Theory of Knowledge
“We know with confidence
only when we know little; with knowledge doubt increases”
(Adapted from JW von Goethe). Discuss
this statement with reference to two areas of knowledge.
May 2018 Examination
Word count: 1583
thought provoking statement alluding to the Socratic paradox; “I know that I
know nothing”. The significance of the statement roots its relevancy in
understanding human thought process and behavior. The matter in question encompasses
a variety of areas of knowledge and is arguably linked to many more, maybe
smaller, areas of life. Initially, the first thought that came to mind was the
correlation strength between my confidence and the extensions of my own
knowledge. In an exam situation or when giving a presentation we source our
confidence in the knowledge we have. This as a small example of how direct our
confidence is linked with knowledge. However, knowledge is a resource used in
many, if not all, fields. This causes the quote at hand to border more themes. So,
does the attainment of knowledge always result in increased confidence?
order to properly develop an understanding and to either refute or accept the
claim of the title, one has to break down the sentence and define all the key
terms. Knowledge and doubt stand out as the key figures to focus on. Firstly,
knowledge is defined as theoretical and practical understanding of a subject;
the awareness or familiarity of a fact or situation1.
Secondly, doubt is defined as the feeling of uncertainty or lack of conviction2.
For the sake of consistency and ease of understanding, the title statement will
be analytically extrapolated into a more defined sentence; this being: an
increase of understanding and awareness of theoretical and practical concepts
is followed by uncertainty or lack of conviction. This essay will apply the
title statement to the following Areas of Knowledge: mathematics and history.
is worth noting that confidence and doubt are subjective terms. A personal standard
exists upon which an individual determines whether they are confident or
doubtful. This standards varies from person to person, and can even change
within the same person depending on what is pressing to be evaluated. To
illustrate, a person’s confidence can be dependent on their mood, their
expectation or ambitions and several other personal factors. Ultimately, the
trigger of one’s confidence varies in each person. Some people are confident
that vaccinations cause autism even though vast irrefutable evidence has been
repeatedly presented which shows otherwise3.
The point being that human emotions also have a large role in deciding whether
a person will be confident within a subject of knowledge4.
In theory, this same examples can be used in both history and mathematics, were
ultimately emotions will decide whether the person has formed a conviction or a
lack of. However, though worth noting that emotions are volatile and vary from
person to person, this argument will not influence the conclusion of the paper
because of the very same nature of it.
when exactly can we say that we are confident about something? I can
confidently say that my banana ice cream tastes like banana ice cream because of
the knowledge I have surrounding bananas and ice cream. I know what banana
tastes like and I know what ice cream tastes like. I can also confidently say
that Ronald Reagan was president in 1981, based on the knowledge that I have
surrounding US politics and history and other subjects, as well as photographic
and video evidence. The result of using my knowledge, on ice cream and banana
tastes, is that I hit a wall; or final stage, at which I can confidently conclude
that the ice cream tastes like banana ice cream. The outcome of stringing all
the evidence together is this wall, there is nothing beyond and the final
question has been answered and thus one can be truly confident about what
happened or what is. As such, the real question of the title is that of whether
a person can hit the “wall” stage in all areas of knowledge.
is the study of past events, particularly in human affairs. In history, the
aims are to uncover and accurately draw the image of what happened in the past.
To do this, one must combine the factual and circumstantial knowledge with the economic,
cultural, political, and among other motives of the people at a certain time. This
knowledge is composed of sources such as pictures, articles, recordings,
archived speeches and expressed perspectives from individuals. History is a
concrete example of an AOK where confidence has a strong and positive
correlation with increased gain in knowledge. Nazi Germany was host to a series
of yearly rallies between 1933 to 1938, commonly known as the Nuremberg
Rallies. Historians know exactly when these happened, why they happened and how
they happened. Available to us are the diary recollections made by Julius
Streicher, leader of the Nazi branch in Nuremberg, the expressed perspectives
of multiple people within the crowd and most importantly the famous propaganda
film, Triumph of the will, by Leni Riefenstahl which depicts
Hitler’s arrival and the rally itself. In this case, the more sources of
evidence that we gather the more we know what happened at these rallies. We know
that Hitler gave a speech and that more than 700,000 party members attended5.
The facts and general belief of what happened those days remain uncontested
because of all the strong and vast evidence supporting the idea of what
happened. Thus here we reach a knowledge wall and can confidently conclude on
what happened at these rallies. However, it can be argued that during process
of investigating a historic event there are stages where doubt arises due to
produced knowledge. For example, flight MH17 which was a commercial plane
flying from Amsterdam to Kuala Lumpur was shot down over Ukraine in 2014. Due
to the location being in a warzone and heavy restriction on investigators from
Ukrainian separatists it took over a year to accurately assess what had
happened. Throughout the investigation, several theories sprung from the facts
uncovered at certain stages of the examination. Theories that were based on the
knowledge known at each stage. Initially it was believed to have crashed due to
mechanical failures, but as investigation continued it was discovered that it
was shot down by the separatists themselves and then ultimately it was proven
that the weapons came from the Russian side of the border6.
When it was first discovered that it was shot down the question of who did it
and why came to fruition. Though ultimately once all evidence was gathered, the
final verdict was proposed and there is little doubt as to what happened that
is the uncovering of abstract topics such as quantity, structure, space and
change. In the subject of mathematics, knowledge is composed of the axioms,
theorems, formulas and equations. Axioms which are statements or proposition on
which an abstractly defined structure is based as they are regarded as accepted
or established ideas. The use of axioms is particular to mathematics because it
opens doors to discovering new formulas and theorems. However, discovering new
theorems upon already existing theorem is also a possibility. So when a theorem
is developed, it is like opening a door to a room full of other doors, a
metaphor explaining that discovering a mathematical theorem opens up to the
possibility of further discovering new theorems based on previous knowledge.
The statement “Increase of understanding
of theoretical and practical concepts is followed by uncertainty” is by a
large degree true. This can be credited by exploring the process that Fibonacci
took to learn and solve the cubic equation (x^3 + 2x^2 + cx = d). The cubic equation
is part of a branch of discoveries, which start all the way back to simple
mathematical concept such as summation and subtraction. Algebra, in particular,
was the main attributor to Fibonacci’s learning of the equation and the
solution to it has offered another route upon which mathematicians can base new
mathematical formulas, theorems and equations7.
What can be deduced by the process is that in mathematics, knowledge produces
more knowledge and thus the subject will always be shadowed by doubt of ever
reaching an end.
conclude, the statement presented for discussion in this essay, though true for
some matters, does not work in all subjects. Increased confidence will usually
follow the increase in knowledge of a subject. However, when knowledge comes
from previous knowledge, confidence in what is known will always be taken with
a grain of salt. Especially, if there are several different ways to arrive at
the same theorems. In mathematics, knowledge is produced from knowledge and
thus the ever expansion of the subject will cause skepticism of the study. On
the other hand, the subject of history is knowledge produced by the uncovering
of evidence. The more evidence the more confident one is that something
happened. And so, with both cases as examples that refute and accept the title,
it can be safe to say that the title is dependent to the areas of knowledge chosen.
In addition, as stated before, confidence is also dependent on the person. A
mathematician could just to believe that a theorem is true no matter what, even
though there might be others that completely refute it, which accentuates to
which degree emotions rule over our confidence. As closure, this essay’s conviction
is that the statement holds truth depending on the circumstance and subject at
– Abel, Reuben. “The Study of History.”
Man Is the Measure: a Cordial Invitation to the Central Problems of Philosophy,
Free Press, 1976, pp. 164–165.
– “Doubt Meaning in the Cambridge
English Dictionary.” Cambridge Dictionary. Accessed December 17, 2017. https://dictionary.cambridge.org/dictionary/english/doubt.
– “Knowledge | Definition of
knowledge in English by Oxford Dictionaries.” Oxford Dictionaries |
English. Accessed December 17, 2017. https://en.oxforddictionaries.com/definition/knowledge.
– “MH17 Ukraine plane crash: What we
know.” BBC News. September 28, 2016. Accessed December 17, 2017. http://www.bbc.com/news/world-europe-28357880.
– Unknown. “History of Algebra”. https://www.algebra.com/algebra/about/history/.
– Nyhan, Brendan, Jason Reifler, Sean
Richey, and Gary L. Freed. “Effective Messages in Vaccine Promotion: A
Randomized Trial.” Pediatrics. March 03, 2014. Accessed December 17, 2017.
– The Editors of Encyclopædia Britannica.
“Nürnberg Rally.” Encyclopædia Britannica. December 10, 2007.
Accessed December 17, 2017. https://www.britannica.com/event/Nurnberg-Rally.
| Definition of knowledge in English by Oxford Dictionaries.” Oxford
Dictionaries | English. Accessed December 17, 2017.
Meaning in the Cambridge English Dictionary.” Cambridge Dictionary.
Accessed December 17, 2017. https://dictionary.cambridge.org/dictionary/english/doubt.
Brendan, Jason Reifler, Sean Richey, and Gary L. Freed. “Effective
Messages in Vaccine Promotion: A Randomized Trial.” Pediatrics. March 03,
2014. Accessed December 17, 2017. http://pediatrics.aappublications.org/content/early/2014/02/25/peds.2013-2365.
Reuben. “The Study of History.” Man Is the Measure: a Cordial Invitation to the
Central Problems of Philosophy, Free Press, 1976, pp. 164–165.
Editors of Encyclopædia Britannica. “Nürnberg Rally.” Encyclopædia
Britannica. December 10, 2007. Accessed December 17, 2017.
Ukraine plane crash: What we know.” BBC News. September 28, 2016. Accessed
December 17, 2017. http://www.bbc.com/news/world-europe-28357880.
Unknown. “History of Algebra”. https://www.algebra.com/algebra/about/history/.