Ali Hammad

“Robust knowledge requires both consensus and disagreement.”

Discuss this claim with reference to two areas of knowledge

”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.