Yew Chung International School of Beijing
IBDP Theory of Knowledge Essay
2010-2011
-Essay Prompt 1: Consider the extent to which knowledge
issues in ethics are similar to those in at least one other area
of knowledge.
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Word Count: 1,600
Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
It is crucial that we explore mathematics and ethics as they arise in many parts of
our lives. They can also apply to other areas of knowledge, influencing the perspective we
use to view the world. To name a few, researchers use mathematical analysis to develop
better ways for voters to express their preferences in elections in attempt to create a fairer
democracy (Brams), and there is an ethical consideration involved when we make the
economic decision of whether to purchase a sweatshirt made from cheap labour. I will
consider the knowledge issues “are mathematics and ethics capable of possessing universal
truths” and “how far are mathematical and ethical axioms similar,” concluding that ethics
and mathematics are only similar to a limited extent.
In relation to my first knowledge issue, the fact that mathematics can explain the
physical world gives us a sense of universal certainty. For example, we can explain the
relationship between surface area and volume using mathematical differentiation, and we
know this is true as we can physically measure the surface area and volume of a sphere,
allowing our perception and observation of the physical world to correspond with
mathematics, altogether providing a more tangible universal mathematical truth.
Humanist mathematicians, however, argue that mathematics are cultural entities
invented by humans as part a “shared consciousness” derived from their social needs
(Moslehian). Evident in the Amazonian Piraha tribe, there are no numbers in their language
as there is no need for quantification in their culture (Kane). Yet, although certain cultures
do not realize the existence of mathematics, which show mathematics can be a social
concept, I do not believe it contradicts to the argument that mathematics is universal. In my
Mathematics IA, my task was to construct a model to describe China’s population growth
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Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
using exponential functions. Although demography is a social concept, the mathematical
calculations are universal as exponential functions can also be applicable to physics, such
as to calculate the exponential decay of radioactivity. Hence, although mathematics can
help us express ideas, construct models, and form new knowledge in other areas of
knowledge (Dombroski 134), the mathematical calculations are unchanging and remain
loyal to themselves. This means there can be universal truths in mathematics as it can be
applicable to all circumstances, cultures, and times.
On the contrary - can ethics possess universal truths, independent of its cultural
context? Similar to mathematics which can be universal regardless of the circumstance, the
establishment of the Universal Declaration of Human Rights recognizes the inherent
dignity and rights entitled to “all people regardless of their race, sex, religion...”(UN) This
suggests that there is a standard ethical code applicable to all of humanity.
Yet, we must be aware that the declaration itself is a man-made document initially
developed by the West only in recent decades. Quite different to mathematics, ethics can be
a social concept that arguably cannot exist independent of the human consciousness and
circumstances, inevitably containing socio-cultural and historical bias. Moral relativism
suggests that morals are only limited to one’s culture, hence there might not be any
universal truth. Although Article 4 of UNDHR states “No one shall be held in slavery,”(UN)
slavery was historically accepted by many societies and cultures, allowing their
civilizations to thrive and prosper. Hence, is slavery a case of moral relativism?
Perhaps we can challenge moral beliefs by examining factual beliefs. Factual beliefs
describe the way the world is, and moral beliefs describe the way the world should be
(Rowlands). Plato supported slavery as he claimed “justice consists in the superior ruling
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Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
over the inferior”(BBC Ethics). This was due to Plato’s ‘factual’ belief that some people
were born as natural slaves with inferior qualities and abilities, creating the moral
consequence that masters were needed to tell them what to do. Yet, we might be able to
realize universal truths in ethics by examining our factual beliefs. Modern technology
allows us to realize the universal knowledge that the human species has biologically similar
makeups and capabilities, creating the factual belief that we are equals, gradually raising
moral concerns regarding the ethics of slavery. Knowing that there are 50,000 modern-day
slaves imported annually into the United States (Patt) –my intuitive reaction is emotional
outrage, but perhaps my belief is further consolidated upon the context that I view them as
equals, allowing me to empathize with their pain, while knowing I would never want the
situation to happen to myself.
Similar to how factual beliefs can develop moral beliefs, we can also discover
scientific knowledge using mathematical facts and calculations. In string theory,
mathematical calculations show that the theory does not work if the universe has three
dimensions of space. By studying the equations, physicians realize the string theory only
works in a universe with 10 dimensions of space and one dimension of time, suggesting
there are more dimensions in the universe than the three that we can visually see with our
naked eye (Greene). Hence, perhaps we can use other areas of knowledge as ‘signposts’ to
gain a better understanding of knowledge in ethics and mathematics/science, and it is this
sense of correspondence that brings us closer to seeking universal truth.
As Einstein suggests ethical axioms are those that withstand the test of time (Alchin
128), perhaps it is only gradually through time that universal truths in ethics emerge,
assuming such truths exist and we are able to recognize it. Otherwise, we can only hold
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Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
beliefs and not universal truths in ethics. Therefore, in the world that we live in today with
conflicting moral beliefs, I believe universal truths are more evident in mathematics than
ethics.
However, although mathematics are more capable of holding universal truths giving
us a larger sense of certainty, there are still limitations to its axiomatic systems, and my
second knowledge issue is “how far are mathematical and ethical axioms similar?”
Mathematics and ethics are both built upon an axiomatic system. An example of a
mathematical axiom can be triangles have three sides, and an ethical axiom can be long
term happiness should be sought for. Axioms create mathematical theorems and ethical
theories, and ultimately mathematical or ethical knowledge. As the initial axioms are “selfevident truths” which cannot be proven since they are the original starting points (Alchin
56), this makes us question how far these initial starting points are ‘true’.
One method to test a claim is to use the coherence truth test, which demands that all
knowledge claims must fit together without any contradictions (Dombrowski 100). In this
sense, mathematics and ethics are different, as mathematical axioms do not contradict each
other while ethical axioms can.
Mathematics axioms pass the coherence truth test, meaning its axioms do not
contradict as I can use different concepts to derive the same solution, such as obtaining the
same answer regardless of whether I use matrices or graphs. Yet, there are limitations to
mathematical axioms. Euclid’s ten axioms were built upon the assumption that space is a
flat infinite plane, but Riemann argued that space could be the surface of a sphere, leading
him to modify Euclid’s first, second, and fifth axioms (Burns). This suggests there are
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Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
different approaches to mathematical truths. Euclid’s axioms are more relevant when
describing the flat planes we see in our everyday lives, while Riemann’s axioms are more
useful in understanding curved surfaces, such as in astronomy. Yet, despite the different
approaches, Euclid and Riemann’s axioms can still co-exist.
Quite differently, ethical dilemmas can occur when there are directly competing
ethical axioms, meaning we have to weigh certain axioms over others. As a student
magazine editor, a friend asked me to publish an article to persuade readers to donate
money for her friend with leukemia in need of expensive surgery. Though I felt I had an
ethical obligation to help my friend, other editors argued that it is unethical as publishing
the article reduces the opportunity of all other leukemia patients from receiving funds.
Unlike mathematics where the outcome remains the same regardless of which method is
used, an ethical outcome can differ depending on one’s choice of premise. Using ethical
egoism as my premise with the axiom “utility should be sought individually”(Alchin 132),
then it is justifiable to publish a personal article to raise money for my friend. If I adopt a
utilitarian approach with the axiom “utility should be sought socially”(134), then I will not
be able to publish my friend’s article and I can only raise awareness on leukemia as a
general cause since social utility must be maximized. Despite my belief that I should help
my friend and all needy leukemia patients to the best of my ability, the existence of
competing axioms means I am facing an ethical dilemma.
Furthermore, theories of moral universalism versus relativism is developed upon
two competing axioms, and we can argue that there are no “truths” to whether ethics is
universal or relative, since the answer will depend on which axiom one chooses to use.
However, one who believes ethics is universal will not acknowledge the existence of a
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Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
relativist’s axiom as self-evident truth, hence the axiomatic system that individuals build for
themselves, based on the axioms they themselves consider to be ‘self-evident’, might not be
contradictory after all.
To conclude, ethics and mathematics are only similar to a limited extent. As
universal truths seem to be harder to recognize in ethics than mathematics, perhaps due to
ethics’ competing axioms as opposed to mathematics’ corresponding axioms – we are less
certain in ethics than mathematics. Nevertheless, we must never stop searching for the
meaning of truth and integrity, while upholding the values and principles that stay true to
us.
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Essay Prompt 1: Consider the extent to which knowledge issues in ethics are similar to those in at
least one other area of knowledge.
Bibliography
Alchin, Nicholas. Theory of Knowledge (second edition). London: Hodder Education, 2006.
Print
BBC Ethics. "BBC- Ethics - Slavery: Philosophers Justifying Slavery." BBC - Homepage. 2011.
Web. 19 Feb. 2011.
<http://www.bbc.co.uk/ethics/slavery/ethics/philosophers_1.shtml>.
Brams, Steven J. "Brams, S.J.: Mathematics and Democracy: Designing Better Voting and
Fair-Division Procedures." Princeton University Press Home Page. Oct. 2010. Web. 18
Feb. 2011. <http://press.princeton.edu/titles/8566.html>.
Brian Greene on String Theory. Perf. Brian Greene. TED: Ideas worth Spreading. TED, Apr.
2008. Web. 19 Feb. 2011.
<http://www.ted.com/talks/brian_greene_on_string_theory.html>.
Burns, Stuart A. "Axiom Systems." An Introduction to Axiom Systems. 2008. Web. 19 Feb.
2011. <http://www3.sympatico.ca/saburns/pg0102.htm>.
Dombrowski, Eileen, Lena Rotenberg and Mimi Bick. Theory of Knowledge Course
Companion. Glasgow: Oxford University Press, 2007. Print
Kane, Ian Luke. "The Pirahã People and Numeracy." Logic Nest. June 2008. Web. 18 Feb.
2011. <http://www.logicnest.com/archives/116>.
Moslehian, Mohammad Sal. "Postmodern View of Humanistic Mathematics." Postmodern
View of Humanistic Mathematics. Department of Mathematics, Ferdowsi University.
Web. <http://people.exeter.ac.uk/PErnest/pome18/pdf/moslehian.pdf>.
Patt, Martin. "Human Trafficking & Modern-day Slavery - USA." 2010. Web. 18 Feb. 2011.
<http://gvnet.com/humantrafficking/USA.htm>.
Rowlands, Mark. "Moral Relativism." The Philosopher at the End of the Universe. London:
Ebury, 2003. 278. Print.
United Nations. "The Universal Declaration of Human Rights." Welcome to the United
Nations: It's Your World. Web. 19 Feb. 2011.
<http://www.un.org/en/documents/udhr/index.shtml>.
Word Count: 1,600
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