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Can Humanism Match Religion's Output?

I don't have time to construct a full response, but I would like to hit a couple of points.

Catholics vs. rationalists: An analog seems to be large institutional investors (market makers) vs. small or independent investors. Clearly both kinds of market players (the very big vs. the small) play important roles, but the market makers, well, they have the ability to move the market in different directions because of the strength of their market position. "Following" the market makers is often viewed as a safe bet (i.e. a cheap risk computation) for a good return, but not always. Small investors seek out opportunities either missed by big investors, or misjudged by big investors.

Being an active member of the Catholic church requires forgoing critical thinking concerning a number of important aspects of reality, but such participants view this arrangement as being beneficial overall: it reduces the amount of mental computation that need be expended on a wide variety of subjects (no need to enumerate, I hope ;-) ). Some of the "benefits" gained by participants are that a number of "important causes" are prepared for them to act on, and many of them will. Although the Catholic church has it's full share of strange quirks, the thing we refer to as the Catholic church today is far more tame and humanistic than say it's 16-17th century version: many of the high-profile causes adopted by the church have pretty broad appeal as worthy issues. Of course, when Catholic missionaries go into an impoverished area to help feed and clothe people there is also an evangelical element. So, at least some of the causes picked up by the church will be "objectively" good, and some bizarre or bad (like condoms and family planning).

Rationalists, on the other hand are likely to explore many of these issues more in depth, as a result will also likely have a more diffuse impact on shaping future outcomes. Take world population (by humans) for example. Given the Catholic view of sexuality and reproduction, it is likely that the "cheap mental computation" that "participants" (and the people they effectively spread the "word" to) adhere to will likely have a negative impact on the human species' ability to survive. Rationalists are free to wander the landscape of ideas and turn their attention to many areas that the Catholic church (or any number of religious organizations) simply cannot find effective ways to engage, like the smaller investors above. In fact, it is precisely this rationalistic pressure on the Catholic church that has tamed it from the rather malevolent imperialistic beast it once was, to the more calculating and insidious beast it is today, only with a more friendly public-relations face.

On the other hand: better sanitation, and sources of clean water are probably the largest contributors to improving world health and longer lifetimes. Neither of these solutions to problems of human life came from religious organizations, and just possibly outrank the "output" of all religious organizations put together. The printing press and the "small" book did more for literacy and the development and spreading of ideas than any active effort by any European religion. The same could (should?0 be said for the Internet today. Could we come up with a better meaning for output?

The Least Convenient Possible World

Although I understand and appreciate your approach the particular examples do not represent particularly good ones:

1: Pascal's Wager:

For an atheist the least convenient possible world is one where testable, reproducible scientific evidence strongly suggests the existence of some "super-natural" (clearly no-longer super-natural) being that we might ascribe the moniker of God to. In such a world any "principled atheist" would believe what the verifiable scientific evidence support as probably true. "Atheists" who did not do that would be engaging in the exact same delusional thinking modern-day theists engage in: belief in "beings" despite the utter lack of evidence supporting the existence of such "beings" only in reverse, like flat-earthers.

2: The God-Shaped Hole:

The use of "Omega" here is a fair bit over the absurd line. It very much sounds like you wish to create the following situation for atheists: suppose there exists an oracle that can tell you that there is a "hole" in you and it's "God shaped", but cannot confirm the existence nor non-existence of the "God" that the hole is "shaped" like. Well, then my hole (being an atheist) is penguin shaped ;-).

It is clear that you want to create a world where some form of definitive information about some other "thing" is true while trying to maintain the "true" state of the existence or non-existence of that thing left undecided. Alas, your not allowed that degree of freedom. If definitive statements are made and accepted as true then the thing that the statement references also must exist in some meaningful way.

3: Extreme Altruism

Lots of leeway is left in your example to re-cast the moral dilemma, for example:

a. Charity X is, in fact, using the money you give it to feed people in Africa, but the population that is being helped lives in a fundamentally unsustainable environment. Suppose changes in weather patterns means that getting a meaningful sustained water supply requires considerable cost. In this case the charity itself is engaging in the morally wrong thing by not supporting efforts to relocate the people to a place that can sustain them better. Your analysis (not literally you, the "you" responding to pleas for money) leads you to extreme altruism. Others follow-suit creating an unsustainable dependant society. In the case of extreme charity you accidentally do harm: they're alive, but utterly dependant of the charity of others.

b. Turn the entire situation amoral: why should their lives there be of such an importance to affect me, in any way, here? I.E. why is this a moral consideration at all? In this context person a may choose to contribute to charity X not knowing if "in the large" a "good overall outcome" will result from such a donation, regardless of amount contributed. Another way of looking at it is if I consider increased happiness being an important element of "good morality" (dubious?) then is my personal depletion of resources and the "net" increase in happiness in the receiving population a net increase of happiness overall? And is that the "right" thing? By who's measure?

The above examples are not meant as a broad-stroke justification for a "let-em starve" thing. The issue simply concerns constraining the examples sufficiently to get the outcome you are looking for. To simplify matters this particular example is closely analogous to the trolley situation above: suppose the doctor offered to the patient with the good organs the option of donating all the organs to the patients in need, but as a result the patient would need to survive on uncomfortable synthetic replacements of his organs.

The Least Convenient Possible World

Formalize this a bit:

"I believe that X’s existence or non-existence can not be rigorously proven."

Where X is of the set of beings imagined by or could be imagined by humans, e.g.: God, Gnomes, Zeus, Wotan, Vishnu, unicorns, leprechauns, Flying Spaghetti Monster, etc. Why is any one of the statements that result from such substitutions more meaningful than any other?