Every single human being thinks in a different way about aspects they

confront day to day. So how is it possible to create shared knowledge, which is

knowledge most people accept and know, if each person has a different

perspective? Therefore, there is robust knowledge. Knowledge is robust when it

is sustained and prevails regardless of criticism and arguments against it, and

it requires both consensus, or a general agreement and disagreement to exist.

This also suggests that there are some types of knowledge, and in this case, it

is not only knowledge, which are facts that are justified by evidence and

valid, but robust knowledge, which needs to be justified, valid, and accepted

and shared by a group of people.

Robust knowledge does require both consensus and disagreement, as the

relation between them help to expand what it is already known. If there were

only one side, either agreement or disagreement, in the first case, no one

would have the motivation to prove if the knowledge that is proposed is valid,

reasonable and true as it is accepted by all the individuals, and in the second

case, people will never get to a consensus as they will have different

perspective, creating no concise and robust knowledge.

Why can discrepancies be fundamental for the construction of robust

knowledge in Natural Sciences? In natural sciences, knowledge is constructed

and created based on previous theories and thoughts, mainly based on shared

knowledge, and other areas of knowledge. From the beginning of time there were

theories which people, mainly scientists and specialists, construct to explain

and understand the world, and they were accepted by ones and denied by other

group of people. The ones that were against that theory, tried to prove it

wrong, by using methods like experimentation and observation, to recollect data

that could refute it. And that is how most of knowledge people considered

nowadays as share knowledge exists, because these people which tried to bring

down the theory proposed, could prove that the theory was wrong, and supported

with evidence such as arguments and data, they create another theory that will

remain and be accepted until someone else could prove the contrary. This is the

case of the atomic model, a scientific theory which created the composition of

an atom. This theory started in the ancient Greece, where some philosophers as

Leucippus thought that matter was made up of units. This is when, centuries later,

Joseph John Thomson, Ernest Rutherford, Niels Bohr and James Chadwick

contributed to the creation of the model of an atom, which composed the modern

model of the atom. This is a perfect example of how robust knowledge requires

both consensus and disagreement, as each of these scientists based their new

model on the previous one, agreeing on the existence of an atom, but missing

its parts, and each of them prove their model by experimentation. Nowadays the electron

cloud model, the most modern model, is considered as robust knowledge, as it is

a shared knowledge that is accepted, and it is valid until other scientific can

prove the contrary.

Natural science is an area of knowledge that constructs knowledge based

on reason and imagination, by founding new theories in previous ones, first idealizing

and generating new possible ideas, and then trying to prove them through explanations,

and arguments given by data, which is why there is a greater amount of

disagreement in this area of knowledge that in other ones. In the case of Mathematics,

it is known that as it is precise and exact, as it uses pure reason, because of

the axioms that already exist, there is not a great amount of disagreement or

not at all, not as much as in Natural Sciences. But both areas construct their

robust knowledge thanks to agreement and disagreement. But in the specific case

of Mathematics, to what extent, the lack of discrepancies within this area of

knowledge, compared to the great number of axioms it has, also contribute in

the construction of robust knowledge? In Mathematics there is less known

disagreement than in Natural Sciences because first, in Mathematics when a

mistake is spotted, it is corrected easily, as there is a basis of exact math,

while in the case of natural science, it is harder to correct an error, so it

creates more points of views and opinions, generating more disagreements.

Second, the different mathematical theorems and models are easier to proof than

the natural sciences theories, as they have a basis of exact math, as it was

already said, while in natural sciences, the methods to gather data are more

meticulous and complex. These is proved, because to study, analyze and evaluate

Mathematics, the same mathematic basis is required, while in the case of Natural

Sciences, it is imperative and essential the use of mathematics and other

science knowledge, so to evaluate natural science it is required a greater amount

of areas of knowledge or disciplines. As it was mentioned before, Mathematics

also requires agreement and disagreement to create robust knowledge, as the

great amount of the recent shared knowledge of mathematics is proven and is

accepted by great portion of the world, and it stands criticism. Nevertheless,

Mathematics is an area that is not recognized by having a lot of famous

disagreements or discrepancies, because the development or evolution of this

area of knowledge, in terms of innovation or new models or theorems, is slow,

as it is difficult to not only create new theorems that explains new aspects of

the world, but to prove wrong the existing theorems and models. An example of a

discrepancy in mathematics is the foundations of mathematics, in which Euclid,

Greek mathematician, published Elements,

a compiled of mathematical theories related to geometry, which were criticized

and tried to prove wrong, but most of the Euclidian geometry was proved,

standing until nowadays, which shows that thanks to the disagreements Elements caused, most of the theories

and postulates could be proven, and they still exist and are studied.

It is possible that the discrepancies or disagreements in both areas of

knowledge could increase in the future, because when a subject is studied in a

greater amount, it creates each time more disagreement, as there will be more

information. This is shown in human history, because as more people knew about

certain subject or discipline, as science, they will propose new theories and

ideas, that will be criticized, and eventually, if they were not able to be

prove wrong, it will expand the knowledge humans had, and then will give the

opportunity to other people to discover new thing about the subject or

discipline, generating a larger branch that will pass through the same process

of evaluation, and will eventually make wither the scope. Therefore, there will

be always consensus and disagreements.

Also, it is important to talk about the personal knowledge in relation

with robust knowledge. Personal knowledge is also important in the creation of

robust knowledge, as it is the potential beginning in the creation of it. Personal

knowledge is the knowledge a person acquires by experience. Personal knowledge

by itself, could not be considered shared knowledge, as it does not have the

sufficient evidence that could give validity and make it a robust shared

knowledge. However, it is the beginning of the creation of shared knowledge and

consequently robust knowledge, as it is the individual´s perspective, that with

the help of data and facts that could verify, support and add validity to its

knowledge, it could be accepted and considered as shared knowledge. An example

is Isaac Newton, thanks to his experience with the famous apple that hits his head,

and inspired by this experience, he developed the universal gravitation law.

This was still personal knowledge, until he achieved to prove his theory with

experiments, which then, were accepted by the people, creating a shared

knowledge, that thanks to time, in which many scientists prove this theory, it

became a law, and consequently robust knowledge, as it remains in present days.

To conclude, consensus and disagreement are essential and required to

create robust knowledge, as it allows humans to expand the knowledge they

already share, giving them the opportunity, due to disagreements, to create new

perspectives, that could become robust knowledge if they can be proved, and to

prove the knowledge that continues to be considered as robust. This is the way

how areas of knowledge expand its content, as they can be evaluated and

improved thanks to the two possible sides of a debate, agree or disagree.