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I didn't mean that your initial beliefs should come out stronger. I meant that having updated for good arguments, and by incorporating them, your beliefs will be more complete, better thought-out, and more sustainable for the future.
Well, one example of such a thing might be the Simulation Argument, which I believe has been mentioned to you. It's an argument for the possible existence of something which might be called a "god" or "gods" (though that's usually inadvisable due to semantic baggage). Our view of what exists and what could exist certainly incorporates an understanding of the possibility that we're living in a simulation.
Theistic arguments per se, however, are generally bad.
The Simulation Argument is certainly quite an interesting one, since it was invented by an atheist (Nick Bostrom), and as far as I can tell is only taken remotely seriously by other atheists. Many of them (including me) think it is a rather better argument for some sort of "god" or "gods" than anything theists themselves ever came up with.
For other interesting quasi-theistic arguments invented by atheists, you might want to consider Tegmark's Level 4 multiverse. Since any "god" which is logically possible can be represented by some sort of mathematical structure, it exists somewhere within the Level 4 multiverse. David Lewis' modal realism has a similar feature.
All these arguments tend to produce massively polytheistic rather than monotheistic conclusions (and also they imply that Santa, the Tooth Fairy, Harry Potter and Captain Kirk exist somewhere or in some simulation or other).
If you want a fun monotheistic argument invented by atheists, try this one, which was published by Robert Meyer and attributed to Hilary Putnam. It's a clever use of the Axiom of Choice and Zorn's Lemma.
Isn't that just the First Cause argument, wrapped up in set-theory language?
Well yes, but it "addresses" one of the really basic responses to the First Cause argument, that there might - for all we know - be an infinite chain of causes of causes, extending infinitely far into the past. One of the premises of Meyer's argument is that any such chain itself has a cause (i.e. something supporting the whole chain). That cause might in turn have a cause and so on. However, by an application of Zorn's Lemma you can show that there must be an uncaused cause somewhere in the system.
If you don't assume the Axiom of Choice you don't have Zorn's Lemma, so the argument doesn't work. Conversely, if God exists, then - being omnipotent - he can pick one element from every non-empty set in any collection of sets, which is the Axiom of Choice. So God is logically equivalent to the Axiom of Choice,
All totally tongue-in-cheek and rather fun.
He also defines away the causal-loop, or time travel, response, leaving only the uncaused cause; and then arbitrarily defines any uncaused cause as God. It looks like a good argument on the surface, but when I look at it carefully it's not so great; it's basically defining away any possible disagreement.
I should also mention that it's not really a monotheistic argument. It only argues for the existence of at least one God. It doesn't argue for the non-existence of fifty million more.
It's reasonably fun as a tongue-in-cheek argument, but I wouldn't want to use it seriously.
Well I think premise 2 just assumes there aren't any causal loops, since if there were, the constructed relation <= would not be a partial order (let alone an inductive order).
There are probably ways of patching that if you want to explicitly consider loops. Consider that if A causes B cause C causes A, then there is some infinite sequence <C, B, A, C, B, A, C, B, A, ... > whereby every entry in the sequence is caused by the next entry in the sequence. So this looks a bit like an infinite descending chain.
The arguer could then tweak premise 2 so it states that any such generalised infinite chain (one allowing repeated elements) still has a lower bound (some strict cause outside the whole chain) and apply an adapted version of Zorn's Lemma to still get an uncaused cause in the whole system.
The intuition being used there is still that any infinite sequence of causes of causes must have some explanation for why the whole sequence exists at all. For instance if there is an infinite sequence of horses, each of which arises from parent horses, we still want an explanation for why there are any horses at all (and not unicorns, say). Even if a pregnant horse if sent back in time to become the ancestor of all horses, then again we still want an explanation for why there are any horses at all.
The weakness of the intuition is that the "explanation" in such a weird case might well not be a causal one, so maybe there is no further cause outside the chain, or loop. (But even then, there is a patch: the arguer could claim that the whole chain or loop should count as a combined "entity" with no cause, ie there is still some sort of uncaused cause in the system).
I agree with you that the really weak part is just defining the uncaused cause to be "God". Apart from confusing people, why do that?
And thanks for spotting the non-uniqueness by the way... the argument as it stands does allow for multiple uncaused causes. To patch that, the arguer could perhaps define a super-entity which contains all these uncaused causes as its "parts". Or else add an additional "common cause" premise, whereby for any two entities a, b, either a is a cause of b, or b is a cause of a, or there is some c which is a cause of both of them.
That's just assuming the result you want. I don't think it makes a strong argument.
Counting a loop as a combined entity, on the other hand, could be very useful. The combined-entity loop would be caused by everything that causes any element in the loop, and would cause anything that is caused by any element in the loop. Do this to all loops, and the end result will be to eliminate loops (at the cost of having a few extremely complex entities).
This seems fine as long as there are only a few, causally independent loops. However, if there are multiple loops that affect each other (e.g. something in loop A causes something in loop B, and something in loop B causes something in loop A) then this simply results in a different set of loops. These loops, of course, can also be combined into a single entity; but if the causality graph is sufficiently well connected, and if there is a large enough loop, the end result of this process might be that all entities end up folding into one giant super-entity, containing and consisting of everything that ever happens.
I have heard the theory before that the universe is a part of God, backed by a different argument.
It honestly looks like a case of writing down the conclusion at the bottom of the page and then back-filling the reasoning. He can't justify that part, so he defines it quickly and hopes no-one pays too much attention to that line.
Why do you want to patch that? A quick patch looks like (again) writing the conclusion first and then filling in the reasoning afterwards.
OK, I think we both agree this is not at all a strong argument, that the bottom line is being written first, and then the premises are being chosen to get to that bottom line and so on. However, I still think it is fun to examine and play with the argument structure.
Basically, what we have here is a recipe:
Take some intuitions.
Encode them in some formal premises.
Stir with some fancy set theory.
Extract the desired conclusion : namely that there is an "uncaused cause"
It's certainly interesting to see how weak you can make the ingredients (in step 1) before the recipe fails. Also, the process of then translating them into premises (step 2) looks interesting, as at least it helps decide whether the intuitions were even coherent in the first place. Finally, if the desired conclusion wasn't quite strong enough for the arguer's taste (hmm, missing that true monotheistic kick), it's fun to work out what extra ingredient should be inserted in to the mix (let's put in a bit of paprika)
That's basically where I'm coming from in all this..
Ah... I think I get it. You want to play with intuitions, and see which premises would have to be proved in order to end up with monotheism via set theory.
I don't think it would be possible to get around the point of defining God in terms of set theory. Once you have a definition, you can see if it turns up; if God is not defined, then you don't know what you're looking for. Looked at from that point of view, the definition of God as a first cause is probably one of the better options.
Loops can still be a problem...
This can still fail in the case where two loops have their external causes in each other. (I think. Or would that simply translate into an alternate set of loops? ...I think I could figure out a set of looped entities, such that each loop has at lest one cause outside that loop, that has no first cause).
Either of those would be sufficient; though the first seems to fit more possible sets.
And here I always thought God corresponded to an inaccessible cardinal axiom.
On reflection, the fact that an atheist would be able to come up with an argument for a god that's more persuasive to atheists is unsurprising, especially when you consider the fact that most religious people don't become religious via being persuaded by arguments. It's definitely still amusing, though.
I'm definitely aware of Tegmark's theory, though I admit I hadn't considered it as an argument for any kind of theism. That seems like an awfully parochial and boring application of the ultimate ensemble, although you're right that it can have that sort of application... although, if we define "supernatural" entities to mean "ontologically basic mental entities" a la Richard Carrier, would it really be the case that Tegmark's multiverse implies the existence of such? I'm not sure it does.
Meyer's argument begins with premises that are hilariously absurd. Defining entities as being able to be causes of themselves? Having "entities" even able to be "causes"? What? And all this without the slightest discussion of what kinds of things an "entity" can even be, or what it means to "exist"? No, this is nonsense.
I think this is mostly a presentational issue. The purpose of the argument was to construct a non-strict partial order "<=" out of the causal relation, and that requires x<=x. This is just to enable the application of Zorn's Lemma.
To avoid the hilarity of things being causes of themselves, we could easily adjust the definition of <= so that "x<=y" if and only if "x=y or x is a cause of y". Or the argument could be presented using a strict partial order <, under which nothing will be a cause of itself. The argument doesn't need to analyse "entity" or "exists" since such an analysis is inessential to the premises.
And finally, please remember that the whole thing was not meant to be taken seriously; though rather amusingly, Alexander Pruss (whose site I linked to) apparently has been treating it as a serious argument. Oh dear.
FWIW, the probability I place on the Simulation Argument being true is only a little higher than the probability I place on traditional theistic gods existing. Could be just me, though.
What are the values for these probabilities and how have you estimated them?
Both of the values are somewhere around epsilon.
God-wise, I've never seen any evidence for anything remotely supernatural, and plenty of evidence for natural things. I know that throughout human history, many phenomena traditionally attributed to gods (f.ex. lightning) have later been demonstrated to occur by natural means; the reverse has never happened. These facts, combined with the internal (as well as mutual) inconsistencies inherent in most major religions, serve to drive the probability down into negligibility.
As for the Simulation Argument, once again, I've never seen any evidence of it, or any Matrix Lords, etc. Until I do, it's simply not parsimonious for me to behave as though the argument was true. However, unlike some forms of theism, the Simulation Argument is at least internally consistent. In additions, I've seen computers before and I know how they can be used to run simulations, which constitutes a small amount of circumstantial evidence toward the Argument.
EDIT: I should mention that the prior for both claims is already very low, due to their complexity.
Epsilon is not a number, it's a cop-out. Unless you put a number you are reasonably confident in on your prior, how would you update it in light of potential new evidence?
Well, so far, I have received zero evidence for the existence of either gods or Matrix Lords. This leaves me with, at best, just the original prior. I said "at best", because some of the observations I'd received could be interpreted as weak evidence against gods (or Matrix Lords), but I'm willing to ignore that for now.
If I'm using some measure of algorithmic complexity for the prior, what values should I arrive at ? Both the gods and the Matrix Lords are intelligent in some general way, which is already pretty complex; probably as complex as we humans are, at the very least. Both of them are supremely powerful, which translates into more complexity. In case of the Matrix Lords, their hardware ought to more complex than our entire Universe (or possibly Multiverse). Some flavors of gods are infinitely powerful, whereas others are "merely" on par with the Matrix Lords.
I could keep listing properties here, but hopefully this is enough for you to decide whether I'm on the right track. Given even the basics that I'd listed above, I find myself hard-pressed to come up with anything other than "epsilon" for my prior.
Well, traditional theistic gods tend to be incoherent as well as improbable. (Or one might say, improbable only to the extent that they are coherent, which is not very much.) So, I'm not sure how we'd integrate that into a probability estimate.
Agreed; but this doesn't apply to lesser gods such as Zeus or Odin or whomever.
That is what many people here have done regarding theism. Seen the best arguments, and decided that they fail utterly. Eliezer quoted above talks about Modern Orthodox Judaism allowing doubt as a ritual, but not doubt as a practice leading to a result. You would have us listen to arguments as ritual, but not actually come to a conclusion that some of them are wrong.