established matters, which implies that not every consensus has equal merit. This is true regardless of whether we are talking about the complete set (the entire species) or a particular subset (e.g., archaeologists). Again, you seemed to agree on this point also, noting that a consensus is "rationally significant" once it has been established by legitimate experts. However, you make an exception for the complete set, arguing that any consensus achieved by the complete set has merit regardless of how it was achieved. I don't think it necessarily has any merit beyond telling us what the majority of human beings believe. It certainly doesn't tell us whether their conclusions in that domain are reliable or not.
It doesn't tell us whether the conclusions are true, but I never claimed that it did.
In order to attack my argument, you need to prescind from the means by which the belief was formed. The only insight my argument offers into the means is general human reliability, which you can oppose if you like.
The rational significance of consensus rests on the notion of reliability. You are attempting to undermine that reliability in particular instances. But even before we look further and move into particular questions of reliability, we already have global reliability. That is our starting point. If, after investigation, nothing is learned regarding reliability, we necessarily default to the position of global reliability (and the burden of proof I already noted). Investigation into particular reliability, means, etc., can produce positive or negative results, but my point is that the neutral position
is already rationally significant.
Therefore you can battle apologists all day long in an attempt to discredit the reliability of this consensus, but if your arguments
against reliability are refuted then you are in the same position you were in before the investigation into reliability: inclination towards belief (i.e. you have the burden of proof). As I already said, the atheist therefore lives or dies by his arguments.
Even accepting the first premise for the sake of argument, we are left wondering whether human beings are reliable in the domain being discussed.
But this is evidence that the first premise is not understood, nor is the idea of global skepticism. Global reliability has to do with the reliability of human beliefs, apart from any "domains" (which are ultimately arbitrary designations anyway).
(As I argued previously, the way in which the consensus is established matters).
It matters in strengthening or weakening the bare fact of consensus. But the question is this: what is the implication of the bare fact of consensus?
As I've said so many times, local reliability (via expertise) presupposes and relies upon global reliability. Heightened reliability presupposes initial reliability.
Good post.

Made me think. I first read it early in the morning and just couldn't organise my thoughts about it at that time. Coffee helped a lot.
Haha, glad to hear it. Yours was good too. I don't know why it took me so long to see your point. I hope this one wasn't too confusing; we seem to be moving fast.