Final ToK Essay

Theory of Knowledge Essay
To what extent is truth different in Mathematics,
Art, and Ethics?
Name: Martin Lai
Teacher: Mr. Cunjak
Date: June 12th, 2013
Word Count: 1576
Truth is the ultimate goal that we strive for when we acquire and process the
information we gain. It may be said that truth is a knowledge claim that can reflects fact or
reality, and can be reasonably justified. However, this is just a single theory regarding truth.
The concept of truth manifests in different forms and can be very subjective to the knower and
the respective area of knowledge. It is essential to understand what the truth really entails and
how we seek to attain it in our daily lives. Knowledge is a justified true belief; and thus it may
be proposed that truth is an integral part of how we form our knowledge and make informed
decisions. To be able to find the meaning of what truth really represents, it must be explored in
three areas of knowledge: mathematics, arts, and ethics, and by comparing them, hope to draw
a conclusion on what truth is and the implications of acquiring truth in these areas.
Truth in mathematics is an area of knowledge based heavily in using reason as a way of
knowing. Truth in math is to form an answer based on the information and guidelines we are
given, and through a logical process justify our conjecture. Mathematics is based on
fundamental principles proposed by mathematicians and accepted as truth by the community
of knowers. These basic truths are then manipulated in the search for new knowledge. This
suggests that truth follows strict existence in mathematics, since new truths must be based on
pre-existing ones and everything must be justified and fit within the established paradigms. For
example, in my calculus class, one of the first things taught to us was how to find the slope of a
tangent, named the derivative, and the formula to do this was called ‘First Principles’. All of
calculus is based on this one concept, and it was through reasoning that mathematicians were
able to create new knowledge based on this idea. Whenever we do math questions, we are
required to show all the work and the process is equally as important and the solution. The
notion of truth being acquired through a systematic and logical process is suggested by the
Coherence Theory of Truth, which proposes that if an argument follows valid deductive
reasoning and the premises are true, then the conclusion must also be true. Therefore, in
mathematics it can be said that there is a single set of truths that we can accept with certainty
since they have been justified and fit a logical progression; the emotions and subjectivity of the
knower do not influence this process and therefore plays no role in determining truth.
However, an argument against this is that since all of this truth is based on a few fundamental
principles, if these principles are disproved or a new set of principles are created, then we will
have multiple sets of truths that are subjective to the specific principles they are based upon.
For example, there is a Euclid math contest in our school each year which is named after a
famous mathematician known as the father of geometry. Even though his claims were
accepted as absolute truth for many centuries, a mathematician named Carl Gauss was able to
work outside of Euclid’s fundamental framework and created a new set of truths for geometry.
According to coherence theory, both are still true since they follow logical progressions, but
approaching math from Gauss’ perspective would yield very different truths from Euclid’s.
Despite this, since mathematical knowledge claims must be accepted by the community of
knowers, it is more valid to suggest that we designate a single framework as truth and put
others aside when dealing with mathematical knowledge claims.
Art on the other hand, is presented in many different forms, with each piece of art being
a unique representation of an idea or a sentiment, and therefore truth cannot be acquired by
simply applying the same logical principles as in mathematics where everything follows a logical
progression and is derived from other truths. Instead, truth is being able to evaluate the
meaning or value of each piece of art as an individual creation. As opposed to in mathematics,
the knower’s interpretation of art, the interpretation of the community of knowers, and the
intention of the artist in presenting art must all be taken into account when dealing with art as
a source of knowledge. An example of this is when I drew a picture of a heart in my biology
class. I thought that I had drawn it very well and showed it to a classmate, who did not consider
it as art and justified it by saying that the purpose of diagrams is to be informative rather than
to invoke an emotional reaction. In this situation, truth was subjective to the classmate’s
interpretation of the art. They did not consider the heart as art, since their logic told them that
a diagram could not be considered art. However, as the artist my intention was to present the
aesthetic qualities of the heart rather than draw attention to its scientific aspects. From this
example, we can claim that truth is very subjective in art, and is linked to the perspective of the
knower and there is no common truth when addressing the meaning or value of a piece of art.
A counter claim against that notion is that while it is difficult to find a single truth in art, there
are undoubtedly guidelines for addressing knowledge claims in art to allow us to compare our
own truths with that of the truth accepted by the community of knowers. For example, in a
wedding photo, the lighting of the photo, the depth and angle at which it was taken, and its
ability to highlight the bride and groom’s smiling faces are all essential to the photographer
when deciding if the photo is good or not, and by using these guidelines they are able to attain
a truth that is not only personal but widely shared amongst other photographers as well.
Ultimately however, even these guidelines can be subjective and be interpreted differently by
others; there is little certainty that the truth gained by an individual will be shared exactly by
others in the community of knowers due to the variations in which art can be interpreted.
When examining truth in ethics, it is important to understand that there are several
theories denoting what the moral code should be. This immediately brings forth the idea that
truth is relative to the moral code of the knower, and in determining if a person’s decisions are
morally correct a combination of reason and emotion as ways of knowing are required to reach
a conclusion. For example, for one of my CAS projects I joined the cross country team. Another
runner from our school had injured their leg but decided to run the race regardless. I did not
want them to be left behind so I ran with them, but it quickly became apparent that we were in
last place. At that moment I had to choose whether to run ahead or stay to motivate them.
This was a difficult decision to make, as I reasoned that sportsmanship and friendship was
important to me as well as being able to put my full effort into a race that I trained rigorously
for. However, my emotion response of wanting to win made me run ahead and helped me
make that tough decision concerning ethics. This example suggests that while we may have a
general moral code, we manipulate it to suit the needs of specific situations, where reason and
emotion are used to make that decision. This is similar to truth in art as there is no absolute
truth, but rather truths that are relative to the perspective of the knower and involves the use
of emotion to make a decision. The difference is that in ethics there is the added use of
reasoning based on specific principles to acquire truth, similar to truth in mathematics.
However, since our moral codes are relative and adaptable to our emotional response to a
situation, completely objective truths are difficult, or even impossible to obtain. On the other
hand, it can be argued that religious theories of ethics present a universal moral code and
following them can lead to the creation of objective ethical truths. Although this is true, many
extreme moral codes such as killing those who work on Sabbath in Christianity conflict with our
ideals against killing, therefore nullifying the argument that we are able to follow these
religious codes completely without introducing aspects of moral relativism.
The concept of truth varies in these three areas of knowledge, but there are conclusions
that can be drawn about the nature of truth. All of these areas share the notion that while
there are guidelines to attaining an objective truth among a community of knowers, there is
certainly no absolute truth. In most situations we manipulate our knowledge based on our own
judgment. Truth in mathematics is more objective since it requires the justification of
knowledge claims, while the arts and ethics focus more on the personal experience of the
knower and involve using emotion as a way of knowing. Ultimately, as a community of knowers
we seek to find objectivity and share common truths, though in each area of knowledge the
criteria for what we accept as truth is inevitably subjective.
Works Cited
"Art and Truth." Art and Truth. N.p., n.d. Web. 13 June 2013.
"The Coherence Theory of Truth." (Stanford Encyclopedia of Philosophy). N.p., 3
Sept. 1996. Web. 13 June 2013. <>.
Dombrowski, Eileen, Lena Rotenberg, Mimi Bick, and Richard Van De. Lagemaat.
Theory of Knowledge: Course Companion. Oxford: Oxford UP, 2007. Print.
"Moral Relativism." (Stanford Encyclopedia of Philosophy). N.p., 9 Feb. 2004.
Web. 13 June 2013. <>.