Quality a purely logical system of knowledge. Reasoning

Quality can be defined as the
state of possessing a higher degree of excellence when compared to other
matters of similar nature. To measure the quality of a piece of knowledge, one
must identify the criterions that distinguish high-quality knowledge from poor
quality knowledge and is easily refuted. Poor quality knowledge would be one
that is vulnerable to criticism. Quality knowledge needs to have a strong and
clear line of argument or basis upon which the knowledge is developed.
Therefore, knowledge of high quality should possess a high degree of accuracy.
It is also important for knowledge to be highly adaptable and remain relevant
as time passes. So it can be assumed that in order to produce such knowledge,
one must exert exhaustive efforts to eliminate any bias or errors. For
knowledge to be directly proportional in terms of quality and its historical
development, the production of the knowledge must be dynamic in nature.  This means that knowledge needs to be continuously
improved to remain relevant and this may be through trial and error,
experiments and other methods that constitute it to disprove or uncover
previously unknown areas of the discipline. Continuous improvement ensures that
old knowledge is continuously replaced with a more accurate knowledge that is
superior to the previous in terms of precision and validity. This essay will
focus on the dynamic versus static nature of knowledge and their role in
producing quality knowledge in the area of Mathematics and Natural Sciences.

 

Mathematics is a purely
logical system of knowledge. Reasoning is the basis on which knowledge in the
area of mathematics is produced, which relies on logic and rationality. The
pursuit of complete subjectivity is the highest priority in knowledge
production, justifying the dynamic nature of the discipline.  Knowledge production in mathematics follows
under the strict rule that every knowledge produced should be objective and
impartial therefore limiting the scope in which a knowledge can be claimed
without rigorous evidence. Before a mathematical statement is accepted as a
theorem, the opinion that was formed by the mathematician from his observations
must go through an order of logical reasoning that can later prove or disprove
the conjecture. This means that when a mathematician has claimed to discover
something, he is obligated to go through a process to convert personal
knowledge into shared knowledge to eliminate any bias.

 

A notable example of a
conjecture that was later disproved was the findings of German mathematician
Peter Gustav Lejeune Dirichlet in 1838 who proposed the mathematical inequality
li(x)>?(x). Later in 1914, an English mathematician John Edensor Littlewood
claimed the inequality was false although he had no evidence to support this
claim. However, South African mathematician Stanley Skewes supported
Littlewood’s claim when he provided the evidence to support it.

 

One example that defies the
concept of direct proportionality is the physical law of buoyancy or the
Archimedes’ principle that coined the term “eureka” itself. “Eureka”, in Greek,
means “I have found it!” and those were the exact words said my Archimedes
while running down the streets of Syracuse after he discovered a method to
measure the volume of gold, which was impossible at that time. Archimedes was
challenged with the task of proving that the new crown given by the goldsmith
for King was not pure gold although his efforts were unproductive. One day, he
went to take a bath when he noticed that the water level rose and overflowed as
he submerged himself in. At that instant, he knew that the amount of water that
had been displaced was equal to the volume of his body he has submerged.
Instead of logical reasoning, Archimedes relied on his intuition, which is
considered personal and defies against the notion that mathematics should be
purely free of bias.

 

While serendipitous
discoveries are assumed to happen by pure chance, other factors also play a
role such as the time period and any prerequisite knowledge that the individual
learned that may increase the chances of the individual discovering something
“by luck”. Such was the case for Archimedes. He was deemed as a mathematical
genius even before his discovery. It is highly unlikely that the king entrusted
a normal man with the task of finding a method to determine real gold from fake
and even more unlikely that his discovery was almost immediately accepted. The
story of Archimedes was first published in the first century B.C but the real
event took place long before that when the proof of knowledge was not as
demanding as it is now. The abundance of knowledge present in the 21st century
would not have allowed Archimedes to claim such a discovery without substantial
evidence and therefore the likeliness of events repeating itself in the mordern
world in highly unlikely. Moreover, the traditional use of the Archimedes
principle that was limited to measuring the volume of irregular objects, has
expanded throughout history and greatly contributed to many developments in
several areas of society, most notably in the development of infrastructure and
the design of the submarine, in which the principle is relied upon. Therefore,
significant developments in the applicability of knowledge supports that the
duration of time spent on improving knowledge will improve its quality.