My reasoning is sort of, If there is no objective moral end, then no moral system is greater than another.
That's exactly what I disagree with, though. What you are calling 'arbitrary' is not. For example, let's say that the guiding principle of my morality is to not do to people what I don't want them to do to me. There is a degree of reason in this, since it's a social contract establishing a pact between people to try and encourage mutually beneficial behaviour. The moral code I derive from this basic premise is certainly not 'arbitrary' (ie. random or based on whim). Nor is it objective though, since clearly the original premise (to not do harm) can be argued, and the resultant moral code is variable.
Therefore we cannot fault a murderer for following her morals.
Subjectively, I would suggest it's possible to justify a murder, but in almost all cases murder is wrong. This isn't written in the stars, or etched in my soul, but it is a very consistent belief across a variety of human societies. A common subjective belief, if you will, which finds itself differing in detail from place to place. In some, for example, murdering a murderer is considered okay, if they have been found guilty of their crimes by their peers. In others, burning a witch is considered okay if the rest of the village largely agrees.
I know of very few groups who would say 'we cannot fault a murderer for following her morals' though, since her actions have obviously and irrevocably harmed another. Only where that harm can be justified by the moral code of the group can it be justified.
Having lived in Papua New Guinea and seen some of the violence done against 'sorcerers' first hand, I can tell you that the moral code that was operating in those locations was severely flawed, and that a 'better' moral code would not have included justification for murdering sorcerers. You can tell me that my beliefs (not to kill people based on accusations of witchcraft) and local beliefs (kill witches by burning) are both equal, and neither is 'better' than the other, but you don't actually believe that. You're simply trying to tell me that ONLY objective morality makes that a meaningful differentiator . And to me, you know which moral code is 'better', just as I do. And it's quite possible to explain why.
If we evaluate her actions from the perspective of our morals, then even that evaluation is arbitrary in the general sense. Why would our criticism in accordance with our morals hold any more weight compared to a criticism in accordance with another system? From our moral standards, we could criticize Nazi Germany policies as bad, but does that criticism hold any weight? If moral ends are truly subjective, then we don't have a solid basis to reason that our criticisms of Nazi Germany policy are any greater than the policies themselves. That is why I say arbitrary.
Arbitrary means whimful, without reason, random. Our criticism of Nazi Germany is anything BUT random.
Ill give an example to illustrate:
Imagine that we had an object (lets say a ball). Now, we also assume that there is no objective fact regarding the color of this ball (just as moral relativism sees no objective principle relating to the morality of actions). Person A, see the ball and says that it is red. Person B, sees the ball and says that is is blue. Now, no matter how much they arguer or criticize each other's position with regards to their own references, we cannot ever make a meaningful evaluation that Person B's claim is any way better or superior to Person A's (or vica versa) simply because of the fact that there ball does not have an objective color. In a similiar way, if we assumed that morality is truly relative, then we cannot meaningfully favor one society's morals over another.
You example doesn't truly hold though. Any moral code, be it subjective or objective (and remember, to me, ALL moral codes are subjective), has underlying principles. Consistent application of these is kinda the point.
Your example completely skips this need, since there is no measureable difference between 'blue' or 'green'. If my underlying principles underpinning my moral code are around harm minimisation, or world peace, then the ball example IS arbitrary. There is no morality tied to how people see the ball. But if a random holy book said that people who saw Red were possessed by the devil, then a VERY destructive moral belief can be readily introduced. The people holding to this belief would swear that they are following objective morality. And me, with my subjective morality, would swear that their holy book and literalist beliefs have resulted in a poorer moral code than mine.
If moral truths were subjective, it allows for evaluation against other subjective morals, but ultimately that evaluation itself is false, because the very values in question are subject to relativity. Arbitrary morals and subjective morals go hand in hand.
I've already argued that 'arbitrary' is entirely the wrong word when talking about 'subjectivity'. So for a different discussion, let's play the mirror game for a second, then. If there are objective morals, how do you know what they are?
Progress is not simply change. It is directional change. It implies a goal.
Yes. Or at least, a means of measure (since I could be progressing in the wrong direction, or down a particular variable path).
There must be an end towards which progress is directed. If that end is subjective, then it is arbitrary.
No. Not arbitrary. If the underlying principles of my subjective morality is to minimise harm or pain in the world, then buying free range eggs is measurably better than buying battery eggs. Shunning Aztec traditions of human sacrifice would also be a progressive step.
I'll illustrate the example with the ball scenario. Person A and Person B, now decide to work together and try and find out the actual color of the ball (but remember there is no actual objective color). They perform a series of tests, observations, and now they see the Ball as green. Could we say that they have made progress regarding the color of the ball? No, because the ball does not have an objective color. Only if the ball did have an objective color (lets say green), could be evaluate the efforts of Persons A and B and label it as progress. Progress implies we are moving towards an end which exists as an objective standard.
Subjectivity indicates variance, and is an acknowledgement that there is more than one approach to defining and measuring morality. It does not suggest that morality is not measurable. In different places it will be measured in different ways, which I would imagine is your point (ie. there is no RIGHT way), but there are common themes around social cohesion. Ultimately we will all measure other people's morality based on our own. But like ANY body of knowledge, the cognitive dissonance this process can introduce can lead to change and improvement (or the opposite!) to our moral code.
For example, my dad has some issues with race and sexuality. I have measurably improved my own moral code (don't treat others as I wouldn't want to be treated) by educating myself on these issues, and shaking free of some of the baggage of my childhood.