Against arbitrariness

A more complete article about unwanted arbitrariness as the fundamental ethical principle, can be found here.

In this article I demonstrate that the anti-arbitrariness principle might be the most fundamental principle in both science and ethics.

What is arbitrariness?

Arbitrariness is difficult to define. It has to do with the absence of a good rule that relates to all the elements of a set or category. Arbitrariness means picking an element or subset of a set, without using a rule. It is the opposite of “uniformity” or “regularity”. There is a simple useful test that allows us to assess whether there is arbitrariness.

There is arbitrariness about X if we can ask a meaningful and nontrivial question: “Why X and not for example, Y or Z?” and if this question cannot be answered by a rule which does not explicitly refer to X (or if there is no reason why X would be so special). The question is meaningful when Y and Z belong to the same set or category as X (and are therefore not something completely different) and the question is non-trivial if Y and Z are not simply “non-X”.

Avoiding arbitrariness in science and ethics

Some kinds of arbitrariness are unavoidable in the sense that it is logically impossible to avoid them. For example, a mathematical system cannot simultaneously contain all possible axioms and an physical theory cannot simultaneously contain all conceivable rules and forces, because this will generate contradictions. The anti-arbitrariness principle in science states that all avoidable arbitrariness should be avoided. 

The same goes for ethics: an ethical system cannot simultaneously contain all possible rules, so there is always unavoidable arbitrariness in ethical systems. But there is more. Some kinds of arbitrariness are avoidable but innocent in the sense that anyone can consistently want this arbitrariness and no-one can consistently object to it. You can consistently want something if that what you want is not in contradiction with a consistent set of all the most important things that you want or prefer.  Consider a rule to drive on the right lane. Such a rule is arbitrary (we can ask the question “Why on the right and not the left?”), it can be avoided (e.g. by allowing to drive everywhere), but this arbitrariness is harmless because no-one cares if everyone collectively decides to drive on one lane instead of the other (in some countries, everyone drives on the left lane and nobody has a problem with that). The only possibilities to avoid this arbitrariness is to say that we can drive nowhere (neither left nor right) or to say that we can drive everywhere (both left and right). Note that ‘everywhere’ is not a direction such as ‘left’ or ‘right’. So ‘everywhere’ does not belong to the set of directions containing ‘left’ and ‘right’. Therefore, the rule to drive everywhere does not contain the same kind of avoidable arbitrariness as the rule to drive on the right. We strongly prefer to avoid accidents and we strongly prefer to use a vehicle, so a rule to drive on the right is compatible with our strongest preferences and wants. No-one has a value system that is incompatible with a rule to drive on the right lane. Everyone can consistently prefer arbitrariness (to drive on the right lane) above a universal prohibition (to drive nowhere) and a universal permission (to drive everywhere) resulting in chaos and accidents.

The unavoidable and innocent kinds of arbitrariness are kinds that anyone could consistently want. The culprit in ethics is the unwanted arbitrariness: the arbitrariness that not everyone can consistently want. You cannot consistently want something if what you want is incompatible with a consistent set of all the most important things that you want or prefer (e.g. your strongest moral values). The anti-arbitrariness principle in ethics states that all unwanted arbitrariness should be avoided. If one thing goes for X, then it must also apply to all Y and Z that are equal to X (in the sense of belonging to the same set as X) according to a rule, unless everyone can consistently want that it just applies for X. Arbitrariness is only allowed if it is not against anyone’s will.

Before we move on with examples, we have to check whether the anti-arbitrariness principle is itself arbitrary and therefore defeats itself. The answer is no. Of course we can always ask the trivial question: “Why be against arbitrariness and not against non-arbitrariness?” But any other nontrivial question becomes meaningless. For example: “Why be against arbitrariness and not against apples or bananas?” Apples and bananas do not belong to the same category as arbitrariness.

Let us look at some examples, starting from the most exact science (mathematics) and ending with ethics.

Anti-arbitrariness in mathematics

Uniformity of axioms

Mathematics studies axiomatic systems and mathematical structures. Consider the theory of natural numbers that is based on axioms such as: “All numbers have one and only one successor that is also a number.” Note that this axiom applies to all numbers. No mathematician studies an arbitrary system that says that all numbers have a successor except 203. This system is arbitrary because we can ask the question: why should 203 be the exception that has no successor and not for example 105 or 316? What makes 203 so special that it would not have a successor? These questions have no answers.

Or consider Euclidean (flat) geometry that is also based on five axioms such as: “Through every two points we can draw a unique straight line.” Note that this applies to all pairs of points. No-one uses a system that says that we can draw lines through every pair of points, except for the points in the left-upper part of the plane. This exclusion is arbitrary, because why would the left-upper part be excluded and not for example the right part or the bottom?

Mathematicians use axiomatic systems with axioms that do not contain arbitrary exclusions. Those examples of arbitrary exclusions are avoidable. The axioms can and should be uniform, which means that they equally apply to all elements of a set or category (e.g. all numbers, all points,…). So the axioms contain words like “all”. But there remains unavoidable arbitrariness. One can ask the question: “Why do you take the 5 axioms of Euclidean geometry and not for example 7 axioms that generate another geometrical system?” Or: “Why would every number have just 1 successor and not for example 2 or 5?” It is impossible to work with a mathematical system that contains all possible axioms at once, and it is impossible to say that every number has all possible numbers of successors. So we are forced to choose the axioms. We end up with many axiomatic systems. Next to the system of natural numbers there is for example the system of Gaussian numbers where every number has not one but two successors.

Symmetry

Uniformity is related to symmetry. An object is symmetrical or uniform if it retains the same property (for example shape) under a transformation such as reflection (mirror symmetry) or rotation. Take a round glass. This glass has a rotational symmetry in the sense that if you rotate it (around the vertical axis of the glass), you see no difference: the initial and final states look the same. On the other hand take a coffee cup with an ear. If you rotate the cup, you see that the position of the ear is shifted. The ear breaks the rotational symmetry of the cup, because based on the position of the ear you know if the cup is rotated or not. The relationship between symmetry breaking and arbitrariness is that it is arbitrary that the ear is attached at this side of the cup instead of somewhere else. We can ask the question: why is the ear here and not here or here? A symmetrical object has less arbitrariness than an asymmetrical object. The study of symmetries is crucial in both mathematics and physics, so let’s move to physics.

Anti-arbitrariness in physics

Universal laws

Also in physics there is an aversion to avoidable arbitrariness. The basic laws of physics are universal. For example gravity works everywhere and at every time in the same way on every object with mass and energy. Physicists do not say that electrons are electrically charged everywhere, except in the bottom-left corner of the universe. They do not say that gravity always affects objects with mass, except from the year 2060 till 3254. Those exceptions would be arbitrary, because why the year 2060 and not for example 1900?

Induction

In inductive reasoning one derives a general rule on the basis of a limited number of specific observations. This reasoning is common in empirical science and is the opposite of deductive reasoning which is common in logic and mathematics, where one derives an individual case out of a general rule.

An example of an inductive argument is: the sun came up this morning, yesterday, the day before yesterday … so the sun rises each morning. The problem of induction is that the argument is not logically valid. One can never know for sure (with the same certainty as a logical or mathematical truth) that the sun will rise tomorrow morning.

But what if tomorrow the sun would not come up? Then we can ask ourselves the nontrivial question: why does the sun not rise tomorrow morning and not on another day, such as yesterday? What is so special about tomorrow morning that the sun does not rise that day? If nature has by way of speaking an aversion to arbitrariness, and if there is no rule that would make tomorrow an exception, then the rule of induction works. The universe seems to be full of regularity. If there are exceptions to a universal law, those exceptions have to be universal as well (see below).

Anti-arbitrariness in metaphysics

Multiverse

Our universe has universal laws of physics that apply everywhere in the universe. But there is an unavoidable arbitrariness: why would the universe contain this set of laws and not other laws? Why these forces and not others? Why 3 space dimensions and not 7? And why would the fundamental constants of nature (e.g. the ratios of natural forces) have these values and not others?

This arbitrariness is unavoidable: you cannot have a universe that has all possible forces, all possible dimensions and all possible values of the fundamental parameters and strengths of the forces. But there is an elegant hypothesis that even avoids this arbitrariness (proposed by cosmologist Max Tegmark): all possible universes exist in a multiverse. Every universe is nothing but a coherent mathematical structure (a mathematical system that is consistent and has no avoidable arbitrariness). We live in but one mathematical structure, our universe, but in a sense all other coherent mathematical structures (possible universes) exist as well. There is no arbitrary exclusion of universes.

This is actually a very simple theory. Compare it with a set of numbers. We can assign a number to every universe, like an address or house number. Our universe is described by for example the number 2358681593. But why would only this number exist? What would be so special about this number, about our universe? A theory that says that only the number 2358681593 exists is less simple (more arbitrary) than a theory that says that all numbers exist. To see this, try to remember both theories. Which theory is the easiest to remember: 2358681593 or “all numbers”?

Atheism

The anti-arbitrariness principle leads to atheism. There are thousands of possible gods (Yahweh, Allah, Brahma, Osiris, Iluvatar, Krishna, Chaos, Chronos,…), and the (lack of) evidence for the existence of those gods is equal. So what would make Yahweh so special that only he would exist? In fact, every theistic believer is 99,9999…% atheist: he or she does not believe in all the other possible gods. It is arbitrary to believe in just one of the possible gods that have equal evidence. We can avoid this arbitrariness by either believing in all possible gods at once (but that is not feasible) or by not believing in any god.

The same goes for the holy scriptures: why would the Bible be the basis of morality, instead of for example the Bhagavat Gita? It is arbitrary to pick one book as holy if there are many possible holy books and if all those holy books have equal evidence. Scientific books have more evidence than religious books, so we can pick scientific books non-arbitrarily. This brings us to science.

Anti-arbitrariness in science

The difference between good science and bad pseudoscience lies in the fact that pseudoscience does not avoid avoidable arbitrariness. Pseudoscience is full of cherry-picking and ad hoc hypotheses.

Cherry-picking

Pseudoscientists often refer to some anecdotes, specific studies, evidence or data and neglect all other anecdotes, studies, evidence and data. If the other data, studies and evidence are as reliable as the ones selected, we can ask the nontrivial question to the pseudoscientists: “why do you pick only those data and studies that confirm your theory and not the other data that disprove it?” Good scientists avoid a selection bias where they arbitrarily select data that confirms their prior beliefs.

Ad hoc hypotheses

When a test falsifies a hypothesis, the pseudoscientist often adds an exception to the hypothesis. The hypothesis turns into an ad hoc (“for here”) hypothesis that says that here, in these particular circumstances of this test, there is an exception that saves the hypothesis. If someone who claims to have paranormal skills is tested by scientists and in the test the person is no longer able to demonstrate his skills, he can add an ad hoc argument that for some reason his paranormal powers do not work in the situation where scientists critically study him.

Ad hoc reasoning is also often called “special pleading”, “moving the goalposts” or “stacking the deck”. The ad hoc exception is arbitrary if the following questions do not have an answer: “Why would these circumstances be the exception and not those?” or “Why would the situation be different here (in this situation) instead of here or here?”

Often the ad hoc exceptions are avoidable, and that means the ad hoc hypothesis violates the anti-arbitrariness principle. But sometimes the exceptions can be translated in universal laws. For example the rule “all objects fall to the ground” is falsified by a test that contains an iron bar that is pulled up towards a magnet. The ad hoc (for here) rule now becomes: “all objects fall to the ground, except for this iron bar when it is here under this object which we call a magnet.” But this new hypothesis can be translated into a new universal law: “all objects fall to the ground except when there is a strong magnetic force working on a susceptible object, and this goes for all susceptible objects and all magnetic forces everywhere and always.”

Anti-arbitrariness in ethics

Coherent ethical systems

As in physics and mathematics, the anti-arbitrariness principle is also fundamental in ethics. Physical theories that describe our universe and axiomatic systems that describe mathematical structures are examples of coherent systems that are consistent and do not contain avoidable arbitrariness. The same goes for ethics, where we can construct coherent ethical systems based on fundamental principles, just like mathematical axioms or physical laws.

The anti-arbitrariness principle specifies some rules for the construction of coherent ethical systems.

1) One should not arbitrarily limit the ethical principles to an arbitrary group of objects, beings or individuals.

2) One should not arbitrarily give weaker moral intuitions stronger priority. One should not arbitrarily change or exclude basic moral judgments. Those basic moral judgments are comparable to data in science.

3) One should not arbitrarily allow inconsistencies and gaps in the ethical system.

4) One should not arbitrarily introduce a vague ethical principle that one can interpret and apply arbitrarily in concrete situations. Compare it with the clarity of scientific laws and mathematical axioms.

5) One should not arbitrarily add artificial, complex, ad hoc constructions to the ethical system.

Constructing incoherent ethical systems is pseudo-ethics. Why is it bad to construct incoherent ethical systems that contain inconsistencies or ad hoc arbitrariness? Suppose that someone believes in an incoherent ethical system, i.e. a system that contains inconsistencies (internal contradictions ) or avoidable arbitrariness. Are we allowed to reject that system and impose our coherent ethical system? Or in other words: is that person able to complain and able to give justified arguments against our imposition of our system.

Suppose that the ethical system of the person is inconsistent. In that case, that person acknowledges that it is permissible to have inconsistencies. If that person is allowed to have two opposing views at once, then so are we. We are allowed to both have the belief that we cannot simply reject someone else’s moral beliefs and ethical system, and we have the belief that we can reject the ethical system held by that person. Even if these two beliefs are mutually contradictory, that person cannot argue against it, because we can always say that we do not reject that system, even if we do, and we are allowed to have contradictions if that person may have contradictions.

Now suppose that the person holds a consistent but arbitrary ethical system. Now we can follow a similar strategy: if that person prefers an ethical system that contains avoidable arbitrariness, then that person acknowledges that arbitrariness is permissible. That means that it is also permissible to arbitrarily ignore someone else’s moral views and ethical systems. We can say to that person that his or her moral values and judgments are not valid. And if that person complains and says that his or her ethics is valid, then we can reply that if s/he is allowed to arbitrarily exclude other moral views and make an ad hoc exception for his or her own ethical system, then so are we. So now we may even make the exception that everyone’s moral views should be respected, except the ethical system of that person. That person is not able to give arguments against that, because all arguments can easily be bounced back by saying: “If you are allowed to arbitrarily do that, then so are we. What would make you so special that you are allowed to arbitrarily exclude others but we are not?”

To conclude: we can even arbitrarily reject that incoherent ethical system, because the person acknowledges that arbitrary exclusions or rejections are permissible by acknowledging that arbitrariness is permissible. After all, that person uses an arbitrary system. The person can only give a valid complaint or argument if s/he accepts the anti-arbitrariness principle. Without that principle, any critique becomes invalid. The impossibility to complain if one has an incoherent ethical system implies that coherent ethical systems gain a more objective or absolute status. Of course there are many possible coherent ethical systems, just like there are many coherent mathematical systems. How do we deal with that plentitude of systems? A special kind of democracy is the solution.

Democracy

We are allowed to reject anyone’s incoherent ethical systems. This allows us to avoid an extreme form of moral relativism that says that all ethical systems, including incoherent ones, are equally valid. This extreme relativism implies that everything would be permissible, and we cannot want that.

But we cannot simply reject someone’s coherent ethical system, even if that system is different from ours. If we are against avoidable arbitrariness, we have to recognize that every equally coherent ethical system is equally valid. Everyone is allowed to construct his or her own ethical system, as long as that system is coherent, i.e. does not contain contradictions or avoidable arbitrariness.

I cannot say that my coherent ethical system is better than yours if both our systems are equally coherent. I prefer my system, but I cannot impose my system onto you, because what would make me so special that I would be allowed to do that? And the same goes for you and everyone else. It would be an avoidable kind of arbitrariness if we claim that our own system is special without good reason.

So everyone constructs their own ethical system, and we can aim for a consensus or democratic compromise between everyone’s system by using a democratic procedure. In a democracy, everyone has one vote, or everyone’s vote is equally important, because we cannot say that one vote (one coherent ethical system) is better than someone else’s.

Note that the coherence of ethical systems imposes very strong constraints on the construction of ethical systems. We can expect that the resulting ethical systems that people construct, if they follow the anti-arbitrariness principle carefully, are not extremely divergent from each other. This strong selection and convergence of ethical systems makes a democracy of ethical systems feasible.

So there are two reasons why our ethical system should not contain avoidable arbitrariness. First, if it contains such arbitrariness, someone else is allowed to arbitrarily reject our system and we are not able to complain. Second, the avoidance of avoidable arbitrariness puts strong constraints on the possible ethical systems, which makes a democratic consensus between the resulting coherent ethical systems more feasible.

Antidiscrimination

A specific result of the anti-arbitrariness principle is the antidiscrimination principle. We can define prejudicial or arbitrary discrimination of individual (or group) A relative to B as a systematically different treatment of A and B (e.g. B gets more advantages than A), whereby

• it is claimed that A has a lower moral status than B (e.g. that A has less intrinsic value or weaker rights than B) in the sense that one would not tolerate swapping positions (treating A as B and B as A), and
• there is no justification or the justification of the previous point refers to morally irrelevant criteria (properties that are not acceptable motives to treat A and B differently in the concerned situation), whereas A and B both meet the same morally relevant criteria to treat and value them more equally.

The first condition reflects the lack of symmetry (swapping positions of A and B) and the second reflects the lack of a rule for justification. The anti-arbitrariness principle specifies what counts as morally irrelevant criteria. For example when it comes to respecting basic rights, a criterion or property is morally irrelevant to a higher degree if more of the following conditions are met:

• the property is arbitrary (there is no non-circular rule that selects the property out of a multitude of similar kinds of properties), or
• the property is contingent (not present in all possible worlds) or not intrinsic (it does not refer solely to the individual possessing the property), or
• the property is inherently difficult to detect, define or delimit (the property is non-empirical or there are no scientific criteria and methods – not even in principle – to clearly see whether the property is present).

Of course if the property is arbitrary, it violates the anti-arbitrariness principle. If the property is contingent or not intrinsic, there is also an arbitrariness in the sense that the property depends on contingent (accidental) circumstances that could have been different in another possible world. Someone’s rights should not depend on contingent properties, because we can ask the question: why should that individual get rights in this possible world but not in that? And if the property is difficult to detect or delimit, there is the risk that one arbitrarily assigns the property as one pleases.

Examples of criteria that are morally irrelevant because they are arbitrary are: physical characteristics and appearances (e.g. skin color, behavior, gender), genetic properties (e.g. race, ethnicity, genetic kinship), preferences (e.g. sexual, political), supernatural properties (e.g. having a soul) or belonging to an arbitrary group (preferring one group when there is a multitude of groups in a complex hierarchy or taxonomy; e.g. Abrahamists, Christians, Catholics, Roman Catholics; or living beings, animals, mammals, primates, great apes, humans, white people).

Universal rules

Anti-arbitrariness results in universal moral rules. The principle of rule universalism says that one must follow the rules that everyone (who is capable, rational and well informed) must follow in all morally similar situations, and that one may follow only the rules that everyone (who is capable, rational and well informed) may follow in all morally similar situations.

The question becomes: what counts as morally similar situations? Situations can be called similar if morally relevant properties of the situation are similar, and those morally relevant properties should not contain avoidable arbitrariness. Examples of morally relevant properties are: well-being (of all sentient beings who have a well-being), preferences (of everyone who has them), rights (of everyone and everything, see next section) and biodiversity (of all ecosystems). Examples of morally irrelevant properties were given in the previous section.

Universal rights

Human rights are arbitrary: why should all and only humans get rights? What makes humans (including for example mentally disabled orphan children) so special? What morally relevant property do all and only humans possess? If you are allowed to arbitrarily exclude other individuals from having rights and if you are allowed to arbitrarily select a group of right holders (e.g. the biological group of humans), then so am I and so is everyone, and you cannot want that. If speciesism is permissible, then so is racism, sexism and all other forms of arbitrary discrimination, and we cannot want that.

So instead of asking the question: “who gets all the basic rights?” we have to ask the question: “which rights should be given to everyone and everything, without arbitrary exceptions?” Everything really implies everything: electrons, planets, plants, animals, humans, computers, clouds,… This guarantees that all possible kinds of discrimination are excluded.

If we give the basic right not to be killed to everything and everyone in the universe, we are not allowed to kill plants for food. But sentient beings cannot want that, and plants do not have a will, so they don’t care about not being killed because they do not have the mental capacity to care (they don’t experience anything so they even don’t feel or know if they are alive or dead). So we can consider basic rights such as the right not to be killed against one’s will, the right not to be confined against one’s will, the right not to be used as a means against one’s will.

With these rights, we can do whatever we like with things that do not possess a will, such as plants and individual living cells, because one cannot treat something against its will if it has no will. So for non-sentient objects (that have no subjective experience of a will), the basic rights are always trivially satisfied. We always respect the basic rights of non-sentient beings for 100%. For sentient beings (for example vertebrate animals and probably some other animals) the rights become nontrivial. These rights result in for example a vegan lifestyle. Abortion would be permissible because the embryo does not yet have a will (it therefore cannot be killed against its will) and the mother has a right not to be used by the embryo as a means (as a reproduction machine) against her will.

The only human right would be a right to be human, but that right is as meaningless as a right to be white or a right to be man. Ethical systems with non-universal rights are not permissible, because these systems contain avoidable arbitrariness.

Golden rule

The golden rule (“treat others as you would like to be treated and do not treat them as you would not like to be treated”) is a consequence of the anti-arbitrariness principle. This is also a symmetry principle, as it asks us to switch positions: put yourself into the position of someone else. An often heard objection is that how you like to be treated might be different from how I want to be treated. A naïve application of the golden rule would imply that rape is permissible: if I would like to have sex with someone, I can force that person to have sex with me.

But that would be an inconsistent or arbitrary application of the golden rule. The golden rule does not only apply to treatments such as “having sex”, but also to “forcing others”. If I don’t want you to force me, I am not allowed to force you. If I don’t want you to project your preferences on me, I am not allowed to project my preferences on you.

A variation of the golden rule that we encountered several times before, is: “If you are allowed to do something, then so am I”, or more precisely: “If you are allowed to do something or follow a rule, then you must be able to consistently want that everyone may do the symmetrically equivalent thing or follow the same rule.” The symmetrical equivalence consists of a similar act by which the description of the pronouns “you” or “your” are exchanged with “I/he/she”, “me/him/her” or “my/his/her”. The positions of you and someone else are completely reversed. Here are some examples that illustrate this rule and demonstrate that we can deduce a lot from this rule.

We can easily derive things that you are not allowed to do, because you do not want them to be done to you. For example: if you may hit my cheek, I may hit your cheek. If you may impose your rules on others, others may impose their rules on you. If you may forbid homosexuality because you find it unclean, unholy or disgusting, then someone else may forbid something that you like and he finds unholy, for example playing guitar. If you may use vague or arbitrary reasons to justify your behavior that I don’t like, I am allowed to use vague reasons as well to justify my behavior that you don’t like. If you may say that we should follow the Bible because the Bible is the true word of God, I may say that we should follow the Bhagavat Gita as the true word of Krishna. If you may say that your moral intuitions are better than mine, I may say that mine are better than yours. If you may arbitrarily choose your victims, I may arbitrarily choose my victims.

We can also easily derive things that you are allowed to do, because you can consistently want that others do the symmetrically equivalent behavior. For example: if you may eat the food that you bought, then I am allowed to eat the food that I bought.

Some derivations require more work. For example if you may kill a living being to eat, can I also kill a living being? You do not want me to kill you to eat. But you will still be able to kill a plant to eat. So you’re going to have to define a group of living beings that we should not kill and eat. For example, your relatives and friends. But if you may say that we are not allowed to eat your preferred group of friends and relatives, then I may prefer my group that might exclude you, which means I can eat you. If you may kill someone who does not belong to your family and friends, then everyone else may kill anyone who does not belong to their own circle of friends. You cannot want that. So you must define a different group. Perhaps the group of humans and dogs? But if you can determine that one should not eat anyone who belongs to the group of humans and dogs, I may decide that we should not eat anyone belonging to the species of pigs or chickens. Or I may decide that we should not eat someone belonging to the classes of mammals, birds or fish. Then you must accept that you are not allowed to eat meat and fish. But if I may decide that we should not kill animals to eat, then you may decide that we should not kill plants to eat, and I do not want that. So I cannot just define the group of animals. We cannot say that we may kill a living being if that living being does not belong to the group of relatives and friends, the group of people and dogs, the group of mammals and fish or the group of animals. So how may we decide who or what we may kill to eat? By not looking for what we may not kill, but by looking for what we may not kill against its will. So if you are not allowed to kill someone against his or her will, then neither am I. That means I may not kill you against your will. But you and I may still kill a plant, because a plant has no will and therefore cannot be treated against its will.

A final example: if you may follow your ethic, are racists allowed to follow their racist ethic? Are pedophiles, rapists and religious fundamentalists allowed to follow their ethics? You cannot want that. But the ethical systems of racists, pedophiles, rapists and religious fundamentalists contain inconsistencies, avoidable arbitrariness, unscientific beliefs and vague principle. So if your ethical system is more coherent than others (if your ethical system does not contain any inconsistencies, ambiguities and avoidable arbitrariness), then you can say that your ethical system is better than others and then you may oppose the incoherent systems of others.

The fundamental ethical formula

With the anti-arbitrariness principle we can derive many rules, such as the golden rule. Another expression that we can derive may be called the fundamental ethical formula, which can be used as a good basic starting point in ethics: everyone must follow those moral rules of which everyone can want that everyone follows them, in all possible worlds. This formula is about what one can want, and any form of arbitrariness is excluded because this formula refers to everyone and to all possible worlds. This formula is a bit related to the Kantian categorical imperative.

To conclude, we have seen that the anti-arbitrariness principle is fundamental in mathematics, physics, scientific research and ethics.