God is not a source of objective moral truth

I mean, right?

I’ve been listening to various youtubers, as mentioned forgetfully in at least two posts, and some of them spend considerable time responding to various Theist, and mostly Christian, Apologists and so on.

This is getting pretty old, to be honest, but one of the arguments that goes by now and then from the apologists is that atheists have no objective basis for moral statements; without God, the argument goes, atheists can’t say that torturing puppies or whatever is objectively bad. Implicit, and generally unexamined, is a corresponding claim that theists have a source of objective moral statements, that source being God.

But this latter claim is wrong.

What is an objective truth? That is a question that tomes can be, and have been, written about, but for now: in general an objective truth is a true statement that, once we’re clear on the meanings of the words, is true or false. A statement on which there is a fact of the matter. If Ben and I can agree on what an apple is, which bowl we’re talking about, what it means to be in the bowl, and so on, sufficient to the situation, then “there are three apples in the bowl” is objectively true, if it is. If Ben insists that there are six apples in the bowl, and we can discover that for some odd reason Ben uses “an apple” to refer to what we would think of as half an apple, we have no objective disagreement.

What is a moral truth? Again, tomes, but for now: a moral truth is (inter alia) one that provides a moral reason for action. A typical moral truth is “You should do X” for some value of X. In fact we can say that that (along with, say, “You should not do X“) is the only moral truth. No other fact or statement has moral bearing, unless it leads to a conclusion about what one should do.

(We will take as read the distinction between conditional and categorical imperatives, at least for now; we’re talking about the categorical imperative, or probably equally well about the “If you want to be a good person, you should X” conditional one.)

What would an objective moral truth look like, and where would it come from? We would have to be able to get to a fact of the matter about “You should do X” from things about which there are facts of the matter, modulo word meanings. The theist is almost certainly thinking that the argument is simple and looks like:

• You should do what God wants,
• God wants you to do X,
• You should do X.

Since we’re talking about whether the theist’s argument works, we stipulate that God exists and wants you (me, us, etc.) to do X for some X. And if we should do what God wants, we should therefore do X.

But is it objectively true that we should do what God wants?

If I disagree, and say that I don’t think we should do what God wants, the theist can claim that we differ on the meanings of words, and that what they mean by “should do” is just “God wants you to do”. But that’s not very interesting; under those definitions it’s just a tautology, and “you should do X” turns out not to be a moral truth, since “should do X” may no longer be motivating.

To get further, the theist will have to claim that “God wants you to do X” implies “You should do X” in the moral sense of “should”; that it’s objectively motivating. And it’s not clear how that would work, how that claim is any stronger than any other. A utilitarian can equally say “X leads to the greatest good for the greatest number” is objectively motivating, a rule-utilitarian can say that “X follows the utility-maximizing feasible rules” is objectively motivating, and so on.

(“You should do X because God will punish you if you don’t” can be seen as objectively motivating, but not for moral reasons; that’s just wanting to avoid punishment, so not relevant here.)

Why would someone think that “You should do what God wants you to do” is any more objectively true than “You should do what maximizes utility” or “You should do what protects your family’s honor”? I don’t find myself with anything useful to say about that; because they grew up hearing it, or they’ve heard it in Church every Sunday or whatever, I suppose?

So that’s that. See title. :) Really we probably could have stopped at the first sentence.

How about that Kalam argument?

While we’re talking about philosophical arguments for the existence of God, we should apparently consider the so-called Kalam argument.

In its simplest form it’s nice and short:

1. Whatever begins to exist has a cause of its beginning.
2. The universe began to exist.
3. Therefore, the universe has a cause to its beginning.

This is, obviously, an argument for the existence of God, only if God is defined as “A cause of the beginning of the universe” and nothing further, which doesn’t seem all that significant, but still. There are further associated arguments attempting to extend the proof more in the direction of a traditional (i.e. Christian) God, being “personal” and all, but let’s look at the simple version for now.

I think it’s relatively straightforward that the conclusion (3) follows from the premises (1) and (2), so that narrows it down. Now, are (1) and (2) true?

First we should figure out what we mean by “the universe”, because that matters a lot here. Three possible definitions occur immediately, in increasing size order:

(U1) All of the matter and energy that’s around, or has been around as far back in time as we can currently theorize with any plausibility. All of the output of the Big Bang, more or less.

(U2) Anything transitively causally connected in any way to anything in U1. Everything in the transitive closure of past and future light-cones of me sitting here typing this (which is, at least arguably, the same as everything in the transitive closure of past and future light-cones of you standing there reading this).

(U3) Anything in any of the disjoint transitively-causally-connected sets of things that are picked out in the same way that U2 is, starting from different seed points that aren’t transitively-causally-connected. The “multiverse”, if you will, consisting of all those things that aren’t logically (or otherwise) impossible.

It’s interesting to note here that “the universe” as used in the Kalam can be at most U1. This is because nothing outside of U2 can be causally connected to, can create or cause or otherwise have any effect at all on, anything in U2. Anything that claims to be a cause of U2 or U3 is either not actually a cause, or is part of U2 or U3 by virtual of being causally connected to it.

This works, I think, via (2) in the argument above; U1 might plausibly be said to have begun to exist, but it’s hard to see how U2 or U3 could.

Or, I dunno, is that true? We can certainly imagine U2, that is, this universe right here, somewhat broadly construed but still undeniably this one, did just start up at some time T0. That it could, I suppose, turn out to be a fact that at all times T >= T0 there are some facts to write down about this universe, but at times T < T0 there simply aren’t.

The reaction of Kalam proponents to that suggestion seems to be just incredulity, but in general I don’t see anything wrong with the idea; a universe simply coming into being doesn’t seem logically contradictory in any way. We can certainly write down equations and state transitions that have a notion of time, and that have well-defined states only at and after a particular time; it’s not hard.

So I guess, even if the Kalam must mean U1 by “universe” even in its first premise, (1), there’s no strong reason to think that (1) is true even then. This universe right here, this collection of matter and energy, could have just sprung into existence eight billion years ago or whatever, without any particular cause. Why not?

Premise (2) is less ambitious, and therefore more plausible. Did this particular batch of matter and energy, U1, begin to exist at some time? Could be. I mean, I can’t prove it or anything, and neither can anyone else, but I might be willing to stipulate it for the sake of argument.

(Even U2 might have, although the Kalam proponent probably has to disagree with that: since they want to have a backwards-eternal God creating U1, that means that that God counts as part of U2, which means that U2 is backwards-eternal, and never came into being. So the Kalam folks are still stuck with U1.)

U3 has the interesting property that it doesn’t have a common clock, even to the limited relativistic extent that U1 and U2 have common clocks. Since U3 contains disjoint sections that have no causal connections to each other, it’s not really meaningful to speak of the state of U3 at “a” time, so referring to it beginning to exist (i.e. at “a” time) turns out not to really mean anything. I think that’s neat. :)

If we’re willing to stipulate (1) and (2) as long as “the universe” means only U1, the conclusion isn’t very powerful; we find out only that this particular batch of matter / energy that existed shortly after the Big Bang (or equivalent) must have been caused by something. And fine, maybe it was, but if it was that something was just some earlier and likely quite ordinary piece of U2. Calling that “God” just because it happens to be so long ago that we can’t theorize about it very well seems very far removed from what “God” is usually supposed to mean.

I’ve read various things on the Kalam argument, including the Craig piece linked above, and the counterarguments both don’t seem to actually understand physics and cosmology very well, and are mostly of the “proof by incredulity” variety; Craig writes, for instance,

To claim that something can come into being from nothing is worse than magic. When a magician pulls a rabbit out of a hat, at least you’ve got the magician, not to mention the hat! But if you deny premise (1′), you’ve got to think that the whole universe just appeared at some point in the past for no reason whatsoever. But nobody sincerely believes that things, say, a horse or an Eskimo village, can just pop into being without a cause.

— William Lane Craig

“Worse than magic” is hardly a logical argument, it’s just ridicule. And to state as a raw fact that no one seriously believes the argument one is attacking is, again, content-free. (The bit about Eskimo villages is a silly evasion; what may have come from nothing is for instance an unimaginably hot and dense ball of energy, not a horse. But even for a horse, expressing incredulity that one might appear spontaneously is not a logical argument; more work is required!)

This reminds me of the rather popular fundamentalist Christian statement that everyone knows deep down that God exists, and atheists are simply in denial. This is of course false and silly.

This also reminds me, now that I think of it, of an excellent lecture that I saw the other week, “God is not a Good Theory“. Among other things, the speaker here makes a similar move to my positing a universe that simply springs into being and seeing no contradiction in it; he describes various simple universes and shows that they can be explained perfectly well with no reference to any external God. “All I need to do is invent a universe that God does not play a role in” (a bit before the 10 minute mark). He also talks about the issue of causes with respect to the universe, and briefly mentions the Kalam. Definitely worth a listen.

On the Kalam in general, then, I find it extremely non-compelling. It doesn’t even have a sort of verbal paradox in it to have fun with, the way the Ontological argument does; it’s just weak. So I do wonder why it’s so popular. Thoughts in the comments are most welcome.

Why the Ontological Argument doesn’t work

Back in the Rocket Car posting, we (following ol’ Gaunilo) showed, via a kind of reductio ad absurdum, that the Ontological Argument for the Existence of God doesn’t work (unless I have a really cool rocket car in my basement, which does not appear to be true).

Reductio arguments of this kind can be a little unsatisfying, because they just show that a thing is false, by showing that it being true would imply other things being true that we aren’t prepared to say are true. But they don’t tell us how the thing is false; in this case, the lack of a Z2500 Rocket Car in my basement doesn’t tell us how the argument fails, only that it fails.

But the other day, somewhere, I saw hints of an old refutation of the Ontological Argument that showed where it went wrong. I only glimpsed a few words of it, while looking for something else, and then forgot where or what it was, but a while later my brain said, “Hey look, I bet this is what that argument was saying!”, so here is that subconscious reconstruction. If anyone knows who made this argument, or an argument like it, anciently, do let me know!

Conversationally, the Ontological Argument goes something like:

A: Let’s define ‘God’ as that entity which has all perfections.

B: Okay.

A: Now, existence is a perfection, therefore since God has all perfections, God has existence, ergo God exists.

B: Wow!

The present argument against the argument changes the conversation, by having B point out problems in the underlying frame:

A: Let’s define ‘God’ as that entity which has all perfections.

B: We should be careful here, since there might not be any such entity. Let’s say instead that ‘God’ is defined as that entity which, if it exists, has all perfections.

A: Why do we have to do that? I can define ‘Humpty’ as a square circle, and that definition holds even though there are no square circles

B: Not really. If we define Humpty simply as a square circle, then if someone says “there are no square circles,” we can reply “sure there is; there is Humpty!”, and that’s wrong. It’s better to say that, strictly speaking, Humpty is a thing that, if it exists, is both a square and a circle. If it doesn’t exist, then of course it’s neither a square nor a circle, so we can hardly define it that way.

A: Hm, Oh. Well, if we define ‘God’ as something which … I guess … has all perfections if it exists, and then note that existence is a perfection —

B: We can conclude that God exists, if it exists! Much like everything else, really. :)

A: Wait, no…

The underlying observation here is that, strictly speaking, when we define or imagine something, we are defining or imagining the properties that that thing would have if it existed. If it doesn’t exist, of course, it has no properties at all. So when we imagine a seven-storey duck, we are imagining what one would be like if it existed. We aren’t imagining what it’s really like, because it doesn’t really exist at all, so it isn’t like anything; it isn’t a duck, doesn’t have seven storeys, and so on.

Therefore when we define God as having all perfections, we are actually saying that for any property which is a perfection, God would have that property if God exists.

And then the conclusion of the Ontological Argument will be just that God exists, if God exists; and that isn’t very interesting.

This isn’t an utterly formal (dis)proof, but I find it attractive.

Can even an omniscient, omnipotent God have certain knowledge?

Or even an omniscient, omnipotent, omnibenevolent one, if that isn’t a contradiction (it seems to me to be, but I’m not certain).

First, we should establish what we mean by “certainty” or “certain knowledge”. An initial (but wrong) attempt would be that a subject S knows a proposition P “with certainty”, or “certainly”, or “has certain knowledge of P”, if S knows that P, and P cannot be false, in the sense that it is necessarily true, or true in all possible worlds, or in general that ◻P in some relatively ordinary modal logic.

This is wrong, because it implies that all knowledge of necessary truths is certain knowledge. But that’s not the case; for instance I know that Khinchin’s theorem (the one with Khinchin’s constant in it) K, “for almost all real numbers x, the coefficients of the continued fraction expansion of x have a finite geometric mean that is independent of the value of x”, is true. But my knowledge is not at all certain; my only evidence for it being true is basically the Wikipedia page and a tweet, and that is far from sufficient for certainty.

One could describe all sorts of situations in which the theorem might be false and still be in Wikipedia and on Twitter: the known proofs of the theorem might have a subtle flaw, the whole thing could be an internet prank, etc. Now if the theorem is actually true, it’s necessarily true, so the worlds described by those situations aren’t possible worlds (in the rather strong sense of mathematical or logical possibility), but they are “for all that I know possible”, and that’s the relevant property here.

In my undergraduate thesis I called this superset of possible worlds “conceivable worlds”, and that seems like a good-enough term for this little essay. The basic idea is that S knows P (for reasons R) iff S believes P, and P is true in all reasonably nearby conceivable worlds in which S believes P for R. (“Reasonably nearby” isn’t directly relevant here yet, but you get the idea.)

Note that here I’m saying only that I can’t be certain that K is true. I can definitely know that it’s true, and I claim that I do know that; it’s an assumption in this discussion that knowledge doesn’t require certainty.

So, if it’s not enough for certainty that S knows P, and that P is true in all possible worlds, what does give certainty? Is it that S knows P, and P is true in all conceivable worlds? That seems plausible. Perhaps equivalently, the criteria could be that S knows P, and that S is not required, as a responsible epistemic agent, to entertain any suggestion that P might be false. S would be reasonable, to put it another way, to risk absolutely anything at all on the bet that P is true.

To say that we are never certain of anything (and I don’t think we are), is to say that it’s never responsible to completely ignore any possibility that any given belief is false. We can certainly ignore contrary evidence in some circumstances; if I get spam about exciting new evidence that the Earth is flat, I can go phht and ignore it, because there are so many false claims like that around, and comparatively little rides on the issue. But there are other circumstances where this would be irresponsible; if some being asks me to bet a dollar against the lives of every person in Maine, that the Earth is not flat, it would be irresponsible of me to accept. That is, perhaps equivalently, my Bayesian prior on the Earth being flat is not quite 100%; if it was, it would be irrational not to take that bet and win the dollar.

For simpler necessary truths, like “two plus two is four”, it seems that one might claim certainty. But would it be responsible to bet a dollar against 1.3 million human lives, on the assumption that one is not somehow mistaken, or has been hypnotized into using the wrong names for numbers, or something so peculiar that one hasn’t thought of it? I think it’s pretty clear that the answer is No; weird stuff happens all the time, and risking lives that there is no sufficiently weird stuff in this case isn’t warranted. So, basically, we can never be certain.

(Another possible reading of “S knows P with certainty” or “S is certain that P” would be something like “S knows that P for reasons R, and in every possible / conceivable world in which S knows P for R, R is true, and furthermore S knows those preceding things”. I think it’s relatively clear that the “something weird might still be going on” argument applies in this case as well, and since something really weird might be going on for all we know, and mere knowledge is not certainty, we also never have certainty under this modified definition.)

Having more or less established what certainty is, and that we ordinary mortals don’t have it, we can now ask whether an omniscient, omnipotent (and optionally omnibenevolent) being G can be certain of anything. At first blush is seems that the answer must be Yes, because being omnipotent G can do anything, and “being certain” is a thing. But this is also like “creating a boulder so heavy that G cannot lift it”, so we ought to think a bit more about how that would work.

G is omniscient, which we can safely take to mean that for all P, G believes P if and only if P is true. I think we can also safely grant that for all P, G knows P if and only if P is true. That is, for all and only true propositions P, G believes P, and in every reasonably nearby conceivable world in which G believes P, P is true. (Note that I’m mostly thinking these thoughts as I go along, and have just noticed that I have nothing in particular to say about the reasons R for which G believes P. We’ll see if we need to think about that as we proceed.)

Since G knows P, and G is omniscient, G also knows that G knows P, and so on. But can G be certain of one or more propositions P? Is God’s Bayesian prior 100% for all, or any, true propositions?

Just what is G’s evidence for any given P? How does God’s knowledge work? (Ah, apparently R is coming up almost immediately; that’s good!) G knows “I am omniscient,” so that’s a start. It seems that, given that, G could go from “I believe P” to “P” more or less directly. That feels rather like cheating, but let’s let G have it for the moment.

If G’s evidence for P is typically “I believe P” and “I am omniscient”, can G get certainty from that? We are often somewhat willing to grant “incorrigibility” to beliefs about one’s own beliefs, and while normally I’d say that only gets one to the level of knowledge, let’s stipulate for the moment that G can be certain “I believe P” for any P for which that’s true.

But what about “I am omniscient”? How does G know that? What is G’s evidence? Can they truly be certain of it?

There is a set of possible beings Q, each of which believes “I am omniscient”, but is mistaken about that. Some of them are quasi-omniscient, and know everything except for some one tiny unimportant detail D of their universe, of which they are unaware, and for the fact that they are not omnipotent due to not knowing D. They believe two false propositions: not-D, and “I am omniscient”. They also believe an infinite number of other false propositions, including those of the form “not-D and 3 > 2” and so on, and perhaps some that are more interesting (depending among other things on just what D is).

Other members of Q are simply deluded, and believe “I am omniscient” even though their knowledge of their universe is in fact extremely spotty, even less than the average human’s, and they have just acquired the belief “I am omniscient” through trauma or inattention or that sort of thing.

Now, how does G know, how is G certain, that G is not in the set Q? This seems like a hard question! For any reasoning that might lead G to believe that G is not in Q, it seems that we can imagine a member of Q who could reason in the same way, at least in broad outline. G can do various experiments to establish that a vast number of G’s beliefs are in fact true, but so can a member of Q. The quasi-omniscient in Q can do experiments not involving D, and the deluded in Q can do experiments but then be mistaken about or misinterpret the results, or unconsciously choose experiments which involve only members of their comparatively small set of true beliefs. G can follow various chains of logic that imply that G is not in Q, but so can many members of Q. The latter chains of logic are invalid, but how can G be certain that the former aren’t?

One conventional sort of being G is one that not only knows everything there is to know about the universe, but also created it in the first place, and in some cases resides outside of it, sub specie aeternitatis, observing it infallibly from the outside. Such a G has a comparatively easy time being omniscient, but can even this G be certain that they are? Again, we can look at various members of Q who also believe that they created the universe, exist outside of it able to see and comprehend it all at once, etc. They have, at least in broad terms, the same evidence for “I am omniscient” that G does, but they are mistaken. The quasi-omniscient created D by accident, perhaps, or created it and then forgot about it, and when looking in from the outside fail to notice it because it is behind a bush or equivalent. The deluded in Q are simply mistaken in more ordinary ways, stuck in a particular sort of psychedelic state, and so on. Those in Q who are in-between, are mistaken for in-between sorts of reasons.

There may be many ways that G can determine “I am not in Q” with relatively high reliability. One can imagine various checks that G can do to confirm “I am not like that” for various subsets of Q, and we can easily grant I think that G can come to know “I am not in Q” and “I am omniscient.” But the question remains of how G can become certain of either of those. It seems that any method will fall victim to some sort of circularity; even if G attempts to become certain of a P by exercising omnipotence, we can imagine a member of Q (or an enhanced Q-prime) who believes “I am omnipotent and have just exercised my omnipotence to become certain of P”, but who is mistaken about that. And then we can ask how G will determine “I am not like that” in a way that confers not merely belief or knowledge, but certainty.

We can imagine a skeptic’s conversation with G going from a discussion of G’s omniscience, to questions about the certainty of G’s knowledge of G’s omniscience, to questions about how G knows that G is not in some particular subset of Q, and ultimately to how G knows that G is not in some subset of Q that the discussants simply haven’t thought of, and to how G can be certain of that. It would seem that every “since I am omniscient, I know that there is no part of Q that we haven’t covered” can be called out as circular, and that “I know that I have certain knowledge of P” can always be countered by observing that knowledge does not imply certainty.

Another consideration (pointed out by a colleague who asked if I wasn’t anthropomorphizing God) is that I am assuming here that G forms beliefs and qualifies for certainty in roughly the same way(s) that we humans do. But shouldn’t we expect G’s ways of knowing and being certain to be very different from our mortal ways? Why should these human-based considerations apply to G at all? The response, again, is that members of Q, and in particular deluded human members of Q, could make exactly that same claim: that they come to know things with certainty through special means that aren’t accessible or understandable to mere humans, and to which none of this logic applies. And, again, if a deluded human member of Q could make this claim without in fact having certainty of anything, then G’s making this claim has no useful traction either, unless G can separately demonstrate not being in Q, which is exactly the point at issue.

To put it roughly and briefly, perhaps, the question comes down to how even G can be certain that G is not just a deeply deluded mortal human, who (in addition to lots of ignorance and false beliefs) is very good at self-deception. Even if G truly is omniscient, can G be certain of that? If so, how? Is it perhaps fundamental to the nature of knowledge and evidence, that no knowledge is ever certain knowledge? Is certainty, more or less by definition, a property that no knowledge can ever in fact have?

And is there anything more to this question than the perhaps rather casual and vaguely-defined (and/or perhaps very important) idea that however confident some being might be in their evidence for a belief, there might always be something weird going on?

That was fun!