Mathematics of Morals.

Abstract: This article tries to analyze the existence and utility of “morals” on human life. “Morals” is a highly overloaded term with different sets of people having different notions of its meaning, and highly likely having different set of morals. It is argued that the existence of morals in human life can be to support: perceivable personal benefit, social benefit, long-term personal benefit, or the “fair” world. Using these four different sets (the intersection of which is not necessarily empty), different possible interpretations of morals are reached at. Not, this article does not argue, what is the correct definition of “morals”, it only analyzes what are the different set of morals. The mathematics used in the article is just to furnish a degree of seriousness, and is elementary enough to be read by someone with no experience in math. The two mathematical abstraction used will be ∪ (for union of sets) and ∩ (for intersection of a set)

Disclaimer: This article is purely from an analysis point of view, and in no way represents personal beliefs or “morals” of the author.

It all started with a small discussion with Aneesh, Shibin and Sikha. The core of the discussion being the question “Is suicide right?”. To start with, this question can be asked in many different words, “Is suicide moral/ethical?” being two such different questions, however, it will be difficult to reach any conclusive grounds if we are not clear about what we mean by the words we choose. Thus I start with some definitions that needs to be established to avoid any misconceptions.

Act: The action performed by an actor (A human for this article). The question of the act being by the “free will” or as a result of a “biological process” is beyond the scope of this article, and both these possibilities are supported by the conclusions.

Free Will: A rational decision making entity separate from the actors physical body.

Biological Process: The sum total of all chemical, electrical and other processes in actor’s physical body.

Society: Someone other than the actor. For completeness sake, let me mention that this article does not debate on existence of society or the actor itself, maybe its in perception, but it does not matter. An important deviation from common definition of society, is that I include the notion of “God” as being part of the society. Again, its existence questions being irrelevant for this article. Moreover, I argue (assume) that society is a necessary condition for a debate on “morals”. If the society does not exist (in perception), then the existence of morals is itself challenged. Finally, two emotions will play an important role in the analysis of morals: Fear and Guilt. I mention them here, as both these emotions depend on society for their sustenance.

Perceivable Personal Benefit Acts: Acts which are intended to produce results perceived by the actor to be in his/her benefit. These acts could be physical necessity, for example the act of drinking water, or perceived personal need, for example shopping. Notice the use of “intended”. This shall be usually omitted hereon, as all acts will be classified based on intention, rather than the results they produce.

Long-term Personal Benefit Acts: Acts which do not have a direct perceivable benefit, but result in one in future. The actor might or might not think about these long term benefits. For example, doing someone a favor (in the hope of/and)  getting a favor in return in future.

Social Benefit Acts: These acts are the ones that necessarily result in benefits of society as defined above. Again, the actor may or may not reap a direct or an indirect benefit. The act of picking up garbage from street and putting in the dustbin would be one such act. Some people might argue that this ultimately leads to the increased “happiness” of the actor. Please see the note on “happiness” for clarifications.

The world of “fair” acts (WOFA): A world of “absolute fair” and “absolute unfair”.  More precisely it means, that in a given situation there is an act that is fair in absolute sense. Its fairness does not depend on personal preferences of the actor. In other words, there exists a “moral highground”. Importantly, this article does not argue for existence of such a world. It is possible that it is a hypothetical construct of the actor’s brain, or otherwise. Many people might be uncomfortable, in accepting the possibility of such a world, and for them, just ignoring the set of such acts would still be sufficient to understand the analysis. For some other, clubbing it with any of the above three sets would be a satisfactory solution. Henceforth, the word “fair” would be used in the sense of “absolute fairness”. An example of the act in this set could be, division of a thing equally between a set of people.

Happiness: This is another overloaded term, and can not be defined by words. However, for the purpose of this article, the assumption (claim) is that all actors act to increase the sum total of their personal happiness at that moment. This is to the extent that the acts of sacrifice, where one might inflict pain on himself, stills lead to an increase in overall happiness (by the satisfaction the actor gets by performing the act). Thus, the actor is actively engaged in increasing his happiness (it is possible, that inspite of the intention, the outcome might not be an increase in happiness)

Right Acts: For many people, “moral” acts are synonymous with “right” acts. If this is the case, then the question “Is it moral?” can be substituted with “Is it right?”. But for some others, since every act is indented to increase the happiness of the actor, all acts are “right” by definition. For simplification, I will follow the latter belief, defining all acts to be intentionally “right” by definition separating it from different possible notions of morals. For those of you who might want go a step further and claim that all acts are moral in the same spirit, please read till the end.

Morals, values, ethics etc: For the purpose of this article, all other terms relating to the notion of “morals” such as values, ethics are considered synonymous. If the reader finds it necessary  to separate them, please let the author know via comments.

Fear, Guilt: Both these emotions carry the commonly accepted definitions. Fear is the  anticipation of pain, and guilt being the pain of not doing an act in a certain way. Fear is easy to understand from a biological point of view, however guilt is a little more complex. It is not clear, why is there guilt. One possible explanation could be, there does exist WOFA and if someone does not do an act from WOFA he will feel guilty, however, it is conceivable that for the same act one might feel guilty, and others might not. Another explanation is that we usually hypothesize ourselves at the receiving end, and if the outcome was not favorable, we feel pain. From an evolutionary point of view, still another is that over time, it has been hard wired into us to feel guilty for acts that could be detrimental to us on average.

Now, finally coming on to the analysis of “morals”. First note that, the four sets of acts defined above, although being exhaustive set of acts, are not mutually exclusive. An act may have benefits personal and societal benefits. Using simple circles to define them as sets, we get a pictorial representation of the set of Acts.

The set of acts

(The small circles in Set C and Set D are intersections with Set B and Set A resp. for completeness).

At first I tried to follow a process of elimination, thinking about all possible sets which could constitute “morals”, but then it became too cumbersome and elusive. Thus, I rather choose to work with few most probable sets of morals.

  1.  Set A: Perceived personal benefits, independent of any other benefits or not
  2.  Set A ∩ C: Perceived personal benefits and social benefits
  3.  Set B ∩ C: Long term personal benefits and social benefits
  4.  Set B: Long term personal benefits
  5. Set C: Social benefits
  6. Set D: Moral Highground

Consider four examples, and how would you classify the acts that follow:

e1) There is a spider in your room, you choose to kill it instead of capturing it and releasing it in a safe place away from the room.

e2) This one is drastic (please note that this example is just for argument sake): There is a country facing population problems. Its socially beneficial to reduce the population of that country, as the resources are limited and there is a strata of population who are not able to contribute anything to the society. The government suggests to exterminate all the people who are unable to contribute positively to the society.

e3) Suppose you want to purchase a commodity. You reach the point of purchase, and you see there is a queue to purchase it.  Every purchase of the commodity needs 5 mins and there are 20 people in the queue.  Your time is as important as time of other people in the queue. You just arrived but see a friend in the middle of the queue. Instead of standing at the back of the queue you choose to join your friend to save time.

e4) You are given a piece of chocolate to share equally with your sibling. You know that you can always overpower your sibling, and he/she is afraid of you and would never complain against you to your parents whom you fear. You decide to keep a major share of chocolate for yourself.

These acts might have no absolute anwers to judge morality of the actor. However, depending upon what your answers are, a definition of morality can be reached for you.

Consider (e1): If someone answers finds the act amoral, then depending on the reasons of his choice, observations about his definitions of morals can be made.

  1. If there is no specific reason, its highly likely that he believes in WOFA, that “killing is amoral”. A rational being is not afraid that the spiders family might know that he killed the spider, and then take a revenge. No one saw him doing the act, so there is no role of society.
  2. Another, possible reason for classifying it as amoral could be that the actor considers the spider as a part of his society and is fearful that his killing the spider, might somehow come back to him. Or at the least, recreates the pain, the spider might feel, and is  guilty. In this case, his morals are more attuned with long term personal benefits

…to be continued.