Ethics is generally defined as the study of human behaviour in terms of right and wrong, good and evil, and other equivalent terms, and it is full of controversial situations, both real and hypothetical, often linked to what us humans individually understand as justice and what we see as correct, points of view that are strongly related to our education and our personal experience. This makes moral philosophy a rather subjective branch of philosophy in its core, not only because it’s shaped by our perception of the world as humans (as most, if not all, of our knowledge is), but also by our perception as individuals.

The controversy we find in ethical and moral judgements could be trivial in our daily lives if it were only related to the academical thought experiments, such as the “tram switch dilemma”. However, ethics is vital in our law systems, and what do those regulate, especially in a democracy, and in our social interactions in general. Depending on what our moral standing point is, we will judge some events or situations differently, often in completely opposite ways. For this matter, many have worked to find some “common ground”, something that we all can agree upon, either from reason, intuition, or even by decree or faith.

Nevertheless we can approach this matter from a more formal and matheatical way, and understand moral (and ethics, more in general) as a set of beliefs which derive deductively from a set of basic principles, a set of axioms. This is a very accurate and precise model for how we understand ethics today, as it’s a branch of philosophy that requires no experimental or phyisical evidence to prove any of its arguments. Viewed this way, we can quickly apply all we know from axiomatic systems of knowledge, most notably what might be the single most beautiful idea in mathematics: Gödel’s Incompleteness Theorem.

From Gödel’s Theorem (and many other ideas in the field), we can firmly state that no set of principles is complete nor absolute. In other words, any consistent set of axioms is equally valid, even if its conclusions are in contradiction with those derived from other sets of principles. We can either regard this as “all consistent ethical systems are valid” or “no consistent ethical system is good enough”. The second of those statements, being more mathematically accurate (due to the incompleteness of the principles), can be read as a form of nihilism, ethical nihilism, though we can harmonise the two by saying “as no consistent ethical system is good enough, we can take all as valid”, shifting the focus of ethics away from the universality and completeness of its beliefs, and into the consistency of them.

In this quest for consistency, a key idea is that of Kant’s Categorical Imperative, which can be stated in plain English as “whatever are your ethical principles, apply them fully all the time with no exceptions”. The Categorical Imperative acts more as part of being consistent with one’s axioms, as doing the opposite of what those are is, by definition, unethical, at least from one’s on point of view. After all, it is hard to argue how one can break his own moral rules without being immoral according to them, or how one is just by not acting according to one’s idea of justice. With this, an individual’s integrity depends on whether his ethical principles are consistent logically and with his actions.

So far, due to the lack of universality of any set of principles, all arguments so far depend on each individual’s view and standing point, which is arbitrary, and most likely is very different from everyone else’s. Just as in mathematics, in fact, where at the time of describing a metric space, there is no absolute reference frame nor set of coordinates, and each reference provides different coordinates for the same objects. Unlike in mathematics however, where the description of metric spaces is in itself based on a set of rules (axioms) that enables us to derive true statements, we lack such a starting point in our discussion of ethics. The choice of one or other place where to start is just as arbitrary as the choice of principles earlier discussed.

Nevertheless, we can provide a different approach. Each individual having a different ethical standing point causes no problem as soon as those individuals are on their own. Issues arise in the interaction of more than one character, in particular in social interaction, leading to the classical debate on where is the limit between the individual and society. Stated in other words: which judgement is best when two different ones collide on the same question. This question is quite empty of value when discussing “who is being ethical” in an idealistic sense, but it is relevant as it is the foundation to law and politics, especially when the idea of justice is in the way.

In this situation, we’re trying to find a way to enable two or more different sensibilities coexist, and the answer may as well simply be just that: reaching an agreement between all those sensibilities involved on what is accepted and what is not. In other words, each society’s ethics and moral is an impicit pact to which all members agree (or at least tolerate) on what actions and behaviours are accepted or not. This system is self sustaining, as breaking the established boundaries will see the offender socially excluded, just like a mean person is excluded from the conversation, eliminating the need for a regulating authority, thus an absolute reference frame.

The lack of an absolute reference frame for all individuals is pivotal for philosophy, not only ethics, and for the same reason exposed earlier: the logic and mathematics through which we construct our ideas and thoughts are based in a axiomatic deduction system, a system that in its core eliminates all starting points, because any consistent set of axioms will lead to a completely different, equally valid picture, and thanks to Gödel, we know none them is complete. Isn’t it amazing that we live in a Universe that, not only has no centre or absolute frame of reference, but anyone can choose any point and view to establish both for oneself?