The Firstly, to what extent does gaining knowledge

The title suggests
that as we gain more knowledge through experience or study, doubt increases. This
claims that our confidence and faith in knowledge is inhibited which hinders
certainty as well as we learn more. For example, when I was studying IGCSE physics,
I was highly confident and certain about what I was studying but as I progressed
to IBDP standard level physics, as concepts became more complicated, my doubt
increased and my confidence of the subject decreased. In a broader sense, this
phenomenon can be recognized across a range of disciplines, academic fields and
from the perspective of experts and non-experts alike. To analyze this claim, I
will respond to the following two knowledge questions. Firstly, to what
extent does gaining knowledge of the natural sciences limit our confidence in
its understanding? Secondly, how far can knowledge gained within the
mathematics provide us with certainty?

In this essay, I am going to illustrate and
evaluate the central claim, with a balanced approach using supporting evidence.
To answer these questions, I will explore the role of
doubt in furthering the development of the Natural Sciences and how far the
application of Mathematical concepts in other areas of knowledge limits the
certainty and therefore confidence of the knowledge produced.

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In the Natural
Sciences, it can be suggested that increased knowledge limits our confidence in
its understanding. The nature of science is a constant development. For
example, if a new hypothesis comes up, it will drag new questions, and proofs
are required if the new hypothesis is to be appreciated as science. According
to Karl Popper, he claimed that scientists don’t use inductive reasoning but use deductive reasoning.
By having more experiment about the theory, new observations that contradict
the conclusion can come out. Scientists then prove that the hypothesis is wrong
and this is called falsification. Therefore, falsifying the theory with new
observation suggests that any current established knowledge can be disregarded.
And since we disregard current established knowledges, our confidence starts to
decrease. For example, Stuart Firestein, a teacher and neuroscientist suggested
that knowledge generates ignorance. He illustrates that James Clerk Maxwell
said that “Thoroughly conscious ignorance is the prelude to every
real advance in science”1. It means in some point of science we have to neglect
what we know. Because the nature of natural science is constant development,
scientists keep research for new knowledge. Thus, knowing a lot of more data
leads to more ignorance. And we use our knowledge to create a higher quality
and better ignorance. According to a graph of what people know about something and
how much do they actually know about it, undergraduate students have a high
interest on everything but they have a shallow knowledge about them. Master’s degree students know more than undergraduates but
their interest has been decreased and PhD students know a lot about nearly nothing.
Therefore, what do students know and how much do they know had indirect
proportional relationship. It shows that as students get higher education,
their certainty on the subject decreases and their confidence might also
decrease as well.


However, there is
also an evidence to suggest that through gaining knowledge in science, our
confidence increases. Scientific method is a rigorous process which provides a
high degree of certainty and reason which increases confidence about developing
new knowledge. Not only reason and confidence, but scientific method provides
us reliability and certainty. Therefore, confidence can increase from
reliability and certainty because scientific method has provided sufficient reasons.
Scientific method includes testing process, analysis of results, comparison
with other similar studies and peer review from other scientists. One example is
the development of vaccination of Ebola. Ebola Virus Disease outburst in
December 2013 and left 27,000 cases and 11,000 deaths in West Africa.2
Due to the problem, an experiment involving 4,000 people has been undertaken by
scientists, doctors and drug companies. When Ebola occurred, lots of researchers
vaccinated every contact of sick people who are willing. To see how well the
vaccine protected people, the group of people were randomly assigned into two
groups. One group received vaccine as Ebola confirmed and another group
received after three weeks. The group which received a vaccine immediately had
no cases of Ebola for 10 days after vaccination but another group had several
cases. This proved to the scientists that receiving vaccination as soon as
possible reduces the risk of getting infected to Ebola from experimenting two
different sample groups. Using an empirical methodology, it allowed the
scientists to generate new knowledge about the Ebola vaccination usage when the
Ebola occurs in a country and this showed scientists how to use the cure in the
future. With this new knowledge, scientist can have more confidence in future
use of vaccination. However, the limitation of the experiment is there are only
thousands of volunteers who got tested for the experiment so experiment is yet
Although there is a limitation, because of this undergone process, people can
trust the vaccination and it will serve people a reliability.


It can be argued
that Mathematics provides us with a highly reliable and certain form of
knowledge which can be applied to a wide range of practical applications,
giving us a confidence about it as an area of knowledge. Mathematics is one of
the most objective and logical areas of knowledge that requires the application
of reason and rational thinking. And because mathematics relies on reason,
answers should be drawn from valid mathematical theorem. For example, Pythagorean theorem is a representative theorem in
mathematics. It illustrates that the square of hypotenuse is equal to the sum
of the square of adjacent and opposite. People can’t debate about this theorem since it has been already
proved by mathematicians. Moreover, I could apply Pythagorean theorem to
concepts I have learned in IB physics. For example, I used Pythagorean theorem when
I tried to find a resultant force vector in a physics lesson. I didn’t have a right-angel triangle but because I had an
obtuse-angle triangle, I extended a line and made a right-angle triangle and
found a resultant force by using Pythagorean theorem. By applying mathematical
knowledge to physics, I could reach a high reliability and certainty. Not only
reason but mathematics also relies on language because unique mathematical
language such as pi( or integral ( can transfer
information to anyone in the world which increases certainty and validity.


Mathematical models don’t always provide
reliable results in their application.

When Mathematics are
applied to a subject such as Economics, it reduces our certainty and
reliability. When I tried to apply mathematical model into Economics, model that
requires probability completely contradicted my mathematical knowledge and it served
me doubt in mathematics. For example, when I was studying microeconomics in year
12, I came across with a concept called “Price Elasticity”. In price elasticity, there is price elasticity of
demand(PED). It shows the responsiveness of
demand after a change in a price of goods. However, where Economic concept
contradicted my mathematical knowledge is when I saw negative percentage sign. In
order to calculate PED, I should figure out the change in percentage of
Quantity demand and the price of goods. When the figure of a previous year is
bigger than the year after, it gives negative percentage value which means that
the amount of price or quantity demand has been decreased compare to the
previous year and in Economics, we express it as –X%. However, what confused me
was in mathematical knowledge, percentage cannot be negative since the
percentage is a certain amount in hundred. But negative percentage came up when
calculating PED (% Change in
Quantity Demand / % Price change). This served me doubt
about my knowledge in mathematical model. Therefore, when I saw negative
percentage, which contracts my existing concept, my certainty started to decrease. Thus, I realized that in a subject such as Economics,
AOK such as Mathematics doesn’t always work.


To conclude, I believe
that the statement “With more knowledge
doubt increases” is fair to some
extent in the areas of knowledge of Natural Science and Mathematics. In Natural
science, because of the nature of Natural Science which constantly develops, if
a new hypothesis comes up, a new question will come up. In order to be
appreciated as a science and gain validity, it has to be proved but because
scientists use deductive reasoning, they always try to falsify their hypothesis
with new observation which disregards current knowledge. Therefore, increased
knowledge of natural science might limit our confidence in its understanding
and more knowledge will enlarge doubt. And this has been experimented by Stuart
Firestein from a survey of how much do bachelor’s students to PhD students know. The survey about how
much they know and what they know showed inverse proportional because PhD
students studies in-depth, which increases doubt. So although increased
knowledge might increase doubt, scientists will have to gain more evidence to
prove their hypothesis and gain validity from other scientists.

Mathematics, one of
the areas of knowledges that relies on reason and language might limit our
confidence when it is applied to certain subjects such as Economics. Although
Mathematics provides us with a reliable knowledge if applied to physics, with a
high degree of certainty, when Mathematical knowledges are applied to
Economics, it contradicts current established mathematical knowledge such as
percentage with a negative sign in some content in Economics, and this will
increase our doubt and decrease our certainty.








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