Ali Hammad “Robust knowledge requires both consensus and disagreement.”Discuss this claim with reference to two areas of knowledge ”Robustknowledge” is defined as knowledge that can withstand criticism, consideredvalid and credible, and can enhance one’s knowledge. Validity can be defined asthe quality of being logical or factually sound.
This implies that in order forknowledge to robust it needs to fit a certain and be considered as aself-evident-truth. It can be argued that self-evident-truth is establishedwhen knowledge can withstand disagreement, and undergoes consensus. It can beargued that knowledge must undergo some degree of disagreement in order to beclassified as ”robust” or valid, asthis allows the questioning in logic, allowing elaboration as to whatcharacteristics of knowledge make it robust. Thus, it would need to result inan agreement, in its validity, in order to be classified as robust. Ultimately,robust knowledge does require both consensus and disagreement.
This will beexplored in the areas of knowledge mathematics, and human sciences. In the AOK mathematics, robustnessis established if the knowledge is logically sound, and this is done by twomethods. The first method is the use of an axiom to establish deductivereasoning to prove theorems.
Theorems can be defined as general propositionthat 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 inmathematics. In the AOK math it is internal self-referencing sense of logic.
Meaning that it is accepted without any evidence needed form an externalsource. This is the nature of proof in mathematics, which shows how axiomsand deductive reasoning is used to prove a theorem. An example of an axiom inmath could be, that all right triangles are equal to each other. Proof isevidence that helps to establish truth, validity, and quality(Dictionary). Inmathematics, a proof is a convincing demonstration that a mathematicalstatement is true. Proof is obtained by deductive reasoning rather thanempirical arguments.
When math is applied to serve real life situations, theproof can be considered valid, if the ”robust” knowledge, fulfills itspurpose or is logically correct according to its theory or an axiom(s). However,if knowledge cannot withstand disagreement in a logical sense, then it losesrobustness. 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 ofa 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 alsois examining the accuracy of calculations, because if circumference divided bythe circles diameter is correct it will equal pi (3.14….).
In terms ofdisagreement, mathematical proposals and theories are tested against thecriteria of agreed axioms. The pi theory, for example, gains its robustnesswhen logic is applied and the reference of an axiom is included, because if thecircumference of a circle, for example, is divided by its diameter equals pi,then in theory, the diameter multiplied by the constant pi (?) should equal tothe exact same value as the circumference, which is true. The use of pi canalso be considered robust, as it is used to ensure the absolute value ofbuilding construction methods, thus showing that it valid to the point that itcan determine the values required to hold our buildings. This would suggestthat both consensus and disagreement has enhanced the robustness of pi. In the AOK of Mathematics, therobustness of knowledge must also be established by whether it is effectively appliedto the real world. For this reason, it should be taken into consideration thatpi has been changed many times upon its discovery till today.
The pi constant haschanged to develop more asymmetrical constructions. Thus, empirical evidence’srole in mathematics is to determine the effectiveness of how knowledge inmathematics is applied in the real world. It also should be considered thatknowledge mathematics are dependent on a premise. A premise is a propositionfrom which another is inferred or follows as a conclusion(Oxford-Dictionaries”).
This is a disadvantage of mathematics becauseif a conclusion based on a false premise, the conclusion is false. A commonexample 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 ofknowledge is completely denied if premise (1) for example is wrong, because itwould suggest the conclusion is false, thus limits robustness. Thus, ifknowledge in mathematics cannot withstand disagreement then it loses theentirety of its robustness.(“The-Math-Forum”) However, when knowledge inmathematics can withstand disagreement and have its premise/axiom accepted astrue, robustness is established.
If the knowledge is also applied effectivelyin the real world, it’s robustness increases. Thus, consensus in math is establishedby axioms, which is a self-evident truth, which does not require any externalsource of clarification. Thus, if reasoning is deduced, then disagreementcannot be applied. However, if knowledge undergoes disagreement and cannotwithstand it, it loses robustness, because it is denying a self-evident truth. Inhuman sciences, different methods are used to determine robustness of knowledge.Robustness is established by how conclusions are representative/applicable tothe real world and valid in evaluation. Characteristics in human sciencesinclude experiments.
Human sciences tend to make sense of complex real-worldsituations. In psychology, for example, experiment often intend to establishcause and effect relationships between variables. An example of an experimentin psychology can be seen in the Stanford Prison experiment. Where participantswere kept in a simulated for 6 days (intentionally 2 weeks but was aborted dueto obsessive violence). As the days progressed the guards gained a more aggressiveand assertive behavior towards the prisoners, as the participants were used tothe environment. Although this created shocking and descriptive results, thestudy breached many ethical guidelines. In terms of the evaluation, the mainconclusion is that people will naturally assume their roles of power.
The robustnessof that knowledge could be supported by the study’s length showing aprogressive change in behavior. Thus, gaining consensus, to an extent. (“StanfordPrison Experiment | Simply Psychology”). However, the study being in anartificial environment prevent the validity of this representing a real-lifesituation.
Therefore, limitations support the disagreement of the conclusion. Consensusin psychology for example is used to establish validity of conclusion orknowledge produced off results of a study. However, disagreement occurs in theform of limitations and feedback. If knowledge produced in psychology cannot fulfilla study’s aim, the knowledge cannot be classified as robust. Thehuman sciences, however, have many forms of disagreement that can limitrobustness of knowledge. In psychology, factors such as researcher bias,artificial environments, and ambiguous results, can affect the validity ofknowledge produced from the AOK. Ambiguous results occurred in the Stanfordprison experiment, where most guards behaved violently, but some did not, whichwould 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’sinterest and evaluation can be influenced by their personal experience,beliefs, or often because the results intent to fulfill the aim. However, humansciences have many methods to reduce or prevent, the limitations effect on thevalidity of the study. This can be done through triangulation.
This means thata study will increase an aspect that provides more data. This can be done throughdata triangulation, investigator, or methodological. This can inevitablyincrease robustness, as more analysis is taken, random errors decrease, andrich data can be collected as a result of multiple examinations. As such, humansciences require consensus in the form of validity to gain robustness, whiledecreasing as many factors of disagreement as possible to maintain robustness.
In conclusion, consensus isimportant in establishing robustness of knowledge, while most AOKs requireknowledge to withstand disagreement to maintain robustness. In the AOK mathematics,robustness is established if the knowledge is logically sound. axiom toestablish deductive reasoning to prove theorems. Theorems can be defined asgeneral proposition that is not self-evident, but is supported by a chain ofreasoning. In mathematics, a proof is a convincing demonstration that amathematical statement is true. Proof is obtained by deductive reasoning ratherthan empirical arguments.
When math is applied to real life situations, theproof can be considered valid, if the ”robust” knowledge, fulfills itspurpose 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, becauseit would suggest the conclusion is false. Thus, if knowledge in mathematicscannot withstand disagreement then it loses the entirety of its robustness. In humansciences, different methods are used to determine robustness of knowledge. Robustnessis established by how conclusions are representative/applicable to the realworld 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 formsof disagreement that can limit robustness of knowledge.
In psychology, factors suchas researcher bias, artificial environments, and ambiguous results, can affectthe validity of knowledge produced. However, triangulation can help enhancevalidity and decrease random errors. As such, human sciences require consensusin the form of validity to gain robustness, while decreasing as many factors ofdisagreement as possible to maintain robustness. Bibliography”Axioms And Proofs |World Of Mathematics.” Mathigon.N.
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