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Within the
International Baccalaureate Diploma Program, most candidates attend their
classes faced with the paradox of knowledge and confidence. Therefore, the
prescribed title of “we know with confidence only when we know
little; with knowledge doubt increases”, is extremely relevant to the experience in our
educational careers. A possible rephrasing of this title would be “the more we
know, the more we doubt our understanding and hence are more confident when we
don’t know a lot”. However, this particular title also contains ambiguous terms
that require clarification in order to accurately analyze and validate its
claim. For the purpose of this essay, the phrase “to know” will be defined as “justified
true belief”. Additionally, “confidence” is being defined as “certainty”, with
the consideration that there can be degrees of certainty. Thus to “know with
confidence” means that the knower is able
to justify or give plausible reasons for their belief. Furthermore, the phrase “know little” is being defined as
a “lack
of knowledge”. The
use of the term “only” when contrasting “confidence” and “doubt”, implies an inverse relationship between
confidence and doubt and that it is impossibility of their coexistence. This raises the issue of whether confidence and doubt are complete
opposites that cannot coexist. When analyzing the second half of the quote, the term “knowledge” will be defined as “something
assumed as facts, which is used to make the basis of reasoning”. The phrase “with knowledge doubt increases” suggests that an increase
in knowledge leads to an increase in the knower’s doubt about their belief.

Thus the issue of whether an increase in knowledge equates to an increase in
confidence or doubt about one’s belief is also raised. With these conditions in
mind, I disagree with the prompt to a large extent.

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Our first consideration is to what extent is confidence the opposite of
doubt, and thus to what extent can they coexist? The quote implies is that
confidence is the complete opposite of doubt and thus cannot coexist. Using
reasoning, this makes sense as my confidence in what I know increases, my doubt
decreases and vice versa. For example, the more confident I am about applying
integration concepts to find the volume of an area under a curve, the less I
doubt that the calculations that I have completed are wrong. Another example
would be that the more I learn about Mao and the way in which he was willing to
sacrifice lives for the “greater good”, the less I doubt my view that he was a
ruthless leader who was willing to put aside “accepted” morals to achieve his goals  as
I have more evidence that supports my claim. However, a counter claim to this
argument is, in considering personal and shared knowledge, it can be claimed
that an increase in confidence in one’s personal knowledge can give the knower
the ability to doubt shared knowledge and vice versa; hence confidence and
doubt can coexist. An example of increasing in personal knowledge leading to increasing
doubt about shared knowledge can be seen in my study about the effects of
Malaysia’s affirmative action policy on its economy from 2000 to 2010. Most
historians and economists would suggest that as, during that time period, the
policy stagnated Malaysia’s economic growth, it would be advisable to remove
the policy immediately. However, after conducting my study and analyzing not
only the economic effects of the policy, but the political and social impacts,
I doubted and challenged the accepted view on how to progress with Malaysia’s
affirmative action policy. I believe that the immediate removal of the policy
could cause more detrimental effects, not only to the economy, but to political
and social stability, as it would potentially cause social tension and the
marginalization of genuinely disadvantaged sections of society and those who reliant
on the patron state. An example of an increase in shared knowledge causing
doubts about personal knowledge can be seen in the acquiring of mathematical
concepts as the knower progresses through their academic career. For example,
in the early years of my mathematics career, I believed that ? was equivalent
to 22/7, and thus was a rational number, and that infinity was a number, thus
making it my personal knowledge. However, as I progressed into the later years
of my mathematics career, I was taught, through shared knowledge, that ? was
not equivalent to 22/7 and was an irrational number, and that infinity was not
a number but rather an abstract concept describing something larger than any
natural number. Considering the claim and the counter claim it can be concluded
that within the realms of pure personal knowledge, confidence and doubt are
almost complete opposites, however, when considering the effects of personal
knowledge on shared knowledge and vice versa, confidence and doubt can easily
coexist.

Another issue raised by the prompt as stated in the introduction is
whether an increase in knowledge equates to an increase in confidence or doubt
about one’s belief and thus raises the question, in terms of mathematics and history, can an
increase in knowledge lead to doubt? In terms of mathematics, as mathematics is built on
definitions, axioms, and proofs the acquired knowledge is objective and thus
only has one answer, hence an increase in knowledge of mathematics leads to a
decrease in doubt. This can be simply exemplified in the example of 1 + 1 = 2
or that a triangle is a polygon made of 3 sides. Often, mathematics is used to
make subjective situations more objective such as when comparing whether Lin
Dan is a better badminton player than Lee Chong Wei. While the question is
subjective from one person to another, one can use mathematics in the form of
statistics to compare the two players without any bias.  However, it can also be argued that an
increase in knowledge of mathematics may lead to doubt when applied to
real-world situations as pure mathematics is built on the assumption of a
“perfect world” which, in that sense, does not exist. An example of this can be
shown through my mathematical investigation in which I attempted to model the
trajectory of an overhead clear in
badminton. To be able to apply mathematical concepts, I had to work on a number
of assumptions which made the situation become unrealistic. When I tried to
replicate the equation that I had achieved through mathematics in real life, I
found that the outcome differed greatly to the theoretical result as a
consequence of the assumptions that had been made. History, on the other hand,
is subjected to the fact that human beings are prone to bias, and
historians often interpret the same facts very differently, and hence, an
increase in knowledge of history could lead to increased doubt, as there can be
many interpretations about the knowledge gained. The fragmented nature of
historical evidence and complexity of historical events, permits multiple
contradicting hypotheses to exist at the same time. Additionally, historians often
study the past through the form of incomplete documents that can themselves be
affected by bias and human error. Furthermore, historical events can never be relived,
and thus, cannot be fully proved as truth. This is evident in Jung Chang’s
study and retelling of Maoist China where she is often accused of being biased
against Mao owing to the hardships her family faced during his regime. It is
also evident in the phrase “history is told by the victors”, where often times
the “victor” in conflicts is often portrayed as the “protagonist”, while the
“loser” is depicted as the “antagonist”. An example of this is the outcome of
World War II where American and the Allies are often painted in a good light
and many of their own atrocities are not recorded in any obvious fashion
whereas the wrongdoings of Germany and the Axis powers are persistently highlighted.

Nevertheless, it can be argued that an increase of knowledge in history does not lead to doubt but
leads to an increase in knowledge and acceptance of different perspectives. Given
that it is very difficult to be certain of historical facts, accepted truth
would often be found in the middle ground. This is exemplified by furthering of
the earlier example about Mao. While Jung Chang has a view that Mao was
extremely cruel and ruthless, Edgar Snow held the almost opposing position,
maintaining extremely positive views on Mao as a strong leader who brought
reform to China. Both historians experienced Mao’s China first-hand and yet
developed very contrasting views. In terms of their perspectives, one reports
on life within the regime, whilst the other reports as an observer. In learning
from both perspectives, arguably, we are able to derive a more rounded view
about Mao’s personality, intentions, beliefs and administration of his regime
and reach a conclusion that the “real” Mao is somewhere in between the two
historians.

Through
analyzing two knowledge issues: “to what extent
is confidence the opposite of doubt, and thus to what extent can they coexist?”
and “in terms of mathematics and history, can an increase in knowledge
lead to doubt?” it can be concluded that, in
terms of history and mathematics, the prompt “we know
with confidence only when we know little; with knowledge doubt increases” is
false to a large extent, as although confidence and doubt are almost complete
opposites in terms of personal knowledge, it is possible for confidence and
doubt to coexist in terms of personal and shared knowledge. Additionally, an
increase in knowledge does not necessarily mean an increase in doubt as
discussed earlier and thus disproves the claim that “with knowledge doubt
increases”.

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