Ethical Principles explained by Mathematical Logic Pt1

The mathematical logic of the Western ethical principle

1. Birth of the the Western ethical principle and its mathematical logic

1. 1. Introductory to the Western ethical principle:

This chapter explains how political philosophers (Ethical theorists) have developed their ethical theory by means of mathematical logic. There are many academic writers who have described the characteristics of these theories and difference among them. However, there are not so many academic writers who have explicitly explained by means of an explicit mathematical formula. It is critically essential to mention the fundamental principle, such as their world view, basing their ethical theories. These western philosophies are very logically constructed like a mathematical formula, and there is always a sort of mathematical axiom basing their theories.

The axiom in philosophical logic is their fundamental principle which can be called their metaphysics or their world view. These Western philosophers, except majority of Postmodernists, always attempt to create their theories to be rationally constructed and objectively explaining human-characteristics and the world as though they were mathematical formulas. The mathematical formula requires an mathematical axiom in order to keep their theory consistent and being able to objectively self-contradict itself. Therefore, these Western philosophies mentioned over here also require something equivalent to the mathematical axiom.

Almost all academic writers who have written about this staff have already known this mechanism of these Western philosophical theories. But, they tend to need to write one book to explain about it. Perhaps, this is because there are not so many individuals who studied both social science and mathematics simultaneously. Only how majority of them demonstrate their knowledge is explaining with words like writing one literature. Therefore, majority of these books tend to consume a lot of pages with a huge volume of words in order to describe these characteristics and their differences.

This project attempts to explain what axiom, i.e. their world view, they had used to set their formulas within one chapter of one book. By referring to how these formulas were set up, it also explains how the theories created later were developed from the theories having existed earlier.


1.2. Birth of the first Western ethical principle:

During the antiquity, the foundation of Western philosophies was born. When Socrates started thinking about what we actually know about ourselves and our world, ethics was established. Before Socrates came into this world, knowledge about truth and social justice were not considered to be an important to think about. At this time, people hardly questioned about biased knowledge and justice existed to deserve for those who were only physically strong, wealthy, and/or good at using rhetoric to intrigue others. Socrates provoked a spiritual revolution against the world without a righteous justice! Socrates then introduced the idea of pursuing knowledge of truth, having cause and reason which make human-beings virtuous, and obtaining the skill to analyse how our physical world and our spirituality (Soul) are formed. This Socrates' contribution was the most significant event to start developing the Western philosophies such as ethics.

Plato took over the works of Socrates, his master, to develop Socrates' philosophy further. Plato succeeded in transforming Socrates' philosophy to the philosophy which provides a strong guidance for us, human-beings. His philosophy was a revolutionary concept which enabled we, human-beings, to think about how our world is formed and how we should seek to become in order to enjoy happy life. Of course, it is still debated to discuss what the way to enjoy happy life is. But, Plato was the first pioneer who started thinking about it, and attempting to discover the universally absolute way. This is the beginning of the Western ethics.

At this time period, Plato provided a method to analyse what the reality and how the reality should be. The way Plato thought of the world was dichotomic unlike the Eastern philosophies. This method succeeded in explicitly distinguishing between something existing and something not existing in reality as well as between real or unreal. For instance, when there is a substance called A, there are A and not A in reality. This can be considered as a very simple idea nowadays. But, at the ancient time period, this was a very revolutionary concept which has enabled an individual to contradict those who say "not A" as A. It also evolved individuals to start thinking what and why A really is and how A ought to be. There is a famous quite of Plato which is "If government is not how government ought to be, this is not a government". This quote helps us to understand why he put emphasis on what is, or supposed to be, A, and what is not, or suppose not to be, A. Furthermore, Plato provided us with our strong objective to live, which has spiritually strengthened us, human-beings, since then.


1.3. The mathematical logic of the Antiquity:


Aristotle, the most famous student of Plato, developed Plato's philosophy to create a furthermore systematic theorem. Aristotle's philosophy focuses more on the consistency than Plato's counterpart, and introduced an algebraic way of philosophical analysis into the Western ethics. Unlike Plato who argued about whether or not an A is really an A, Aristotle rigorously stated that when a substance A exists as A, this is how A naturally is.

For example, meanwhile Plato believed there is one universally absolute form of how government should be, Aristotle thought that each form of government has its own advantage and disadvantage. Plato claimed that there is one ideal perfect government. By contrast, Aristotle argued that there will not be any perfectly ideal government, and there are only various different optimum choices of forming government at different time periods, regions, and occasions. Thus, when a government consequently resulted in how this government now is, this is an inevitable outcome to become like it under the given circumstances.

Aristotle was also known as a mathematician who created a very discrete (clear cut) logic which leads us to clearly understand and explicitly analyse things in our world. E.g. When only A exists, there are only the component composed of A, A itself, and no A. He tried to prevent any confusing abstract concepts in order to offer clear, consistent, and imaginable analyses. He distinguished between pure mathematics studied in academia and applied mathematics frequently used in our daily life. He had already understood that the imagination and the mathematical estimation are detached from our real world. Even Plato said that the mathematical estimation is merely a tool to lead us to the idea and not quite related to our real world. Thus, if we can neither measure the infinity and complex numbers by a physical tool nor discover the real existence of infinity and complex numbers as a physical form in reality, that both the infinity and complex numbers cannot exist. So, in reality where we human-beings live, there are only A=ℝ\0 (A is any real number except for zero) and so A=0.

Since this ethical principle was formed, it has become a logical foundation of the law from the antiquity to the Renaissance and the mainstream economics. Both the law and the economics attempt to solve problems in our daily life within the limit we are facing in reality. When there is an A supplied, then the demand available for an A is an A or zero. When there is no A supplied, but there is the demand for an A, then we may eventually incur the debt to pay back for -A (Negative A). Otherwise, both the demand and the supply remain to be zero i.e. not A. When a case contains the element of A, then A implies to this case so that this cause is A. Otherwise, this cause is not A. In terms of Civil Law, an A varies across time, place, and occasion. This condition of Civil Law is determined by means of the normative in culture and law makers' interests under a prudent measure. In terms of Natural Law, an A changes overtime but always remains in our world universally regardless of different time, place, and occasion. The condition of Natural Law is determined by referring to this unremovable condition such as a universally existing fundamental morality and principle, which is frequently referred to making laws.