How is faith used in Mathematics?

Faith is one of the least accepted WoK, since it is considered by many to not bring any new knowledge to several AoK, and only really be useful in Areas such as Religious Knowledge systems. Although this is not true, since Faith can actually be used in many other AoK (such as Natural Science when doing experiments), the statement that it does not apply to all AoK may not be completely false.

Faith finds its complete opposite in Mathematics. Mathematics is based entirely on proof: the way in which we understand and explore it is through theorems, and in order to be approved theorems need proof. For example, the Pythagoras Theorem states that in a right triangle (a triangle in which to of the sides make a right angle), the square of the side opposite the right angle (hypotenuse) equals the square of the other two sides: c2 = a2 + b2. It can be proven with this simple image:

Squares and Triangles

(Here, c represents the hypotenuse, and a and b represent the other two sides of each triangle.)

Since Faith implies believing without proof, it seems that there is no way in which Mathematics and Faith could ever be reconciled. Though it could be argued that theorems are based on axioms, which do not require proof, this is not a very solid argument, since axioms are, by definition, “self-evidently true, and therefore do not require proof”. However, it may be fair to say that, in order to create a theorem, one must put together different axioms and have faith that they will work out the way they are supposed to.

To sum up, though Faith may have some minor uses in Mathematics, it is not used much, if at all, when gaining knowledge in this particular AoK.




How does censorship affect the way we gain or investigate knowledge in the Arts?

Often, when talking about knowledge, one key factor is how the knowledge was gained: what experiments were done in Natural Sciences, what research was undertaken in History, or what mathematical process was used in Mathematics. This is, of course, because the way in which knowledge is gained usually affects the knowledge itself. One of the most important factors that can influence knowledge is the society in which it is produced or discovered, how its people react to it, and the censorship that exists in it.

A prime example of this is William Shakespeare’s “Othello”. One widely accepted theory about the play is that Shakespeare uses it to criticize the society of his time due to it being mysoginistic and racist. However, since he could not say what he thought explicitly, he had to add different connotative meanings in the form of symbols inside the play to express his criticism. Had he been able to express himself freely, Shakespeare would probably not have killed Desdemona, Emilia or Othello, he would have given them a happy ending instead. The society in which he lived in affected the way in which he expressed his knowledge, which therefore affected our way of understanding and investigating it. Had Shakespeare written Othello in today’s more open-minded society, he would probably have expressed his criticism denotatively. This would have helped us confirm what we can only speculate about now: that “Othello” was really about criticizing society.

As can be seen in the example, censorship usually affects knowledge in the Arts by having connotative meanings be used rather than denotative meanings. And while this may produce very interesting art, it is also a major setback in the search for knowledge: many different connotative meanings can be read in a single piece of art, and some of them may conflict with each other. In “Othello”, Desdemona may have stood up to her father by disobeying him and marrying Othello, defying society’s rules, but she also remained obedient to Othello even if it meant being mistreated, and eventually killed. Two readings can be taken out of this: that Desdemona was killed because she defied society and its view on her, or that she was killed because Shakespeare had no choice but to kill her in order to avoid censorship. Which one is understood may depend on the reader: members of a relatively more tolerant society such as ourselves will probably lean towards the second meaning.

So to sum up, the subjectivity of knowledge in the Arts makes it difficult to decipher, and censorship only contributes to this by not allowing us to have any confirmation of any theories we may come up with.

How can we know whether our knowledge is correct?

The Tempest by Giorgione is one of the most controversial paintings in existence. This is due to the many interpretations of it. The painting shows a man standing up and holding a spike, and a woman sitting down and holding a baby. There is a city in the background. 1508_giorgione_tempest

Some believe that the two figures are Adam and Eve with their son Cain, and that the city represents Paradise. Others think that the painting is a representation of one of two ancient Greek myths: either the myth of the goddess Demeter and her lover Iasion, who was killed by Zeus; or the myth of the hero Paris and his wife, the mountain nymph Oenone.

All of these interpretations have one thing in common: none of them are confirmed. There is no way to know what connotative meaning the artist wanted to give to the painting, or whether he wanted it this way. This is just an example: many paintings are interpreted in different ways, but there is no way to know which interpretation is correct.

And this does not only happen in the Arts. There is uncertainty in all the Areas of Knowledge. In Natural Sciences, for example, many theories have been proven wrong even after being accepted as correct, such as Dalton’s theory of the atomical structure.

So, if there is no real confirmation of knowledge, how can we decide that our knowledge is correct?

The truth is that there has always been controversy in every Area of Knowledge, and there always will be. There will always be different opinions, different theories, different approaches, and there may never be an absolute, undeniable truth. But knowledge is about combining all opinions, all theories, and all approaches, and try to reach the consensus that makes sense. This is our way of knowing, and though it may not always work, it is our best chance of understanding the world around us.



To what extent is it fair to say that some AoK are more useful than others?

In order to understand Areas of Knowledge, a metaphor is often used. If each Area of Knowledge is a map, then the knowledge each one studies is the territory reflected in the map. There are many different maps to study each territory, that vary in size and in ways of studying the territory, and that study specific territories within the Areas of Knowledge in more detail. However, having all of these different territories may make us wonder whether there are some that have more applications in our lives, and therefore are more useful, and others that do not provide important knowledge.

For example, some may argue that Natural Sciences is the most important Area of Knowledge, since it tries to study and understand the world around us, which is vital for our survival. But others could disagree, seeing as the sciences have been wrong many times and are not completely reliable. The different scientific methods or the equipment used are only two of the many factors that may influence a result and make the conclusions dubitable.

Mathematics could also be considered a useful Area of Knowledge, since it is applied to problems in our daily lives. However, there is only so much knowledge in Mathematics that is truly useful in day to day situations: while adding, subtracting or multiplying have a real-life application, limits (the value that a function approaches) do not. And although they may be useful in certain areas, they are not essential.

To many, Art is an important Area of Knowledge because it helps us express ourselves and convey messages that we could not get across any other way. To others, however, the subjectivity involved in understanding the Arts may be an obstacle, and they may think that Art does not provide any true knowledge since the information each person can extract from it may be different.

All in all, each Area of Knowledge has its pros and cons, and each provides a different kind of knowledge, but this does not mean that some are better than others. Each Area of Knowledge provides unique and important knowledge that should be known to everyone. Then, each person may decide in which Area they wish to specialize in, but it is essential to know the basics of every Area of Knowledge in order to understand our world and the people who live in it.

How do the Arts provide knowledge?


Usually, when thinking about knowledge, we tend to think more about Natural Sciences or Maths, which give us specific knowledge with a clear objective, whether it be understanding the world around us, solving a problem… However, we usually do not tend to think about Areas of Knowledge such as The Arts, since the knowledge that we can gain from them is more subjective, and therefore arguably less reliable. Still, it is undeniable that Art provides knowledge. But how does it do it?

Art is mostly used as a means to communicate. This means that the knowledge we gain from art usually comes in the form of a message from someone else. There is a wide variety of messages that can be sent through art, ranging from simple jokes to political or ethical statements. Each form of art has its own ways of communication, and is fit for a different kind of message.

For example, Literature is usually used for two main purposes: to provide a moral (the moral of the story) or to help us understand somebody else’s experience. An example of this could be the book “The Curious Incident of the Dog in the Nighttime” by Mark Haddon, which tells the story of a 15 year-old  boy with autism. By narrating in the first person, Haddon helps the reader understand what goes on in an autistic boy’s mind, how he sees the world around him and the difficulties that he is subjected to because of his autism, such as being forced to go to a school that does not offer the course he wants to study.

The knowledge the author wants to provide to the reader in this particular example is how autistic people differ from non-autistics, and how despite being very smart, they are set apart because of their lack of ability to understand human emotions. So, he is trying to help readers understand the experiences and difficulties of a group of people, passing on his knowledge in the process.

To sum up, knowledge in the Arts is usually a message sent by the artist that can have many different intentions: making the public laugh, changing a certain situation or understanding each other better are just a few of the endless possibilities.

To what extent is Memory reliable?

Every day, every minute, even right now, we are using our Ways of Knowing to perceive and understand the world around us. The Ways of Knowing are our only tools in our endless search for knowledge, so we must always make sure that they are ready to be used in order to obtain true, correct knowledge. We use glasses to correct our sight or pills to improve our memory.

However, no matter how much we try to polish our Ways of Knowing, they will never be perfect. Every Way of Knowing is imperfect in one way or another, and may lead to error. One in particular can be especially faulty: Memory. When creating new memories, our neurons create new connections, called synapses, in order to encode the memory. These new connections are then stored and established again when it is recalled. However, every time we recall a memory, we add slight variations to it: perhaps, that one time I fell off my bike, there was actually a cat on the road that startled me and made me fall. The real problem comes when the original memory is erased and this new memory is stored instead.

And not only do we alter memories, we can also forget them completely. For example, many rape victims block their memories of the attack completely, and cannot recall them without the help of a psychologist, because they are too painful. Sometimes we even make up new ones. A study by the PNAS (Proceeedings of the National Academy of Sciences), conducted by Lawrence Patihis of the University of California, Irvine, subjected two groups of people (some with ordinary memory and others with highly superior autobiographical memory) to the same test in order to see whether there were people who were immune to false memories. While talking about the 9/11 terrorist attack, footage of United Flight 93 crashing in Pennsylvania was mentioned; footage that actually did not exist. However, when asked about it later, at least 1 in 5 people in each group was convinced they had seen it. This proves that we can most definitely create false memories, and that nobody is immune to them.

So, if our memories truly are unreliable, what are we to do? Memory is not just a Way of Knowing, it is how we store our knowledge. Without Memory, it does not matter how much knowledge we can gain, because we will not be able to recall it. But the truth is, though it may fail us, memory is usually very accurate. It might not be perfect, but every Way of Knowing has its own inaccuracies. Besides, changes in memory are usually only produced in memories with which we have a deep emotional connection.

To sum up, though memory does have inaccuracies, it is mostly reliable.



Remember That? No You Don’t. Study Shows False Memories Afflict Us All

To what extent are some WoK more important than others?

In ToK, there are eight Ways of Knowing (WoK), each of which is used to gain more knowledge. However, there are those who think that some Ways of Knowing are less important than others, since they seem to be simply a combination of already existing WoK. With this being said, how is it possible to know whether some WoK are more important than others?

First, we must find which WoK are considered important, and which ones are not. Without a doubt, sense perception, reason, memory and language are essential. Intuition is also widely accepted. However, emotion, imagination and faith are quite controversial.

Many consider emotion to not be a reliable WoK, since feelings are subjective and do not seem to bring objective knowledge. But emotion is actually necessary to gain knowledge. One can only get so far using reason alone in areas such as Ethics. In Ethics, we can only feel what is right. This makes emotion a necessary WoK.

Imagination is also highly controversial, as some consider that it is based on memory and cannot stand its ground as its own WoK. However, as Theodule Ribot says, “No one knows how many acts of imagination it took to transform the plough… into what it became after a long series of alterations.” Though, undoubtedly, imagination uses memory, it gives us knowledge that memory alone cannot provide. Every invention and scientific discovery has needed imagination at some point, which makes it an essential WoK.

As for faith, we need only look at Aristotle’s definition of knowledge as a “justified, true BELIEF” to find our answer. Knowledge is always a belief. If we do not believe in our knowledge, we cannot truly know it. Therefore, faith is an indispensable WoK.

In conclusion, though at first glance some WoK may appear more important than others, they are all equally important and provide us different types of knowledge.


Bryan-Zaykov, C. & Thomas, G. (2016). Theory of knowledge (2nd ed., pp. 1-66). London: Pearson.

To what extent should Ethics be a part of politics?

The recent US elections have shown that a candidate’s moral code plays a big part in who chooses to vote for them. As a matter of fact, the media seemed to represent the elections not as a conflict between two politicians and their economical policies, but rather as an ethical matter. This has made many disregard the actual policies of either candidate and focus only on their ethical values, which may have disastrous consequences for the country should either candidate rely only on ethical regulations to govern.

This does not mean, of course, that ethics should not play a part in elections at all. There are many topics up for debate that each candidate should be able to have an opinion about. However, in these elections the involvement of ethics has been extreme. So extreme, in fact, that there were those who could not vote for a certain candidate without losing basic rights. Here is an example of my point. The next piece is directly taken from Donald Trump’s official web page:

No gay marriage; no same-sex partner benefits

On Thursday, Trump talked about “exploring” a presidential run, and was asked if he supports “allowing same-sex couples to marry.”

Trump said “no,” but didn’t stop there. When asked whether gay couples should have access to “the same benefits as married couples,” the mogul initially replied that his attitude on the issue was not yet “fully formed.”

After thinking about it for a moment, however, Trump said: “As of this moment, I would say no and no” to gay marriage and civil benefits.

That answer may have resonated with Iowa conservatives who overwhelmingly opposed the Iowa Supreme Court’s 2009 decision to overturn the state’s gay marriage ban. But not in New York, home to one of the largest gay and lesbian communities in the US.

Trump was traveling Sunday and could not be reached for comment. Through a spokesman, he said only: “I’m opposed to gay marriage.”


After reading this, any gay person could not vote for Trump, no matter how much they agree with his policies, because they know that they would lose a basic right that everyone should have. And politicians are not elected to tamper with their people’s rights, but to take care of the social, political and economical situation of a country.

In conclusion, Ethics should definitely be a part of politics, but never to a point where they compromise the basic rights of any person or group.

How are Ethics involved in advertising?

It is undeniable that nowadays ethics play a crucial part in business activities. Businesses who do not have an ethical behaviour will undoubtedly lose customers, since many refuse to buy from those who do not follow a strict ethical code. Especially in today’s world, where technology makes their decisions visible to all, businesses must be careful and behave ethically in order to make the public view them positively. Without a good reputation, very few businesses would be able to survive.

But ethical behaviour does not only apply to the condition of the workers, or to how many projects the business may have started for charity. In fact, the most prominent way of showing ethical behaviour is through advertising. A business’s advertisements are essential to the image the business wants to provide, since they are the first, and many times the only, image customers have in mind when buying their products.

This can be clearly seen in discriminatory advertising. For example, Nivea’s ad featuring a black man with the slogan “Re-civilize yourself” had huge backlash on social media, and the company even had to issue a formal apology stating that it was not their intention to send a racist message in order to maintain their image.

However, the implications of ethics in advertising can also be used to a business’s advantage. For example, the company MO, that sells glasses, recently created and ad with the theme of accepting oneself as one is. This is a value that society strives to achieve, so the company is appealing to all those who support the notion, and therefore gaining customers.

Yet another example of using advertising to show a business’s values is Principe’s advertisement: “El héroe que llevan dentro”. In it, some children are performing a play where the girl is playing a princess who must be saved from a dragon by a knight in shining armour. However, after eating the cookies, she jumps into the battle and saves herself. The company uses the stereotypes in fairytales and turns them around in order to show how both men and women can “be the hero”. Especially considering all the social movements advocating for equal rights for every sex, this ad is a very smart move that makes the ethical code of the business quite clear, and gives a good image of it.

So to sum up, ethics play a massive part in advertising, since businesses need to behave ethically in order to have a good reputation and keep their customers, and advertising is the main image of a business that the public has. Therefore, businesses can use advertising to make their moral code clear and appeal to customers.

What proof can be used to justify knowledge?

According to Plato, knowledge is “a justified, true belief”. But how can one justify knowledge? The answer is obvious: proof. However, this is where the problem begins: what can we deem as proof?

The truth is, the only real proof is the one that we choose to believe. After all, there is no knowledge without belief, since knowledge is, by definition, a belief. Proof is the same.

For example, there are those who say that science is really a religion, since it is a way of seeing the world: instead of it being created by a God, it was created by a massive explosion. Some argue that science is different, since it can be proven, but can it really? The only way to “prove” scientific beliefs is with artifacts created by humans, which have failed in more than one occasion. Not to mention the many ridiculous theories and “proven” facts that science has provided throughout History, such as the Earth being flat or women being thought to release atoms from their eyes. In the end, science and religion alike are just attempts at understanding a world that we cannot comprehend. We are just too stubborn and stuck in our own ego to accept it.

But let’s say that science is proven. So is religion. Jesus proved that he had been sent by God when he walked on water, or when he cured countless people, and yet many choose not to believe it. One could argue that the only source that could confirm this information is the Bible, which is not reliable. But if the Bible is not reliable, then how can any other historical text be trusted? What makes, say, the Declaration of Independence acceptable as proof, and not the Bible?

Even language is something we choose to believe. The only thing that makes a duck “a duck” and not “a bear” is that we choose to call it a duck.

This world is so complex that not even our best attempts at explaining it can be proven right or wrong. In the end, the only proof that can justify knowledge is the one that each individual chooses to believe.