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

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

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.