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drnickbone comments on Welcome to Less Wrong! (5th thread, March 2013) - Less Wrong
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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.
I think if two loops were caused by each other, then there would be a super-loop which included all the elements from both of them, and then you could look for the cause of the super-loop. The Axiom of Choice would still be needed to show that this process stops somewhere.
Finally, I rather liked your thought that causality may be so loopy that everything is a cause of everything else. The only way to get a first cause out of that mess is to treat the entire "super-duper-loop" of all things as a single uncaused entity, and if you insist on calling that "God", you're a pantheist.
Let's consider loops A->B->C->A->B->C and D->E->F->D->E->F.
Let's say, further, that B is a cause of E and D is a cause of A. Then each loop has an external cause.
Then there are also a few other loops possible:
A->B->E->F->D->A->B->E->F->D (external cause: C) A->B->E->F->D->A->B->C->A->B->E->F->D... huh. That includes all of them, in a sort of double-loop with no external cause. I guess that would be the super-loop.
Better yet; no matter what causality looks like, you can still always combine everything into a single giant, uncaused entity. You don't need to assume away loops or infinite chains without external causes if you do that.
Well now, here's a devious approach, which would probably appeal to me if I ever needed to make a career as a philosopher of religion.
Let's suppose a theist wants to "prove" that God - by his favourite definition - exists. For instance he could define a type G, whereby an entity g is of type G if and only if g is omnipotent, omniscient, perfectly good and so on, and has all those characteristics essentially and necessarily. Something like that. Then the theist finds a set of premises P, with some intuitive support, such that P => There is an uncaused cause.
And then he adds one other premise "Every entity that is not of type G has a cause" into the recipe to form a new set P'. He cranks the handle, and then P' => There is an entity of type G. Job done!
Just in case someone accuses him of "begging the question" or "assuming what he set out to prove" he then pulls out the modal trick. He just claims that it is possible that P' is true. This leads to the conclusion that "It is possible that there is an entity of type G". And then, remembering he's defined G so it includes necessary existence (if such a being is possible at all, it must exist), he can still conclude "There is a being of type G". Job done even better!
Can I have the Templeton Prize now please?
Huh. That modal trick is devious. But it doesn't work. I can assume an entity that does something easily measurable (e.g. gives Christmas present to children worldwide), and then slap on a necessary existence clause; but that doesn't necessarily mean that I can expect Santa later this year.
I think the 'necessary existence' clause requires a better justification in orderto be Templeton-worthy.
The modal trick reminds me of Descarte's approach... God is definitionally perfectly good, which implies existence (since something good that doesn't exist isn't as good as something good that does), therefore God exists.
ZZZZzzzzzz....
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.