In modern times society has come to understand that some moral standards are unfair - Most people agree that racism is unfair and should not be tolerated. What is interesting is that almost any given ethical system will be considered unfair only if it is logically inconsistent. That is, an ethical system is fair precisely because it is logically consistent with itself. While racism is commonly considered unfair because thinking another human being is inferior to oneself based on some arbitrary physical attribute makes no sense, the entire concept of a superior race being allowed to make another race suffer is logically inconsistent. This, in turn, leads us to the problem of animal rights.
It is generally accepted that humans are superior to animals, at least for the sake of moral consideration. This is usually rationalized by a number of logical reasons, such as a sentience, or simply that any creature has a right to favor its own species over another. While this is a common aspect of several environmental ethical structures, it isn't necessary. It is a known fact that some people respond well to vegetarian diets, while others suffer from serious nutrient deficiencies. This is because humans are omnivores; we do not eat vegetables OR meat, we eat vegetables AND meat. We usually require both to remain healthy, although some individuals can successfully short-circuit this. However, it only justifies killing the animal for the purposes of a food source, not for torturing, poaching or other activities that are, coincidentally, illegal. We are therefore obligated to make an animal's death as painless as possible - something PETA has repeatedly brought up in its war against factory farming.
Factory farming itself is obviously immoral as it involves inflicting substantial amounts of suffering on animals that are then slaughtered. One can say its immoral for all the reasons PETA loves, usually involving graphic pictures of mistreatment, but we are more interested in the fundamental aspects of an ethical system. Specifically, a logically consistent ethical system can be constructed using only two postulates: Living things can suffer, and living things don't want to die. More accurately, the ethical system only applies to things that can suffer and things that have a survival instinct. From these postulates, we can formulate two simple theorems: One should not cause unnecessary harm, and one shouldn't kill unless necessary. From this, it is obvious that PETA is, surprisingly, correct - Factory farming is inescapably immoral. Unfortunately, things are never that simple.
The problem with factory farming is that almost the entire meat industry relies on it, all across the world. If it was made illegal, it would simply be done illegally, or the entire world meat industry would collapse and things would really, really suck. This kind of suffering is unnecessary, but it would be more accurate to come up with a new theorem: One should minimize the amount of suffering. This is why factory farming still exists and why we ignore what is clearly an immoral situation - there is no current alternative. PETA, in a brief flash of sanity, recognized this and has since been pushing for better treatment of the animals in the factories; but even this has problems. While there is obviously widespread animal mistreatment, there is also widespread rape, murder, extortion, bribery, theft, bullying, racism, sexism, anything-ism, homophobia, poaching, global warming, lying, hate crimes, harassment, trolling, abuse, etc. etc. etc. There is literally so much stuff going wrong that fixing factory farming simply isn't a priority right now, and so we end up in a case where an obviously immoral act must be tolerated for the sake of practicality. At some point in the future when we have presumably reached a more utopian society, we will be able to make fixing this a realistic priority. Clearly, the simple fact that something is immoral does not paint a black and white picture. Life is always a shade of gray.
This, of course, brings us back to racism. Racism is commonly discarded as an invalid belief because you can't assume that you are better than someone else just because they're skin color is different. What this ignores is the more fundamental question - what if you are better than someone else? Most moral systems try to do away with this by invoking the standard equality statement, "All men are created equal". This, unfortunately, does not really solve any problems. Is Albert Einstein on the same level as a hobo on the street? For the sake of the general public, the answer is usually yes, because considering everyone as an equal simplifies an ethical system greatly. Unfortunately, it stops working with things like animal rights. However, our previous two postulates can be brought to bear on this situation, because we know that one should not cause unnecessary suffering. Just because you are somehow superior to someone else does not give you a right to do anything to them. The only reason we are allowed to herd cattle for slaughter is because we require sustenance. Consequently the fundamental idea of racism is totally flawed - even if, by some insane, misguided logic, black people were on the same level as animals, it doesn't actually justify jack shit. Slavery would still be immoral. Discrimination would still be immoral. All of this stuff is still immoral. Racism is not only wrong between human beings, its wrong for anything. Being better than something else does not let you torture it.
Our modern day equivalent to racism is same-sex marriage. There are still a large percentage of the population that maintain that homosexuality is immoral. This is logically inconsistent, and surprisingly a lot of arguments used against homosexuality can actually be proven to be logically inconsistent, and therefore unfair. Many people state that homosexuality is unnatural and therefore bad. The common response to this is that homosexuality is present in nature and therefore not unnatural, but this ignores the more fundamental assumption that something unnatural is bad. This assumption can be proven false using proof by contradiction: Someone has a heart attack. A defibrillator is used to restart their heart and they go on to lead a happy, fulfilling life. The defibrillator is obviously very unnatural, but it prevented loss of life. Preventing loss of life is inherently moral because all beings that this moral system applies to have a desire to live. Consequently something unnatural cannot be inherently bad.
But what if same-sex marriage is against your religion? This line of thinking doesn't work for several reasons. For one, someone can simply invent a religion where your existence, and only your existence, is against the religion and therefore you must be killed. More fundamentally, however, you can't force your religious convictions on someone else, unless someone is using your religion to deliberately harass you, which is a problem of harassment, not religion. Consequently if someone needs to draw Muhammad to make a political point, you have to let them do this even if its insulting to your religion because they aren't deliberately trying to make you suffer, and so if you oppose them you are instead forcing your own religious opinions on them, which simply does not make any sense, because anyone can have a religion that does anything they want. You must have a better reason than "its against my religion", like "that is a deliberate attempt to aggravate me". Ironically, this same line of thinking is why someone is allowed to not say the pledge of allegiance if its against their religion. It isn't because its against their religion, its because they simply chose to not say the pledge, and not saying the pledge doesn't cause harm to anything, and therefore cannot be forbidden for any ethical reason.
This idea of something not causing harm to anything else is the basis for a famous ancient moral system, "If you harm none, do what you will". This has to be inferred from our two ethical postulates, because all our postulates state is that one should not cause harm or kill things. However, it is the very fact that these are the only postulates that lead us to this new inference - you can't use the ethical system to prevent someone from doing something if that something doesn't harm anything. You can try to justify it using some other system, but the ethical system will not allow you to make a valid logical argument against an action if that action doesn't cause unnecessary harm.
The fact that ethics are inherently based on logical consistency suggests that a sort of Ethical Calculus should, in fact, be possible. While one constructs the basis of an ethical system on moral absolutes, (do not kill or cause suffering), this foundation is given a qualifier, "unless necessary". The complex interactions that arise from minimizing suffering are what form the complex relative moral systems that govern our higher-order ethical considerations. Like economics, moral relativism exists because the absence of suffering is a scarce resource. This relativism, however, is formed from a logical basis, and so can be represented by an abstract logical system and analyzed as such. Perhaps a system of Ethical Math will one day allow us to quickly decipher the best ethical course of action, or failing that, what exactly makes a given ethical situation so complex.
Besides, if ethics are logical, and computers can evaluate logical statements, what is stopping us from making ethical AI?