# Ali that can withstand criticism, considered valid and credible,

“Robust knowledge requires both consensus and disagreement.”
Discuss this claim with reference to two areas of knowledge

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”Robust
knowledge” is defined as knowledge that can withstand criticism, considered
valid and credible, and can enhance one’s knowledge. Validity can be defined as
the quality of being logical or factually sound. This implies that in order for
knowledge to robust it needs to fit a certain and be considered as a
self-evident-truth. It can be argued that self-evident-truth is established
when knowledge can withstand disagreement, and undergoes consensus. It can be
argued that knowledge must undergo some degree of disagreement in order to be
classified as ”robust” or  valid, as
this allows the questioning in logic, allowing elaboration as to what
characteristics of knowledge make it robust. Thus, it would need to result in
an agreement, in its validity, in order to be classified as robust. Ultimately,
robust knowledge does require both consensus and disagreement. This will be
explored in the areas of knowledge mathematics, and human sciences.

In the AOK mathematics, robustness
is established if the knowledge is logically sound, and this is done by two
methods. The first method is the use of an axiom to establish deductive
reasoning to prove theorems. Theorems can be defined as general proposition
that is not self-evident, but is supported by a chain of reasoning (Dictionary).

Axioms are statements that are self-evidently true and function as premises in
mathematics. In the AOK math it is internal self-referencing sense of logic.

Meaning that it is accepted without any evidence needed form an external
source. This is the nature of proof in mathematics, which shows how axioms
and deductive reasoning is used to prove a theorem. An example of an axiom in
math could be, that all right triangles are equal to each other. Proof is
evidence that helps to establish truth, validity, and quality(Dictionary). In
mathematics, a proof is a convincing demonstration that a mathematical
statement is true. Proof is obtained by deductive reasoning rather than
empirical arguments. When math is applied to serve real life situations, the
proof can be considered valid, if the ”robust” knowledge, fulfills its
purpose or is logically correct according to its theory or an axiom(s). However,
if knowledge cannot withstand disagreement in a logical sense, then it loses
robustness. A real-life example of knowledge in math’s being considered
”robust” is the use of pi in determining values of shapes. Pi is the ratio of
a circumference of a circle to its diameter, and pi is classified as constant.

The fact that it is a constant play a significant role in pi’s robustness,
because no matter the size the ratio will stay the same. The formula of pi also
is examining the accuracy of calculations, because if circumference divided by
the circles diameter is correct it will equal pi (3.14….). In terms of
disagreement, mathematical proposals and theories are tested against the
criteria of agreed axioms. The pi theory, for example, gains its robustness
when logic is applied and the reference of an axiom is included, because if the
circumference of a circle, for example, is divided by its diameter equals pi,
then in theory, the diameter multiplied by the constant pi (?) should equal to
the exact same value as the circumference, which is true. The use of pi can
also be considered robust, as it is used to ensure the absolute value of
building construction methods, thus showing that it valid to the point that it
can determine the values required to hold our buildings. This would suggest
that both consensus and disagreement has enhanced the robustness of pi.

In the AOK of Mathematics, the
robustness of knowledge must also be established by whether it is effectively applied
to the real world. For this reason, it should be taken into consideration that
pi has been changed many times upon its discovery till today. The pi constant has
changed to develop more asymmetrical constructions. Thus, empirical evidence’s
role in mathematics is to determine the effectiveness of how knowledge in
mathematics is applied in the real world. It also should be considered that
knowledge mathematics are dependent on a premise. A premise is a proposition
from which another is inferred or follows as a conclusion(Oxford-Dictionaries”).  This is a disadvantage of mathematics because
if a conclusion based on a false premise, the conclusion is false. A common
example where this concept is explained is by the following syllogism:(Lagemaat)

All human beings are mortal1)

Socrates is a human being (2)

There for Socrates is mortal (Conclusion/3)

The conclusion is deduced from premise.

The conclusion is true since the premise is true. However, the robustness of
knowledge is completely denied if premise (1) for example is wrong, because it
would suggest the conclusion is false, thus limits robustness. Thus, if
knowledge in mathematics cannot withstand disagreement then it loses the
entirety of its robustness.(“The-Math-Forum”)

However, when knowledge in
mathematics can withstand disagreement and have its premise/axiom accepted as
true, robustness is established. If the knowledge is also applied effectively
in the real world, it’s robustness increases. Thus, consensus in math is established
by axioms, which is a self-evident truth, which does not require any external
source of clarification. Thus, if reasoning is deduced, then disagreement
cannot be applied. However, if knowledge undergoes disagreement and cannot
withstand it, it loses robustness, because it is denying a self-evident truth.

In
human sciences, different methods are used to determine robustness of knowledge.

Robustness is established by how conclusions are representative/applicable to
the real world and valid in evaluation. Characteristics in human sciences
include experiments. Human sciences tend to make sense of complex real-world
situations. In psychology, for example, experiment often intend to establish
cause and effect relationships between variables. An example of an experiment
in psychology can be seen in the Stanford Prison experiment. Where participants
were kept in a simulated for 6 days (intentionally 2 weeks but was aborted due
to obsessive violence). As the days progressed the guards gained a more aggressive
and assertive behavior towards the prisoners, as the participants were used to
the environment. Although this created shocking and descriptive results, the
study breached many ethical guidelines. In terms of the evaluation, the main
conclusion is that people will naturally assume their roles of power. The robustness
of that knowledge could be supported by the study’s length showing a
progressive change in behavior. Thus, gaining consensus, to an extent. (“Stanford
Prison Experiment | Simply Psychology”). However, the study being in an
artificial environment prevent the validity of this representing a real-life
situation. Therefore, limitations support the disagreement of the conclusion. Consensus
in psychology for example is used to establish validity of conclusion or
knowledge produced off results of a study. However, disagreement occurs in the
form of limitations and feedback. If knowledge produced in psychology cannot fulfill
a study’s aim, the knowledge cannot be classified as robust.

The
human sciences, however, have many forms of disagreement that can limit
robustness of knowledge. In psychology, factors such as researcher bias,
artificial environments, and ambiguous results, can affect the validity of
knowledge produced from the AOK. Ambiguous results occurred in the Stanford
prison experiment, where most guards behaved violently, but some did not, which
would suggest that a bad situation does not turn everyone into a sadist(Lagemaat).

The concept of bias is also a limitation of most studies. A researcher’s
interest and evaluation can be influenced by their personal experience,
beliefs, or often because the results intent to fulfill the aim. However, human
sciences have many methods to reduce or prevent, the limitations effect on the
validity of the study. This can be done through triangulation. This means that
a study will increase an aspect that provides more data. This can be done through
data triangulation, investigator, or methodological. This can inevitably
increase robustness, as more analysis is taken, random errors decrease, and
rich data can be collected as a result of multiple examinations. As such, human
sciences require consensus in the form of validity to gain robustness, while
decreasing as many factors of disagreement as possible to maintain robustness.

In conclusion, consensus is
important in establishing robustness of knowledge, while most AOKs require
knowledge to withstand disagreement to maintain robustness. In the AOK mathematics,
robustness is established if the knowledge is logically sound. axiom to
establish deductive reasoning to prove theorems. Theorems can be defined as
general proposition that is not self-evident, but is supported by a chain of
reasoning. In mathematics, a proof is a convincing demonstration that a
mathematical statement is true. Proof is obtained by deductive reasoning rather
than empirical arguments. When math is applied to real life situations, the
proof can be considered valid, if the ”robust” knowledge, fulfills its
purpose or is logically correct according to its theory or an axiom(s). However,
the robustness of knowledge is completely denied if a premise is wrong, because
it would suggest the conclusion is false. Thus, if knowledge in mathematics
cannot withstand disagreement then it loses the entirety of its robustness. In human
sciences, different methods are used to determine robustness of knowledge. Robustness
is established by how conclusions are representative/applicable to the real
world and valid in evaluation. Characteristics in human sciences include experiments.

Human sciences tend to make sense of complex real-world situations.  The human sciences, however, have many forms
of disagreement that can limit robustness of knowledge. In psychology, factors such
as researcher bias, artificial environments, and ambiguous results, can affect
the validity of knowledge produced. However, triangulation can help enhance
validity and decrease random errors. As such, human sciences require consensus
in the form of validity to gain robustness, while decreasing as many factors of
disagreement as possible to maintain robustness.

Bibliography

“Axioms And Proofs |
World Of Mathematics.” Mathigon.

N. p., 2018. Web. 26 Jan. 2018.

Dictionary, axiom. “Axiom Meaning In The
Cambridge English Dictionary.” Dictionary.cambridge.org. N.p., 2018.

Web. 24 Jan. 2018.

Dictionary, theorem. “Theorem Meaning In The Cambridge
English Dictionary.” Dictionary.cambridge.org. N.p., 2018. Web. 24
Jan. 2018.

H-M, PsychPedia. “Hawthorne Effect.” GoodTherapy.org
Therapy Blog. N.p., 2018. Web. 27 Jan. 2018.

Lagemaat, Richard van de. Theory Of Knowledge.

Cambridge: Cambridge University Press, 2016. Print.

“Premise | Definition Of Premise In English By Oxford
Dictionaries.” Oxford Dictionaries | English. N.p., 2018. Web. 26
Jan. 2018.

“Pythagoras’ Dream: Is Maths Real? (Scientific
Realism).” Iai.tv. N. p., 2018. Web. 26 Jan. 2018.

“Stanford Prison Experiment | Simply
Psychology.” Simplypsychology.org. N.p., 2018. Web. 27 Jan. 2018.

“The Math Forum.” Mathforum.org. N.p.,
2018. Web. 26 Jan. 2018.