# After in the process. The agreement between two mathematical

After taking a glance at the title, I questioned what
classifies knowledge as robust. This is because each and every individual
values knowledge depending on how strongly they believe, or want to believe in
something. Therefore, consensus plays a significant role in determining whether
knowledge is classified as robust or not. More importantly, for knowledge to be
considered robust, there should be little or no criticism associated with the
knowledge. In other words, knowledge of that sort cannot be disproven by any
methods of disagreement. Mathematics will be explored in relation to consensus
as it is built upon certainty and reasoning. On the other hand, the subjective
nature of art has an influence on the validity of knowledge due to the presence
of emotions within the individuals’ interpretation of a certain piece.
Therefore, it is safe to say that the existence of both consensus and
disagreement is required to formulate knowledge that is robust.

To what extent does consensus provide certainty in
knowledge?

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The level of certainty within robust knowledge should be
very high. Therefore, in order to confirm that robust knowledge requires
consensus, a connection between consensus and certainty must be established.
This will be done through the application to the study of the field of
mathematics as it is built upon certainty and reasoning. This means that strong
evidence must be provided for the certainty of a mathematical concept.
Knowledge that is certain can never be disproven by another individual or
concept. The fact that the solution to a mathematical problem is not open to
negotiation or personal interpretation can provide us with a reason as to why
consensus can provide us with certainty. This also indicates that we as humans
must apply reason to our understanding of mathematical concepts in order to
accurately produce analysis and develop answers using these concepts. For
instance, in order to calculate the gradient of a straight line, the
will be the same regardless of the equation used in the process. The agreement
between two mathematical equations can be seen as evidence that consensus
provides us with certainty in knowledge as a consequence of the reasoning we
apply to it.  Without the existence of
reasoning, the mathematical concepts that are present today would not provide
certainty. The mathematician, Hilbert for example, used reasoning to find
errors in the theory of another mathematician, Frege (Blanchette, 2007). The
controversy between the two mathematicians Hilbert and Frege has helped in the
achievement of certainty. Therefore, this demonstrates the importance of
reasoning and more importantly disagreement in the process of formulating
robust knowledge.

Another factor that plays an important role in the
formation of robust knowledge is disagreement. Knowledge that is robust must
withstand criticism, in the form of disagreement and can only be identified as
robust if the final outcome is consensus. In society, it is much easier to find
a consensus rather than a disagreement. This is because it is more time
efficient for people to accept knowledge the way it is presented rather than to
carry out procedures to ensure whether a concept has certainty or not. I,
myself have experienced a situation whereby I was taught something and later on
came to the realization that it was not true. As a biology student, I was
initially taught that the equation for aerobic respiration is C6H12O6 +
6O2 ? 6CO2 + 6H2O. However, as I further developed my knowledge, I
came to the realization that all the knowledge I have previously gained about
respiration is false. It was from this point onwards that I started to question
the certainty of knowledge which led me to think that the disagreement of
previous knowledge plays an important role in getting one step closer to
achieving the verification of truth. Therefore, robust knowledge does require
consensus however, disagreement must be used as a method to verify the level of
certainty in knowledge, allowing it to be classified as robust.

To what extent does the subjective nature of art
influence the validity of aesthetic knowledge?

The field of art represents the ideas of consensus and
disagreement as every artist has their own creative techniques that do not
correspond with different techniques adopted by other artists. Therefore
subjectivity, more specifically emotions, have a significant impact on the
validity of aesthetic knowledge. The beauty of a masterpiece is determined by
the emotional connection between the artist and the observer. If disagreement
was not that common in the field of art, then all pieces of art would be
identical rather than unique. This defies the whole purpose of art as
masterpieces should be used to express the emotions within an artist rather
than achieving acceptance from society. Therefore, if a person does not agree
with a piece of art, it does not mean that the piece is invalid. In fact, it
means that there is no connection between the person observing the piece of art
and the artist. For example, as I was walking on the street one day, I was
exposed to several graffiti paintings on the wall. Despite the fact, I was only
able to understand the meaning of a few paintings, I still knew that these
paintings were meaningful to someone else that does not share an emotional
connection with me. Therefore, the subjective nature of art validates aesthetic
knowledge.

Art can also be perceived as objective, limiting the
validity of aesthetic knowledge and creativity. The judgements made by art
professionals provide an indication of whether a piece of art is of high
quality or not. For example, Jonathan Richardson in the year 1719 developed a
system of critique for art which judges artistic perfection from a scale of 1-
20 (Encyclopædia Britannica, inc., 2017). This development coincides with the
point that art back in the day had to meet the requirements of the
professionals in art, giving it a more objective meaning. Therefore, art in the
18th century was built upon consensus rather than disagreement. However, in
this century, art has a more subjective meaning therefore a numerical value cannot
be given to pieces of art. If a value were to be given to a piece of art, then
the creativity of art would be very limited. This means that all paintings
composed would be very similar to one another which defies the whole purpose of
art. Nowadays, art does not have to accepted by professionals as it is a form
of expression that relates to personal experiences and emotions. The validity
of aesthetic knowledge is dependent on whether art is perceived as objective or
subjective. The progression of art from being objective to subjective has
enhanced creativity which has led to the disagreement between members of
society on their views regarding pieces of art. Thus, robust knowledge can
still exist with both the presence of a disagreement or the absence of an
agreement.

To conclude, both consensus and disagreement are required
in the process of forming knowledge that is classified as robust. However,
disagreement plays a more significant role as it is used to test existing
knowledge that is robust and to verify its certainty. Therefore, certainty in
consensus is dependent on disagreement. Specially in mathematics, the existence
of new theories constantly challenge current theories through the use of
evidence and reasoning. Alternatively, the subjective nature of art validates
the existence of aesthetic knowledge as pieces of art are used as a way to
express our emotions. Without the existence of subjectivity in art, it would be
interpreted the way we are told to by art professionals, rather than how we actually
want to interpret it. People in society are more likely to agree than disagree
with a given statement as it is more time efficient to accept knowledge than to
find evidence as to why the knowledge presented does not have certainty.
Moreover, as art produced in society nowadays is subjective rather than
objective, it means that art has become more valid in the sense that is now a
method of expressing emotions. This is because art should not be restricted

by certain criterion, instead artists should be given
freedom when producing a piece of art