I don't understand why murder is bad, if not because God said so.

If you look more deeply at that claim you will find that the God of the Bible is quite fine with comitting genocide and murdering a lot of people via a flood when an almighty God might have done a lot of other things to treat those people who "misbehave" then comitting genocide. 

If you believe in heaven and hell, then allowing souls to be tortured for an eternity would be according to my personal morality be morally wrong. 

If you think that only things that good says bad are bad, then allowing eternal torture or genocide is morally okay. Ask your gut level whether eternal torture and genocide are morally okay. 

I would expect your gut level to come back with "eternal torture and genocide aren't morally okay". If that's your gut level position then morality according to your gut level has to be something besides "Whatever God declares to be moral is moral". 

Just read the First Testament and ask yourself whenever God does something "Is this morally okay?" if your gut level considers some of those things not morally okay, then morality means something else for your gut level. 

It isn't clear from your post how the existence of God relates to the world being moral. It could be:

1. God decides what is moral, and only god's decisions on the matter count, either because of some inherent property of divinity or your definition of morality or because of consequences God imposes
2. God has no choice in what is or isn't moral, god's nature or the definition of morality predetermine that, but god somehow makes it real, or meaningful, or existent in the world
3. God created a world in accordance with whatever morality is, and a non-god-created world wouldn't have been , and so would be vanishingly unlikely to have moral value

I've mostly come across the first line of thinking in the past, not exclusively, but enough that I'll assume it here. Let's try a least-convenient-possible-world thought experiment. As you requested, let's assume there exists exactly one God. This weekend, a joyful chorus rings out from the sky, and a beam of light shines down onto each and every human, young and old, and an angel appears before each of us and pronounces that God wants to reveal the true divine commandments to the people of Earth, which we have forgotten. (If you want to add more conditions to make the evidence more convincing that this experience is genuine and not aliens or delusions or drugs or something, be my guest). Actually, God says, the Aztecs were the people that originally received the true revelation, the world was made through divine sacrifice, human sacrifice is needed to pay the debt, and we have a lot of accrued debt we haven't been paying off, so make with the pyramid-building and heart-removing and live-flaying.  God gives no details on the afterlife, if any, or on what happens if we fail to carry out these orders.

What's your next move?

If you believe such a scenario is impossible, that God couldn't do such a thing, then God lacks the freedom to choose the moral law. How, then, could that law depend on God's existence?

If you believe God simply wouldn't do such a thing, why not? I don't know of any religion whose gods don't demand some form of unpleasant sacrifice from their followers, so what precludes this one, given that God has freedom of choice?

If you experienced this and did believe God had made such a revelation, and so did everyone else, would you obey? Would you expect and want others to obey? Is that the world you want to live in? 

My own opinion is that in this world, I would have a moral duty to defy this order, and if possible, overthrow and replace God, because this one isn't worthy of my worship or obedience. But I can only say that because I reject the premise that whatever is moral has no dependance on what any particular God wants.

You could consider morality to be like money or artistic beauty. There are no money particles. There are metal circles and plastic rectangles. But the concept of money as a means of transaction is something that exists in peoples heads. Money shapes the world by affecting what people do. Changing when they pick up and use objects. Causing people to do work they otherwise wouldn't. Such abstract and powerful forces can greatly shape the world. Little metal circles just sit there being little metal circles. That too is the force morality has in this world. All those people who consider morality and choose to do the right thing. There is light in this world, and it is us.

Different people have different preferences in paintings. Imagine you are programming a computer to calculate artistic beauty. Imagine coding a function func1(person, picture). This function takes as inputs a detailed brain scan of a person, and a particular picture. It calculates how much the person would enjoy looking at the picture. You can use this to define func2(picture)=func1(Bob,picture) . It happens that Bob has a rather simple taste in pictures. Bob likes red and symmetrical pictures. So we code func3(picture). This function just measures redness and symmetricalnes. It makes no reference to Bob. func2 calculates Bob's thoughts, it reasons about how bob will think. And yet both functions produce the same answers. 

Morality is similar. We can define moral1( person, situation) which measures how moral a particular person thinks a particular situation is.  A large value for moral1( Alice, situation) means that Alice actually feels motivated towards the situation and tries to cause it to happen. 

Now suppose that Eve is just evil. moral1( Alice, situation) might be wildly different from moral1( Eve, situation). But both Alice and Eve can (assuming both were knowledgable)  calculate both of these functions. When Bob looks at a picture, they aren't reasoning about their own reasoning, they are just thinking about how wonderfully red it is, the function within his mind is func3. When Alice looks at a situation, they aren't thinking about their own thinking either (in general) they are looking at all the cute bunnies and thinking how fluffy they are. 

So is morality subjective or objective? That depends on how you define your words. By morality, do you mean the equivalents of func1, func2 or func3? (Possibly with yourself or the average human in place of Bob?)This is just a question of definitions. 

On to how you should think and act. Imagine god gave you the complete and unambiguous guide to morality. Totally complete, totally superseding all previous instructions. Can you imagine being disappointed in this guide? Feeling that it wasn't as nice as it could be. Or perhaps horrified as god orders a human sacrifice? Can you imagine good news instead. That the guide to morality was everything you hoped it would be. What if you could somehow write the guide to morality, what would you write? Why not just do that. It is, after all, your choice. 

You can if you want delegate. You can fully acknowledge that god is fictional, and try to work out what god would want if he did exist, and do that. You could try to work out what Harry Potter would do if he did exist, and do that. Even if god does exist, its your choice whether to follow his instructions or to do something else. You could go with what feels right, your instinctive sense of niceness. You could calculate, weighing up lives with statistics to choose the greatest good. You could delegate to a hypothetical version of yourself who was smarter and kinder, and try to figure out what they would do. 

While it is your choice, choosing is in itself a process. Your choices are shaped by the kind of person you are. Which is itself shaped by the genes and words that lead to your existence as it is now. So in a sense, you are learning about the sort of person you are, a fact determined but not known to you. You must go through the process of choosing to learn this fact about yourself. It is your choice how you see the choice, you can see it as an onerous imposition of responsibility, or you can treat it lightly. A freedom from any external morality weighing you down. A feather that can drift in whatever direction their whims may take them. 

This is, I suspect, where your morality came from all along. Some would have come from deep within yourself. From the genes that specify the brain circuits of empathy. Some will come from the ethical advice of friends and neighbours. Some may come from the bible. The ink and paper of the bible is still there. You can use it as a source of ethical advice if you think it is good. I would recommend not using the bible as a source of ethical advice. Maybe look https://forum.effectivealtruism.org/ instead? But it is, after all, your choice. You can trust and rely on others, but it is your choice of who to trust. It always was. Even if the decision to trust was implicit and invisible. 

A thought experiment: Imagine that you are taking a hike away from civilization, and you meet some person. You start talking, the person is generally nice, but at some moment mentions having an Amalekite ancestry. You remember from your Bible studies that God wants you to kill all Amalekites. You are pretty sure that if you kill this person now, no one will see you (i.e. no risk of secular punishment). What would you do?

a) Kill the person, of course. It's fun, and there is nothing wrong about it! Remember, the only reason murder is generally considered wrong is because God forbids it... but in this specific case, God approves of killing Amalekites, so there is absolutely no reason not to do so.

b) Kill the person, because obeying God is the most important thing... but you will feel kinda bad about it and kinda wish that God didn't give you this command. (Later you realize that second-guessing God is also wrong, and then you will feel even worse.)

c) Not kill the person... and hope that merciful God will forgive you for this horrible act of disobedience.

d) Not kill the person, because you decide that God certainly didn't mean literal killing of literal Amalekites. It is known that killing people just because they belong to some ethnic group is a bad thing, and certainly God would not command a bad thing. Later you check with your priest who confirms that "killing Amalekites" is definitely just a metaphor for... well, no one really knows what, but certainly nothing important.

In my opinion, any answer other than (a) means that your gut already has a source of morality different from "because God said so".

I think you are pointing in the right direction when you say you understand that societies that discourage murder probably have better prospects than those that do. I'm far from well read in this topic but I think the basis of ethics/morality (in a general way, at least) is our evolution.

A collective with a feeling that murdering is bad will, in the long run, outlive a collective without that feeling. Keep that feeling for long enough and their society as a whole will rationalise it. Something similar can be said for, at least, many of our other moral preferences.

Societies which embed these "feelings" better in their norms will tend to outlive the other societies and, at the same time, will reinforce those feelings. In ancient times before proper justice institutions that could enforce these norms, religions were a good way to guard them. 

Thinking this way, morality is broadly the set of feelings we have that help a society (or pack, or family, etc) to thrive. We have them because we are descendents of the members of the societies with 1) more subjects having roughly these feelings and 2) which were better at reinforcing them (the feelings) culturally.

As side note, I am pretty convinced that incest and inter-family romantic relations will stop being morally wrong in the future (in a similar way that homosexual relations are not morally wrong any more). Incest being morally wrong makes sense when the purpose of having sex is reproduction, because it may lead to progeny with problems. However, sex and progeny are now pretty much decoupled. I don't see any reason why, if two members of the same family want to have a relation, they should not. And, indeed, I don't feel any moral reaction to that. It may take some time, as it is taking quite some time for humans to develop feelings for humanity as a whole (as opposed to in/out group thinking), but I think the process is running already.

Your answer is in your own question - "societies that discourage murder will probably fare better than societies that promote it. I don't understand why murder is bad".

Our sense of good and evil is shaped by what helped our ancestors survive in competition with other tribes. Societies with less murder - because of people who abhor murder - fared better, resulting in descendants who also abhor murder (us).

People who didn't abhor murder didn't form societies or formed societies that were less successful, leaving behind few descendants with those instincts. People mixed, societies formed and disbanded. Over time, people who instinctively and culturally abhorred murder relatively flourished, while those who didn't relatively diminished.

That's it - there's nothing more to the story than that. 

All our modern philosophy about good and evil and law is post-hoc justification, regularization, and exploitation of our instinctive disdain for murder (and other evils). Intellectuals among us try to extend our instincts and observations about what makes for successful societies (morals, ethics, law...) in a regular, predictable, and logical way, but have trouble coming up with tight, closed, well-argued positions that don't lead to perceived absurd consequences. Because the universe isn't necessarily compatible with our ideas of justice and morality.

First, congratulations on seeking out opposing points of view, I know it’s not easy.

A parable to answer your question: You are leaving a bar after a merry Saturday night and you see an attractive person of your preferred gender and you feel tempted to rape them. You don’t do it because there is a policeman on the street and you don’t want to go to jail. Is this a moral decision? I would say clearly not. It’s a pragmatic decision based on what will benefit you.

Now imagine the same situation but with no policeman. Instead you believe that God is watching you and you don’t want to go to hell, so you don’t commit the rape. Is this a moral decision? Still no. It’s exactly the same as the policeman example: you make a pragmatic decision to avoid punishment.

Now imagine that you are tempted to rape the attractive person but you choose not to do it because you understand that they are a fellow human being and they deserve to choose what happens to their own body and you understand that raping them will inflict horrible suffering on them. That is a moral decision, not a pragmatic decision. No God required.

Another way to make the point: imagine you were really sure there was no God. (If you can’t imagine this, imagine that the archangel Gabriel comes to tell you that God has made another bet with the devil, like in the Book of Job, and he guarantees that you will go to heaven no matter what you do on Earth.) Would you personally choose to murder, rape, steal, defraud etc? Or would you choose to behave decently to people anyway? If the latter, that implies you already have a personal morality separate from your desire to go to Heaven / avoid Hell.

Setting aside (for the moment) the question of whether the world actually is moral or not, how could adding God possibly help?

The notion that God's command is the source of morality is untenable due to the Euthyphro Dilemma: Is what is morally good commanded by God because it is morally good, or is it morally good because it is commanded by God? Both answers have problems.

If it's the former, then the good is a principle independent of God. Accepting that horn means we'd have to accept the possibility of the "godless moral world". We're done.

If it's the latter, then isn't what is "good" completely arbitrary? The good is whatever God decides it is at the moment. Think about what this means. If God decreed that something you considered evil now were good, then it would be so! God could command you to rape your children to death and eat them for breakfast. And this would be morally right, your feelings be damned! Not because of any other reason! Not because it served some greater utilitarian purpose; because God said so, full stop.

But then what possible bearing could your "gut-level" intuitions have on morality? To take the latter horn, you must give up your gut-level intuitions. You can't have them. And without them, why is your "moral" gut still an obstacle to thinking God couldn't exist?

Some have tried to thread the needle saying that it's the latter horn, but this isn't really arbitrary because the good is identical to God's nature. This doesn't help. It just pushes the question back a step:

Does God possess whatever "good" properties like loving-kindness, impartiality, and generosity (etc.) in his nature because they are good? Or are they good because God possesses them in his nature?

Again, if it's the former, good properties are independent of God. Accepting that horn means we'd have to accept the possibility of the "godless moral world". We're done.

If it's the latter, then it must be that if God exists, wherever humans express these good properties can be called good and if God does not exist, this exact same situation cannot be called good.

For example two humans' love for each other. This expression of love has the same basic motivations behind it, and the same effects on both parties if God exists or not. Is it morally intuitive on a "gut level" why the former case is good and the latter case isn't? Then why is your "moral" gut still an obstacle to thinking a moral world without God couldn't exist? Same problem.

Before I say anything else, a couple of quotes from Pratchett's Night Watch:

'You haven't killed your wife,' he said. 'Anywhere. There is nowhere, however huge the multiverse is, where Sam Vimes as he is now has murdered Lady Sybil. But the theory is quite clear. It says that if anything could happen without breaking any physical laws, it must happen. But it hasn't.[...]'

"He wanted to go home. He wanted it so much that he trembled at the thought. But if the price of that was selling good men to the night, if the price was filling those graves, if the price was not fighting with every trick he knew … then it was too high.

It wasn’t a decision he was making, he knew that. It happened far below the levels of the brain where decisions were made. It was something built in. There was no universe, anywhere, where a Sam Vimes would give in on this, because if he did then he wouldn’t be Sam Vimes, anymore."

And that, basically, is it. We are who we are, and our minds, our personalities, our very natures, our sense of morality and aesthetics... you cannot simply swap them out without changing who we are. 

Being human, and being you-in-particular, entails certain ways of looking at things; morality is part of that. Is morality part of reality, then? It's part of you, and you are part of reality.

"Immoral" interactions between people are mostly interactions that reduce the total pie. So groups that are best at suppressing such interactions within the group (while maybe still allowing harm to outsiders) end up with the biggest total pie - the nicest goods, the best weapons and so on. That's why all Earth is now ruled by governments that reduce murder far below hunter-gatherer level. That doesn't explain all niceness we see, but a big part of it, I think.

There are already many good answers in this thread but your question as stated can be answered very simply. First I ask if you can accept that I have within me “a morality.” I have beliefs about right and wrong, and a system for judging actions and outcomes; that’s probably all that’s required to qualify. So that’s one morality that exists, namely mine. It’s not a cosmic, all-pervading, True morality, but it’s a morality, and that’s what you asked for.

I don’t know if the following will appeal to the gut or not, but here goes: people only very rarely make decisions based on morality, or on expected utility, or on any kind of explicit basis for distinguishing the better choice. Most choices have no obvious moral dimension. The only times when someone invokes morality or utilitarianism is when two different parts of their mind want two different things and they need some kind of judgement call from the ref on which option will be more in alignment with all the stuff you want. The reason you don’t commit mass murder has nothing to do with morality. The reason you choose to reduce your meat consumption might have something to do with morality, or might not.

The reason I bring that up is that the existence or nonexistence of ultimate cosmic morality is probably not all that important, practically speaking. You won’t do things that you deeply feel are immoral for the same reason you won’t intentionally smash your hand with a hammer. If you find yourself frequently doing immoral things, you probably don’t really think they’re all that immoral, and/or “immoral” has become a dangerously meaningless symbol in your mind.

Some interesting responses here, and although I didn't read through all of them, I read enough to get a sense of the kind of approach most people seem to be taking here.

As someone who was where you are now about five years ago, I will share the way I think about it, especially since it seems quite distinct from the approach most people are taking here.

Short answer (and hot take for this crowd): it's not. The kind of morality I believed in as a Christian (an objective truth about things being Right and Wrong) is not possible without a god. 

The illusion of such a world, however, is very possible, and in fact predicted by some pretty prominent evolutionary psychology theories of behavior. If you have not read The Selfish Gene, I highly recommend it as Dawkins' treatment of this issue is the best I've heard and the (I'm pretty sure) origin of every other good explanation I've heard from elsewhere. 

In essence, the illusion of a world with an objective moral reality is the evolutionary response to the cooperation problem associated with repeated games where actors have the ability to hold a grudge: for any single game, the optimal strategy is to pursue the course which grants the maximum individual reward (the defect strategy in the prisoner's dilemma), but with repeated games in a population with the ability to hold a grudge, this strategy is out-competed by a "tit-for-tat with initial cooperation" strategy. Therefore, a person who is likely to cooperate with others trying to work toward the optimal group strategy, at least until betrayed, will outcompete someone who looks out only for himself. The tendency manifests as a general feeling of "the right way to do things" was the easiest evolutionary pathway toward achieving this tendency.

But why not have a sense of "pretend to cooperate until no one is looking, then do what's best for yourself"? Well for one, because then you wouldn't be righteously indignant and impassioned when you caught someone else following this strategy (important for the tit-for-tat part), but also because pretending involves lying. If the evolved strategy is to lie, then an expected co-evolution would be the ability to detect lies, a feedback loop would then result until a solution is developed so that a person can lie without realizing it himself so that he doesn't give himself away. This is in fact what we find when people passionately defend their behavior that to everyone else is blatant hypocrisy: they are self-deceived and therefore don't realize the inconsistency (this is also a large part of many of the fallacies discussed in the sequences). 

Let's test this against your (and some of the others posted here) example: murder. What we consider to be "murder" is usually undeserved killing, usually to benefit oneself. 
Does this improve the outcome for an individual game? Yes, you get to take what he has.
But what about repeated games, where other players can hold a grudge? No, the other villagers will gang up on you when they see what you have done. And when the other villagers execute you as a group, this is "justice", not "murder". Why? Because it solves the cooperation problem by disincentivizing potential murderers. (Incidentally, this is why it's so easy to come up with ethical dilemmas involving killing; because we pit two competing psychological solutions against each other: "don't kill" vs. "justice".)

How else to test this? Go through the commands the Bible, and do your best to answer "would I feel this way if I hadn't read this?" I predict that >90% of the ones for which you say "yes" can be shown to solve a cooperation problem found in the ancestral environment. (With lesser confidence, I predict that >50% of the ones for which you said "no" can be shown to have solved a cooperation problem found at the time of its writing.)

In retrospect, the alignment of psychology to the ancestral environment that the sequences demonstrated was one of the arguments which most strongly (downwardly) updated my belief in God. Why does the killing of a pre-pubescent seem so much worse than someone older? because the older person is a competitor, rather than a descendant/kin. Why does abortion seem so much worse the older the baby gets? because it is becoming increasingly viable. Why am I more emotionally motivated by the fate of those close to me than the fate of an entire neighboring city? because increased relatedness means more shared genes.

One final note: from a purely practical perspective, consider how much utility you are currently gaining from your beliefs. It may be too late to just choose to not pursue this to it's conclusion (it was for me), but consider the possibility that if you're wrong, knowing doesn't actually improve your utility. It was world-shattering for me to change my mind on this, and I honestly don't know what I would do if I had an "unknow" button.

A different way of going about this is to unpack what we mean by "god". We can ask about morality in worlds that contains something similar, something that is arguably "god" and arguably not. 

Polytheism. A whole bunch of gods that worked together to create the world. Between them they wrote the bible, koran and most other religious texts. 

A god matching all the typical descriptions, spaceless timeless creator of life and earth.. Responsible for all the bible and jesus stuff. This god is made out of particles behaving under physical laws. 

Perhaps this god is actually an alien that evolved billions of years ago, then used their advanced tech to travel to earth, create life and write the bible.

Maybe a ASI that is simulating the world as we know it. A team of human sociologists are instructing the AI, and told it to write some books and perform some miracles, to see how that effected society.

Stand off god. Spaceless timeless all knowing creator of the universe. Didn't write the bible, or even inspire it. Not related to Jesus in any way. Jesus was just a normal human skilled in magic tricks. This god isn't actually that interested in humans, they care more about pulsars, black holes etc.

Imagine you were in these worlds. Would the beings be what you called "god"? Well that's just a question of how you define words. Where would your morality come from in these worlds?

By “a moral world”, I mean that many actions or states are categorized as good or evil, and that this is a good measure to evaluate whether we should do these actions of reach these states, regardless of other measures such as expected utility or pleasure.

The last 10 words beg a lot of the question.

I would argue that living in a non-murdery society is good in terms of expected utility, and that breaking a social contract to avoid murder is bad, because breaking contracts is bad.

But you've ruled out that approach by fiat.

By "a moral world", I mean that many actions or states are categorized as good or evil, and that this is a good measure to evaluate whether we should do these actions of reach these states, regardless of other measures such as expected utility or pleasure.
For example, I can understand why societies that discourage murder will probably fare better than societies that promote it. I don't understand why murder is bad, if not because God said so.

So it seems like "moral world" doesn't mean world that is fundamentally moral, but rather, world in which things are good and bad, am I right?

Seems like most answers here don't try to answer this :P

I think it is conceptually similar to property rights. In the beginning, there is no fundamental fact of who own what. At first, it's a game of dibs. Animals squat on territory and defend it. It's a tooth-and-claw negotiation. Eventually, we end up with a highly systematized notion of property rights, which mostly avoids conflict. Who owns what is mostly a straightforward fact.

Indeed, "don't steal" is part of moral reality, so this is an example, not just an analogy.

We can easily extend this story to other parts of "natural law", for example, murder. A person's life is sort of their own property, and so, murder is similar to theft.

Thing like lying are a bit less analogous, but I claim that we can think of these things as the result of a complex distributed negotiation in the same way.

Skeptic: if ownership and morality are the result of a complex distributed negotiation, how can they be fundamental facts? Isn't my story contrary to that idea?

Me: A fact is just something that is true. Are you saying it's not true that (EG) I own my computer? This isn't such a strange state of affairs. An extreme materialist might say that only particles exist. But I think tables and chairs exist. Particles might be more "fundamental", but tables and chairs are real. A materialist might call tables and chairs social constructs, but this does not make them less real.

Skeptic: But you admit that property rights are the result of a complex negotiation. This suggests that the negotiation could have gone differently. Wouldn't that make morality different? How can we rely on morality, if it's arbitrary?

Me: We rely on facts that could have been different all the time. For example, I'm currently sitting in a chair which could have easily been placed in a different location. If that were the case, I could not be sitting here. So what is the objection, exactly?

Skeptic: But moral facts don't seem like that. They seem more like mathematical facts: 1+1 is necessarily 2.

Me: Well, just because our current beliefs about moral concepts are the result of a complex negotiation, doesn't mean morality is defined as the result of such a negotiation. We could be wrong about moral facts. We've changed our minds on such topics in the past, so, we could change our minds in the future.

Skeptic: Which is it, then? Are moral facts necessarily one way, or are they contingent?

Me: I don't have to make my mind up on that. I'm just trying to defend the idea that there are, indeed, moral facts.

Skeptic: I already believe that. I'm looking for an explanation of how there could be such a thing, if not because God said so.

Me: Well, I'm not 100% sure on that, but I think it's similar to looking for an explanation of tables and chairs. Which would be: it's nice to have flat surfaces to put things on. Similarly for morality: it's nice to have.

Skeptic: Using Aristotle's terminology, that's a final cause. I'm looking for a material cause, like how light is explained by photons. What do moral facts consist of?

Me: How very physical-reductionist.

Skeptic: Hardly. I think the material cause is God's word.

Me: If I say that killing is wrong, I think that fact consists of all the anguish felt by people when loved ones die, together with the fear of death, plus other negative consequences which would plague society if murder wasn't seen as wrong.

Skeptic: That seems very inspecific.

Me: If I had described what murder consists of, it would have been simpler. The material cause of tables and chairs is simply wood and nails (or, whatever it happens to be made of). That's simple because tables are an object. The material cause of a fact like "it's conventient to set things on tables" would be much more complex, consisting of facts about how center of balance works, the height of human hands, etc. Maybe I don't think facts have nice material causes like objects do.

Skeptic: I think the fact that something is good consists of God's word. I also think the good consists of God's word.

Me: I guess I think the good is just, like, all the good things in the world taken together.

Skeptic: Then how do you decide what's on that list?

Me: I still think the fact that something is good consists of all the positive consequences.

Skeptic: Doesn't that just go into an infinite regress?

Me: Not really? I think there's some stuff that's just good, and the rest is derived from that. Like how in physics, there's got to be some stuff at the beginning which just happened (IE, the big bang). But that's efficient cause. For material cause, I guess the analogue is that particles or strings or something just are, they aren't made by any further things.

Skeptic: But isn't it dissatisfying to have something that just is good, with no explanation?

Me: You won't let me have an infinite regress, and you also won't let me cut off an infinite regress? I could similarly ask you want "God's Word" is made of, and put you in a similar dilemma. You have to stop somewhere. Or go on forever. One of the two.

Skeptic: The difference is that I've explained "good" purely in terms of something else, where you've stopped short of that.

Me: I think that's a weird standard to apply here. Particles aren't explained in terms of something else. And your story will similarly have to stop somewhere, like with "God" or something.

Skeptic: Particles can be explained with equations.

Me: Particles don't consist of equations. You asked for "material cause" type explanation, not description. I think I could describe the good purely in terms of other things. Not easily, and not completely, but I think the holes would be due to my imperfect knowledge of the good, which seems like an acceptable excuse.

Skeptic: It sounds like such a description would be long and detailed. Sort of like asking for a description of particles, and getting a big list of things that happen in experiments, the current locations of specific particles, and so on. I want a simple explanation -- the sort of thing scientists demand.

Me: Well, scientific explanations aren't necessarily material causes. Material composition can be complex, agreed? My scientific explanation is the property rights thing.

Skeptic: That was supposed to be a scientific explanation?

Me: I have in mind evolutionary game theory.

Skeptic: Wait, you're saying morality is genetic, or something?

Me: Not biological evolution -- not necessarily. Although, certainly many species including humans have genes relating to territorial behavior. But, no, I'm saying that the math of game theory relates to the evolution of property rights and other facets of morality. I don't have the full equations, like physicists have for the standard model, but I think game theory would be the place to look. I'd recommend The Evolution of the Social Contract by Skyrms, which shows how some basic ideas like fairness can emerge. I am fairly confident that these ideas explain how these concepts got into human brains in actual historical terms, at least.

Skeptic: I don't know why you think that's plausible, but let's suppose that to be true. I'm still baffled why that would make them true, or make them real. Presumably, you think similar things explain how religions got into human brains, but you don't think those things are true and real.

Me: Humans suppose that something is "real" if it's a supposition which helps them explain the world. I think religions have been surpassed by better explanations. I don't think the same is true of morality. Hence, I still think morality is real.

Skeptic: I agree that humans have a tendency to suppose things when they help make sense of the world -- but that doesn't make those things real. It sounds like you think morality is a useful mass hallucination.

Me: I wouldn't disagree with that statement, but I further think it's real.

Skeptic: Because you're going along with what you see as a useful mass hallucination.

Me: Not just that. As a general principle, it doesn't make sense to discard an idea that helps you make sense of the world, until you've found a better idea which makes more sense.

Skeptic: But this isn't like tables and chairs. It's not made of anything. It doesn't exist anywhere. 

Me: It's a bit more like 1+1=2. It makes sense to postulate numbers, because they help me make sense of the world.

Skeptic: But numbers don't physically exist. They're mental constructs.

Me: I thought you weren't a materialist?

Skeptic: I thought you were.

Me: I think numbers exist in the same way other things exist. To be honest, I believe in tables and chairs, and that's already a pretty big departure from extreme physical reductionism. Numbers are a mental construct the same way tables and chairs are. That is: they're not. The mental construct describes numbers. The numbers themselves exist independently of the minds.

Skeptic: That's quite a statement.

Me: It's about what "exists" is supposed to mean. Do you want to hand over "exists" purely to physicists, and place other things, like tables and chairs, into a grey zone of "sort of exists for everyday purposes, but actually, when we're talking seriously, only physical particles and such exist"?

Skeptic: Obviously not.

Me: So don't be so reductionist. Tables and chairs exist without a simple scientific description. So morality can, too. I think there may be a good theory of morality, but I don't have to believe that in order to believe in moral facts. Why do you have to reduce morality to God's word? Don't get me wrong, reductionism is great. You should reduce things to parts if you can. But that doesn't mean things don't exist if you can't. 

This isn't quite relevant, but I'm curious what you think of Beyond the Reach of God, and it seems a little related.

Scott Alexander ... claimed that many theists would change their mind if you could convince them on a gut-level that there could exist a godless moral world.

I guess I, and apatheists in general, are exceptions to this prediction, for while I personally am a theistic apatheist -- and of the polytheist variety at that --, I don't believe morality depends on divine will, be it either that of an absolute god, or that of a pantheon of gods. Reality, as I understand it, is essentially amoral, with morals being features we mortals add to it. Hence, my view is essentially similar to that of a godless moral world, except it has gods in it (or, more precisely, transcendent to it).

I would be grateful if someone could give me not only reasons why and how there can be a morality without God, but also arguments that could speak to my gut-level.

An usual approach is to find morality as a distillation from natural impulses filtered through high level cognition.

Dr. Larry Arnhardt, author of a number of books merging classic philosophy, classic liberalism, and evolutionary biology, identify 20 natural desires in human nature, all evolved through natural selection, which determine how humans interact with the world. Each one of those can be thought of a different axis along which uses and customs (a.k.a mores, from which "morals" and "morality") develop; then are reasoned about, leading to the development of formal moral codes, to different ethical system, and to meta-ethical frameworks, through so many abstraction layers.

Different individuals hierarchize those desires differently, and different societies also have their own hierarchies for them, their members aligning or not with their societies' hierarchy. One of those desires is "religious understanding", so it isn't really surprising that so many societies, and individuals, seek to interpret the entire set of desires, the uses and customs surrounding each one, and their corresponding abstractions, in terms of, and as part of, a religious understanding, which is, I venture, where the notion of morality sourced in divine design finds its root.

Notice, on the other hand, that "intellectual understanding" is also an evolved desire, so it isn't surprising those who place it at the top of their hierarchy of desires will see things in non-religious terms. Or maybe, if both religious and intellectual understanding are at the top, from an intellectually-rich theological perspective.

In fact, we can notice the interplay between the 20 desires diversely hierarchized in the Christian Bible itself, as it provides not one, but at least four distinct moral codes:

1. The way God himself behaves as the basis of imitatio dei;
2. The commandments of God to the Hebrews;
3. The commandments of God to the Christians;
4. The way Christians are described acting in the afterlife.

There's some minimal overlapping between these four moral codes, but on the whole they oppose each other. And one can disagree and criticize them either from a moral perspective based on none of the four, or from one based on a subset of one of those complemented by reasons outside all four.

Hence, if morality were to be of divine origin, then either only the minimalist set of behaviors at the intersection of all customs of all human societies in all times and places counts as the one spark of divinity amidst humanity, or, conversely, the maximalist set of the entire multidimensional ethics-space comprised of the full 20 axes counts. Anything in between would seem, at best, arbitrary, leading to a discussion about which meta-ethical decision making process is of divine origin, and which isn't etc.

Myself, I have my own ethical framework, which is a combination of Virtue Ethics with a Consequentialism based not on utilitarian criteria, but on the preservation of information. Taking the four Biblical moral codes, it intersects with a subset of the commandments given to the Christians, but it certainly doesn't align with the other three. I wouldn't, however, assign my ethical code to any deity affirming it's authoritative because of that assigning. But if I met a deity who opposed and acted contrary to it I'd feel quite on my right to criticize that deity as immoral from the perspective of my own ethics, irrespective of it being divine or not, and not out of hubris, but because I really would think of them as acting immorally.

"I mean that many actions or states are categorized as good or evil," - you're using the passive voice here. Categorized by who? I can categorize things as good or evil. So can you. Do you mean to write into your definition of "moral world" that god must be the one doing the categorizing? If so, then you have defined your terms in such a way that there cannot be a "moral world" without a god, but also in a way where I at least don't particularly care for a moral world. If not, then you should think out who can do the categorizing and why.

"and that this is a good measure to evaluate whether we should do these actions of reach these states, regardless of other measures such as expected utility or pleasure." - this part of the sentence pretty much hides the entire issue inside the word "should". To my mind, we should do things precisely because they maximize expected utility.

The classic argument I have to point you at is called Euthyphro's Dilemma, and it goes like this. Are things moral because god categorizes them as good, or does god categorize them as good because they are moral? Which direction does the causality go in? 

Option #1 is to say that things are moral because god categorizes them as good. This is a logically coherent position, but also an enormous bullet to bite. It implies that god could have said "murder is good" just as easily as "murder is bad", and that would make it so. Which things are good or bad becomes completely arbitrary, a matter of god's random whims. It turns the statement "god is good" into a meaningless tautology. It implies that we can't worship god out of any kind of admiration, as the choices god made are no better than any other choices god could have made. Our only basis for worshiping god is fear of god's power.

Option #2 is to say that god categorizes things as good because they actually are good, by some standard other than god's say-so. This avoids all of the problems with option #1 described above. There is an actual standard of morality, outside of god, by which we can look at god's actions and evaluate them to be good. "God is good" is no longer a tautology, it is a meaningful claim, and a basis for worship. "Murder is bad" isn't just an arbitrary choice god made, god had to say that, because that is what this morality-outside-of-god says. But this option moves god into the role of a reporter of what is moral, rather than a chooser, a judge, not a legislature. It doesn't actually answer the question of why murder is bad, it just removes "because god said so" as an explanation. And if there is such a reason why murder is bad, then this opens up the possibility of humans knowing this standard of morality and applying it without going through god. It asserts that there can be a godless moral world, without explaining how.

The other answers out there for where morality comes from are basically consequentialism (which I think most here, including myself, favor), and deontology, and maybe virtue ethics, all of which you can look up and read about. I particularly recommend Sam Harris' The Moral Landscape.

Deontological ethics approaches morality from a non-utilitarian standpoint. It’s probably best if you read the Britannica article and report back with your impressions:

https://www.britannica.com/topic/deontological-ethics

This will depend on what you mean by "moral world". In my view morality is a property of the human brain, the universe itself doesn't have morality built into it apart from the fact that human brains are inside the universe. Do you mean something like a "Just World" where moral behaviour is rewarded and immoral behaviour is punished? 

As an argument for not requiring God, I'd say that in my experience immoral behaviour is its own punishment. Anger, hate, jealousy and all of those emotions are very unpleasant to feel, and they bias the brain away from kindness, joy and compassion, which are immensely more pleasurable (purely as a matter of feeling tone). Immoral acts themselves lead away from these positive brain states, and this causes a certain built-in justice to the world, no need for God, a world where immoral acts prevent you from experiencing the most pleasant and refined mind-states is Just on its own.

I think that the argument that morality can only exist with god depends on a logical fallacy.

The first step is to say that morality is defined as whatever god says. You then say that morality cannot exist without god, because the definition of morality is what god says.

Of course this argument is transparently meaningless. I could equally well say that morality is defined as whatever a monkey typing at a typewriter comes up with and make the same argument.

The fallacy only works because the word morality already has meaning. It means that gut feeling I have that something is good or bad. Then somebody comes along and uses that exact same word, but defines it differently - as what god says. Since they both happen to be reasonably well correlated I don't necessarily notice this switch. Then I'm convinced that morality is defined as what god says, and so there can't be morality without god.

If we were strict we would say: don't define what god does as moral. Make up a new word for it e.g. 'godral', and allow morality to keep it's classic meaning. At that point it becomes clear that we need to prove that 'godral' = 'moral', which is far from obvious.

The Euthyphro dilemma is a good search term to find a lot more on this topic.

I don't understand why murder needs to be bad, in a meaning different from 'bad for self/society'. I also don't understand how God or any entity saying anything will make murder 'bad' in a nonutilitarian meaning.