Jaynes' perspective on the historical behaviour of biased coins would make no mention of probability - unless he was talking about the history of the expectations of some observer with partial information about the situation. Do you see anything wrong with that?

I see nothing wrong with that. Similarly, if someone mentions only the atoms in my body, and never mentions me, there is nothing wrong with that. However, I am also there.

What I have pointed out is that seemingly unproblematic statements can indeed be made of the sort that I described. That Jaynes himself makes no such statements says nothing one way or another about this. There are different possible responses, including:

1) It might be shown that certain classes of factual statements about history, including the one I gave, are in fact in some sense relative, may incorporate a tacit perspective and therefore may be in that sense subjective. An example of such a statement might be a statement that an object is "at rest" rather than "in motion". This statement tacitly presupposes a frame of reference, and so is in that sense not fully objective.

2) It might be shown that there was something wrong about the sort of statement that I gave as an example.

Not under the view we are discussing.

That was my point.

Probability isn't only used as an expression of a person's own subjective uncertainty when predicting the future. It is also used when making factual statements about the past. If a coin was flipped yesterday and came up heads 60% of the time, then it may have been a fair coin which happened to come up heads 60% of the time, or it may have been a trick, biased, coin, whose bias caused it to come up heads 60% of the time. To say that a coin is biased is to make a statement about probability. As Wikipedia explains:

In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin.

So a statement about probability can enter into a factual claim about the causes of past events.

There aren't necessarily any common elements, besides utterly trivial ones.

Maybe, maybe not. You won't know without looking. You have to start somewhere.

If you look at examples of misspelled words in various languages and examine their individual properties, you won't find what unites them in a category.

But then, what about correctly spelled words? There will be many observable systematic relationships between those. I happen to think you have the analogy backwards. In the good/evil dichotomy, it is the evil acts, not the not-evil acts, which are narrowly defined and systematically related (I think). If you try to find what is in common between the not-evil acts, those are the acts which have nothing in particular in common. Meanwhile, in the well-spelled/misspelled dichotomy, it is the correctly-spelled words that are narrowly defined and systematically related. In short, I think morality is fundamentally a narrow set of prohibitions rather than a narrow set of requirements. In contrast, the rules of spelling form a narrow set of requirements.

But whether you are right or I am right is something that we won't know without looking.

You have to understand their relationship to the spelling rules in the various languages - rules which themselves are likely to be incompatible and mutually incoherent - to understand what properties make them examples of 'misspelled words'.

Nobody told Galileo and Newton what the rules generating the world's behavior were, but they were able to go a long way toward figuring them out. And isn't that what science is? If you claim that the science can't start without knowing the rules first, then aren't you asserting that science is hopeless?

Are you willing to have a neverending discussion, with everyone talking past each other, and no working definition for the central concept we're supposed to be examining?

I'm not in charge of the discussion, so it's not a question of what I'm willing to do. I've told you how to get the starting definition you're looking for. As I said: you can start with an ostensive definition by listing examples of evil acts. Then you can find common elements. For example, it might become apparent, after surveying them, that evil acts have in common that they all have victims against whose will the evil acts were committed and who are harmed by the evil acts. It might also become apparent that the evil acts involved one or another form of transgression or trespass against certain boundaries. You might like to study what the boundaries are.

Basic scientific methodology - you can't study what you can't produce a provisional definition for. Once you have that, you can learn more about what's defined, but you don't get anywhere without that starting point.

The first concepts that more less denoted, say, water, may have included things which today we would reject as not water (e.g., possibly clear alcohol), failed to distinguish water from things dissolved in the water, and excluded forms of water (such as steam and ice). The very first definitions of water were probably ostensive definitions (this here is water, that is water) rather than descriptive or explanatory definitions. The definitions were subject to revision as knowledge improved.

Are you willing to accept an ostensive and potentially erroneous definition of morality that may very well be subject to revision as knowledge improves? One is easy enough to supply by listing a bunch of acts currently believed to be evil, then listing a bunch of believed-to-be morally neutral acts, and pointing out that the first group is evil and the second group isn't. Would that be satisfactory?

Is it an arbitrary grouping, or do we use the label to refer to certain properties that things in that grouping possess?

I think the better question is, do recognized examples of evil have something in common - never mind what we intend by the label. Maybe by the label "water" we initially intended "Chronos's tears" or some such useless thing. The intention isn't necessarily of any particular interest. You are interested in scientific inquiry into morality, yes? - seeing as you talk about "scientific methodology." Science studies the properties of things in themselves independently of whatever nonsense ideas we might have about them; if you want to study our intents then become a philosopher, not a scientist.

Anyway, this question - do examples of evil have something in common - is something for the scientists to answer, no? It doesn't need to be answered before scientific inquiry begins.

Constant, if moral truths were mathematical truths, then ethics would be a branch of mathematics. There would be axiomatic formalizations of morality that do not fall apart when we try to explore their logical consequences. There would be mathematicians proving theorems about morality. We don't see any of this.

If Tegmark is correct, then everything is mathematics. Do you dispute Tegmark's claim that "there is only mathematics; that is all that exists"? Do you think your argument is any good against Tegmark's hypothesis? Will you tell Tegmark, "the department of physics and the department of biology are separate departments from the department of mathematics, and therefore you are wrong"? I don't think it is quite so easy to dismiss Tegmark's hypothesis merely on the basis that all the sciences are not treated as branches of mathematics. Tegmark's point is that something that we don't realize is mathematics nevertheless is mathematics. All your observation shows is that we don't treat it as mathematics. Which doesn't even touch Tegmark's hypothesis.

Isn't it simpler to suppose that morality was a hypothesis people used to explain their moral perceptions (such as "murder seems wrong") before we knew the real explanations, but now we find it hard to give up the word due to a kind of memetic inertia?

Moral truths pass some basic criteria of reality. They are, importantly, not a matter of opinion. If, as some claim, morality is intuitive game theory (which I think is very much on track), then morality is not a matter of opinion, because whether something is or is not a good strategy is not a matter of opinion. Optimal strategies are what they are regardless of what we think, and therefore pass an important criterion of reality.

Now, there seem to be some who think that discovering that morality is intuitive game theory debunks its reality. But to my mind that is a bit like discovering what fire is debunks the idea that fire is real. It does not: discovering what it is does not debunk it, if anything it reaffirms its reality. If fire is a kind of exothermic chemical reaction then it is most definitely not just in my imagination! And if morality is intuitive game theory then it is most definitely not just in my imagination.

And game theory happens to be... guess what... Starts with an "m".

Dynamically Linked writes: But, it seems pretty obvious, at least to me, that game theory, evolutionary psychology, and memetics are not contingent on anything except mathematics and the environment that we happened to evolve in.

According to Tegmark "there is only mathematics; that is all that exists". Suppose he is right. Then moral truths, if there are any, are (along with all other truths) mathematical truths. Unless you presuppose that moral truths cannot be mathematical truths then you have not ruled out moral truths when you say that so-and-so is not contingent on anything except mathematics and such-and-such. For my part I fail to see why moral truths could not be mathematical truths.

Before I go on, do you actually believe this [Bayesian net diagram] to be the case?

I'm sorry to say that I can't read Bayesian net diagrams. Hopefully I answered your question anyway.

Z. M. Davis writes: ... objective illness is just as problematic as objective morality

I would argue that to answer Robin's challenge is not necessarily to assert that there is such a thing as objective illness.

Accounts have been given of the pressure producing the ability to see beauty (google sexual selection or see e.g. this). This does not require that there is some eternal beauty written in the fabric of the universe - it may be, for example, that each species has evolved its own standard of beauty, and that selection is operating on both sides, i.e., selecting against individuals who are insufficiently beautiful and also selecting against admirers who differ too far from the norm.

However, this evolutionary concept of "illness" cannot be the ordinary meaning of the word, because no one actually cares about fitness.

My argument is: people can distinguish illness because it enhances their fitness to do so. Compare this to the following argument: people can distinguish the opposite sex because it enhances their fitness to do so. Now, okay, suppose that people don't care about fitness, as you say. Nevertheless, unbeknownst to them, telling women apart from men enhances their fitness. Similarly for illness.

Take homosexuality. It's often considered a mental disorder, but if someone is gay and happy being so, I would challenge (as evil, even) any attempt to define them as "ill" in anything more than the irrelevant evolutionary sense.

Homosexuality reduces fitness (so you seem to to agree), but this does not make it an illness. Not everything that reduces fitness is an illness. Rather, illness tends to reduce fitness. Let me put it this way. Blindness tends to reduce fitness. But not everything that reduces fitness is blindness. Similarly, illness tends to reduce fitness. But that doesn't mean that everything that reduces fitness is illness.

... that which the patient desires in herself is health, and that which the patient does not desire in herself is sickness.

We can similarly say, that which a person desires in a mate is beauty. However, I think the most that can be said for this is that it is one concept of beauty. It is not the only concept. The idea that there is a shared standard of beauty is, despite much thought and argument to the contrary, still with us, and not illegitimate.

Richard, we can understand how there would be evolutionary pressure to produce an ability to see light, even if imperfect. But what possible pressure could produce an ability to see morality?

Let's detail the explanation for light to see if we can find a parallel explanation for morality. Brief explanation for light: light bounces off things in the environment in a way which can in principle be used to draw correct inferences about distant objects in the environment. Eventually, some animals evolve a mechanism for doing just this.

Let's attempt the same for morality. Brief explanation for morality: unlike light, evil is not a simple thing that comes in its own fundamental particles. It is more similar to illness. An alien looking at a human cell might not, from first principles, be able to tell whether the cell was healthy or sick - e.g. whether it has not, or has, fallen victim to an attack rewriting its genetic code. The alien may need to look at the wider context in order to draw a distinction between a healthy cell and an ill cell, and by extension, between a healthy human and an ill human. Nevertheless, illness is real and we are able to tell the difference between illness and health. We have at least two reasons for doing this: an illness might pass to us (if it is infectious), and if we select an ill partner for producing offspring we may produce no offspring.

Evil is more akin to illness than to light, and is even more akin to mental illness. Just to continue the case of mating, if we select a partner who is unusually capable of evil (as compared to the human average) then we may find ourselves dead, or harmed, or at odds with our neighbors who are victimized by our partner. If we select a business partner who is honest then we have an advantage over someone who selects a business partner who is dishonest. In order to tell apart an evil person from a good person we need to be able to distinguish an evil act from a good act.

This is only part of it, but there's a 400-word limit.