To what extent is truth different in mathematics, the arts, and ethics?

International Baccalaureate Theory of Knowledge

In order to answer this question effectively, one must begin to identify what exactly the question implies. Because the question is asking the ‘extent’ that truth is different in mathematics, the arts, and ethics; one must examine how different and similar each area of knowledge is concerning the truth. ‘Truth’ can be defined as something with justification, so one must examine how justified elements are related in the areas of knowledge (AOKs). One must clarify assumptions that though mathematics, the arts, and ethics are different subjects and require different ways of thinking; one should realize that there are parallels between them. Though truth in the arts and ethics are more similar to that in mathematics, there are connections between all of the truths. One must investigate the AOKs and the associated ways of knowing (WOKs) such as perception, emotion, reason, and language. At a first glance, it can be viewed that there is a ‘universal truth’ that connects everything, and in this essay, this will be explored in detail.

In order to discern the difference between the truths in mathematics, the arts, and ethics; we must first question whether or not mathematics is an ‘absolute’ truth. The mathematician Joel Spencer once claimed that mathematics is “as close to absolute truth as [he] can see [it] getting.” Mathematics is considered to be axiomatic and based on axioms; where the truth is self-evident and undeniable. It is as such because it is based on numerical theorems and formulas (that are universally accepted as true). Therefore, it is assumed that the truth is ‘absolute’. Evidence that mathematics is an ‘absolute’ truth can be found in the Pythagorean Theorem.

An example can be viewed from my own experience as an IB student. In mathematics, we learned about the Pythagorean Theorem. The Pythagorean Theorem’s purpose is to find the unknown length ‘c’ by using the above equation. If ‘a’ is 3 and ‘b’ is 4, then how does one find ‘c’? By using the Pythagorean Theorem (on a right triangle), we add the squared versions of 3 and 4 to equal 25. We then find the square root of 25 to find 5. Therefore, ‘c’ is equal to 5. By rearranging the equation, one can prove that the Pythagorean Theorem works. Instead of 𝒂²+𝒃²=𝒄², one can use 𝒄²−𝒃²=𝒂². So 25 minus 16 equal 9. And the square root of 9 equals 3. This shows how the truth in mathematics is ‘absolute’ and that it is reliable because the answer found in the equation 𝒂²+𝒃²=𝒄² was the only answer that could have worked for the proving formula; 𝒄²−𝒃²=𝒂². Accordingly, one can say that because of this, mathematics refers to the correspondent theory of truth. This is because it can be justified with incontrovertible empirical evidence and the application of deductive reasoning (i.e. the Pythagorean Theorem). It also can be seen to refer to Plato’s idea of ‘true, justified belief’. Mathematics can be viewed as an ideal of Plato’s beliefs because (as seen above) mathematics is about justifying itself in order to determine the truth.

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On the other hand, there are instances where the truth in mathematics is not ‘absolute’. Limitations in mathematics are the fact that it can only be true if the axiom that it is based on is true. If an exception to the formula to determine a circle’s radius (for example) is discovered, then the answers to any variation of the formula would be disproven. Also, another way that mathematics doesn’t have an absolute truth is because there are mathematical uncertainties. If there are mathematical uncertainties, then mathematics would become ‘partially’ true instead of ‘absolutely’ true. An example of such an uncertainty is whether or not the number 10 is a solitary number. A solitary number is a number that is a prime number, a power of a prime number, and a number with a greatest common divisor of 1. It also doesn’t have (what is called) a friendly pair. Friendly pairs are numbers that have divisors adding up to the other number. According to mathematicians, the number ten doesn’t seem to have a friendly pair, but this cannot be strictly proven. Because of this uncertainty, one can say that mathematics is not ‘absolute’.

I believe that mathematics is ‘absolute’ because I’ve learned mathematics in class, and have succeeded in obtaining an ‘absolute’ truth for various equations. Because I’ve done a large amount of mathematics from a certified mathematics teacher, my view that mathematics is ‘absolute’ will differ from someone with less mathematical experience. One should note the fact that the way of knowing, language, that mathematics is universally recognized all over the world (the same symbols and numbers are used everywhere). Because it is a universally accepted ‘language’ that further emphasizes that it is a universal truth. Though there are exceptions in mathematics in discovering the truth, one comes to the conclusion that mathematics is still an absolute truth because the numerical relationships that exists in mathematics is the for the most part objective. And depending on the circumstances that mathematics is under (such as the use of the Pythagorean Theorem) the truth that can be discovered is actually ‘absolute’.

Next, one must ask themselves if the truth in the arts is as strong and objective as the truth in mathematics. In the arts, the truth is often discovered by experts in the form of beauty. The creator of the art in question usually creates the art in (what they believe) a shape that they find beautiful. The arts can be seen in a form of objectivity and subjectivity. One way that the arts can be viewed as objective and as strong as mathematics is from the idea of ‘universal beauty’.

If one were to look at Vincent van Gogh’s ‘Sunflowers’ as an example, there are many people (experts, other artists, the general public, etc.) that view this painting as beautiful. Because so many different people have the same view of the painting, one can say that it has a ‘universal beauty’ where it appeals to different people. This is similar to the truth in mathematics being ‘absolute’ in that there is objectivity in the art. Though we are limited to the confines of our senses and feelings because we are humans, the fact that some art has a ‘universal beauty’ where it is universally accepted as beautiful proves that art can be objective. In this case, truth in the arts refers to the pragmatic theory of truth. Even though it seems that there is subjectivity (due to the fact that emotions/feelings play a part) the fact that there is an agreement through a consensus, makes this type of truth objective.

By contrast however, art can be viewed as being more subjective than mathematics. Instead of art being ‘universal beautiful’, it can be seen as ‘regionally beautiful’. For example, I am a fan of paintings from Vincent van Gogh (especially The Starry Night). However, when I showed a picture of the painting to one of my friends in Bangkok, they said that they didn’t like it. It’s possible that because of the region that we both grew up in has changed our perspective. I was born and raised in Texas and just recently moved to Thailand, whereas my friend has lived in Thailand his whole life. Therefore, one can say art is more subjective because of the fact that there are so many other influences (i.e. age, gender, religion, etc) that can alter one’s perception of art. Because of such aspects, the truth in the arts is different than that in mathematics because (for the most part) gender, religion, age, etc. won’t influence the final result in mathematics. One could also say that truth in the arts is different from the truth in mathematics because it refers most to the coherence theory of truth. It refers to this theory of truth because it involves the application of inductive reasoning, which can lead to a bias of opinion. Though art being ‘beautiful’ can be objective, the fact that there are so many different biases in society today leads one to believe that the truth in the arts is less strong and objective to the truth in mathematics.

The last area of knowledge that one needs to look at is ethics. Are ethical choices truer when based on objectivity or subjectivity? The truth in ethics is based on not only one’s moral decisions and beliefs, but also the legal system (which exists to give out fairness and objectivity) in which we live by. One can say that there is an ‘absolute’ truth (as in mathematics) because of the fact that there is a ‘universal’ set of ethics. And because there is a ‘universal’ set of ethics, the ethical choices for people are unchanging and fair. And one must note that when ethics are used in this way, reason plays a large part because one must think objectively. For instance, I have a reasonable amount of education on a few of the major religions in world – Judaism, Christianity, and Islam. And because of the knowledge that I possess on each religion, I know that killing for selfish reasons (i.e. for one’s own desires) is considered to be ‘wrong’, and is strictly forbidden in all the religions. The truth in ethics can also be considered ‘absolute’ because there are some rules that (depending on the person) will never change – i.e. the Ten Commandments. The truth in ethics refers to the pragmatic theory of truth (as does the arts). Because the truth in ethics has a practical use for individuals (i.e. reducing crime in the world) that works (to an extent), then one realizes that it is useful to believe in these rules of ethics.

On the other hand, one could claim that if a person is more subjective when dealing with his/her set of ethics, the choices that are made could become truer. If one only deals with their ethics in an objective and rational manner, then the outcome would be a ‘cold’ solution and therefore unethical. For instance, if I was in a situation where I had to kill in order to survive (self-defense), I must be subjective. If my ethical set of rules was completely objective, I would be against the very notion of murder and would allow myself to be killed. However, many people would view that as an unethical choice because I allowed myself (an innocent person) to be killed by a murderer. Therefore, one would assume that it would be more ethical to defend against such an attack. One should realize that emotion takes a large part here because if one doesn’t feel the emotions at the moment, and were thinking with more reason, then it would be impossible to use one’s ethics subjectively. By being subjective, the ethical issues would be technically truer because my actions would be viewed as more ethically correct. One should note that the truth in ethics is similar to that in the arts because depending on one’s age, religion, gender, and other biases; one would be more inclined to kill in self-defense. The truth in the ethics is similar to that of mathematics because there are always exceptions to the rules. In mathematics, most of the equations in the world have solutions that scientists at least believe to be correct. However, there is always some exceptions to that rule (i.e. 10 as a solitary number). The same process is with the truth in the ethics. People generally have a set of ethics that can always contain exceptions when they are in a situation that demands that it would be ethical to do so. When considering both sides of the argument, one concludes that when ethics are used subjectively, than the ethical choices become truer.

In conclusion, one can say that though there are differences in the truths of mathematics, the arts, and the ethics; there are also similarities. In mathematics, there is generally an ‘absolute’ truth that is objective, yet there are some uncertainties in mathematics that can classify it as a ‘partial’ truth.

The truth in arts, though it is normally associated with subjectivity, there are cases when in can be objective. And for the truth in ethics, it should be subjective, yet if there were no objectivity involved, there would be no legal power controlling the chaos. The implication for this question is whether or not there are consequences if the truth in each is different. These three areas of knowledge are important in day-to-day, and the fact that the truths are different is beneficial and negative. If the truths in life cover a wide array of different aspects of knowing – perception, reason, emotion, reason, objectivity, subjectivity, etc. then we will be able to comprehend more about our surroundings. However, since the truths are different, we are more perceptible to influence – and therefore to having an inaccurate picture of what truth is.

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