Through different methods of justification, we can reach conclusions in ethics that are as well-supported as those provided in mathematics.' To what extent would you agree?
As the question indicates, the two areas of knowledge, mathematics and ethics, should be considered and revised thoroughly. Firstly, I would like to define the key words which are going to be analyzed in this essay. Mathematics can be defined as the abstract science of number, quantity and space. This definition of mathematics is quite clear. However, the definition for ethics is much more complex. As the word 'ethics' comes from Greek, it becomes vague and can have various definitions depending on the context through which it is being examined. Roman culture has also made the word ‘morals’ into a synonym, but the two words are not, in fact, the same. For example, an ethical code is the integration of individual moral codes; this is why morality is part of ethics. Ethics can be defined as a system of moral values, as well as a set of principles of right conduct. Furthermore, ethics can be divided into two groups: ethic absolutism - which implies that there is a right or wrong applicable universally; and ethic relativism - which states that such a concept as right or wrong does not exist outside of the values of particular individuals or groups.
Now that the key words have been defined, I would like to consider the way in which we reach conclusions about ethics. This can be done using a form of Kantian argument (by Immanuel Kant, an argument which is based on the rationality of moral behavior) where a question can be asked: “What if doing action x is considered to be morally good, compared to not doing action x?” and figure out the consequences. By considering this rational method of thinking, we can reach the conclusion that murder is an unethical act because if everyone committed murder then there wouldn't be ethics. This argument can also be applied to other examples such as the use of contraceptives, but it will lead to logical consequences.
Mathematics can only be partially applied to other fields, and is only perfect on its own. Mathematical knowledge cannot be used to study human beings or their emotions, as humans are constantly exposed to change and transformation on a daily basis. This makes it impossible to form any general rules in relation to human behavior. Math is closely linked to the use of logic and perception.
In my opinion, it seems that the ethic absolutism approach is slightly more supportive of the statement. When considering ethic absolutism, particular situations in ethics can be as justifiable as those provided in mathematics by using certain methods of justification. Examples of these are: logic, reasoning, empiricism and memory. However, in ethic relativism, conclusions in ethics are only accepted by a certain group of individuals. This causes them to be less supported than mathematics, which is universally accepted for all cultures and situations. For example, ethic absolutism would reach a conclusion that it is wrong to eat human flesh. On the other hand, relativism (for a cannibal) would say that it is acceptable to eat human flesh. An example for absolutism applied to mathematics would be: a math statement such as 1 + 1 = 2. This statement is true, and it does not depend on any factors such as if anyone knows it. It remains true at all times, in all cultures, and in all situations. Additionally, there are four methods of justification (identified by Michael Woolman) which are: justifying through logic, justifying using empiricism, justifying using memory and justifying with a reference of authority. If a knowledge claim is supported by any of these methods, then it is a well-supported justification.
There are three main schools of thought that rise from the question on philosophy regarding mathematics. These theories overlap with one another, respectively, and are called platonism, logicism and formalism.
The Platonist view is fairly straightforward. Central to philosophy is the notion that ideas exist objectively and are independent of us and of our opinions of them. Therefore, a statement such as 1+1=2 is factually correct because one plus one does, indeed, add up to two. Put another way, from a Platonist perspective, mathematical statements are alike to statements like “that pencil is on the chair,” despite the fact that mathematical objects are not as perceptible as physical objects (dpmms).
Logicism attempts to validate our assurance in mathematical statements and overlaps with platonism. Logicism is the position that all maths can be assumed from straightforward and unquestionably correct truisms through the use of logical stages.
Formalism is in direct contrast with Platonism. It can be characterised by the formalist’s certainty that mathematics is but a set of directions used to substitute one set of irrelevant codes with a different set (dpmms).
These three perspectives are helpful in ascertaining the difference between ethics and mathematics. Although a formalist would argue that mathematic statements are meaningless and, therefore, unable to hold a ‘truth’ within them, the rigid structure of it means that its statements are true within the discipline, if nothing else. For the sake of this argument it is sensible to assume that as mathematic statements are true within the field of mathematics, they can be compared to ethical statements which are, debatably, never defined as factually true.
There are different methods of justification in both ethics and math. In math there are different ways of proving a solution, while in ethics the methods of justification can vary as well. Ethics is more an open subject than is mathematics, and it is hard to consider ethics without philosophy. Within ethics, I think that absolutism is slightly better-supported as it looks at the proof and the nature of the proof and it is justified by emotion, reasoning, and observation. Also, in both absolutism and mathematics, the final result is justified by the process of reaching it. It is wrong to commit murder, and this is not justified by the process of making the decision to kill someone and all the events that led up to it. This is also the case in mathematics where a final wrong answer doesn't justify the process of getting there. I think it is the universality and logic of conclusions provided in mathematics which makes them better supported than conclusions in ethics. However, in ethic absolutism it is possible, in part, to reach outcomes that are as well-supported as those obtained in mathematics.
References
DPMMS. “Does Mathematics Need a Philosophy?” Web. 28 Jan 2012.
http://www.dpmms.cam.ac.uk/~wtg10/philosophy.html
