TOK #17: Math Scope

  1. What is the difference between a conjecture and a theorem?
    It’s a conjecture is a proposition made in math, a conclusion that has not yet been proven. When proof is found, a conjecture becomes known as a theorem. The theorem then is something that is eternally true and will last forever. 


  1. In THE VIDEO  Eduardo Saenz de Cabezon uses the example of people being surprised that folding a normal piece of paper 50 times, will reach a thickness as high as the sun. He challenges us to ‘do the math’ and see that he is correct. What do you think meant when he said that Maths dominates intuition and tames creativity? Do you agree with this?
    I agree with this. Mathematics is both about logical and illogical thinking. Paradoxes are a central part of math, and they are defined as a seemingly contradictory statement. Paradoxes go against intuition, so thus it can be said that math dominates intuition, by using logic and reason to uncover truths. I think that math tames creativity because it’s focused on using abstract reasoning as a method of finding proof – there are no multiple interpretations, or inventive types of thinking. There only exists definite truths (if it’s a theorem).


  1. Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?
    I think that this does give math a privileged position in TOK as one of the areas of knowledge where truths are definite and absolute. This is in comparison to other AOKs, like the natural sciences for example where conclusions are always being disproven and nothing is clear-cut. Many of the common rules we learn in science turn out to be imperfect, and many exceptions exist. For example, one of the main rules of cell theory is that all living cells are made of cells that are fundamental unit of life, but viruses, which are considered alive, are not made up of cells. These types of discrepancies and exceptions are very common. In this regard, math can be regarded as superior because the knowledge can be considered more trustworthy or reliable.

TOK #16: Comparing Arts and Science

Art vs Science Summary
Both art and science convey truth. There are different definitions of truth – first, there are factual and informative ones that are provided by areas of knowledge such as history or science. For example, names, dates, statistics, concepts  – unemotional reports on causes, effects, and events. The second, and more important definition is the emotional side of truth, the part that tells us something about humanity. It’s the conveyance of the tendencies and experiences of the human condition. This type of fundamental truth can only be conveyed through the arts. For example, in a history book you can read about what happened during the Vietnam War – the causes of it, the statistics of how many were hurt. However, this is not the whole image of the Vietnam War – through photographs and paintings is where you can find the pain and anguish felt by the Vietnamese. This emotional truth is just as, if not more important as scientific truths.

Art and Truth Summary
It is wrong to place the responsibility of “conveying truth” onto the arts. The truth in question is a more abstract, emotional truth about humanity deeper than simply factually true statements. Art is unique and is seen to have that responsibility because of it’s special form of communication – the type of truth it addresses cannot be chalked down into a few statements, it’s something that simply cannot be put into words. And perhaps it shouldn’t be – there is no need to find truth in art, because in doing so the whole value of what is being conveyed would be diminished. Art should not be reduced to a source of finding true statements.

How do both of these essays reflect what is presented in chapter reading about truth in art?
The first essay restates what is written in the chapter reading about the different types of knowledge/truth that is conveyed from science vs art. Going further however, the reading questions the validity of truth in art – because it’s such a subjective to the artist, can it still be considered the truth? Artists also like to create completely unrealistic creations, so is it still conveying knowledge? There are different true emotional experiences that can be found in a piece of art, but it seems to depend on the individual who looks at the work.

TOK #15 – Arts

Do you think that theories such as the elements and principles of design or the Darwinian explanation of art proposed by Dutton mean that beauty is not in the eye of the beholder?

Provide claims with examples in support of this KQ, and counter-claims and examples.

Support Claim:
Yes, because the Darwinian explanation of art describes how, as humans, we have been wired to find beauty in certain shapes or designs. This means that beauty is not in the eye of the beholder, as to some extent the idea of aesthetic has been predetermined for us. Darwin taught us that evolution operates through natural selection and sexual selection, with the latter being the focus. Sexual selection is the idea that a mate is chosen because of a physical factor that makes them seem more attractive to the partner. In the case of peacocks, a more alluring, colorful tail would attract peahens. From this example, animals have been shown to desire common qualities of beauty, to make adaptive decisions for reproduction. Another object that is wired into our brains to view as beauty comes from prehistoric artifacts. Acheulian hand axes are stone tools dating back two and a half million years. Although the tools have been around for thousands of centuries, it was not until our ancestors started shaping the stone into a thin blade, or rounded oval, that the crude tool became an object of beauty. Perhaps there was an attraction to the symmetrical pointed leaf or teardrop shape, the smoothness of the material, or the lustre – but these axes have been unearthed by the thousands all over the earth. Examination shows that the tools weren’t just used as tools – without evidence of wear on the delicate blade edges, it proves that these were kept around for admiration. While there are regional preferences or tastes in aesthetics, there are some objects that are universally acknowledged to be representative of beauty – jewels, gold, ores.  Therefore, beauty is not in the eye of the beholder, rather, our sense of beauty has been passed down from distant ancestors.

No, theories such as the elements and principles of design do not disprove the statement that beauty is in the eye of the beholder. What the elements and principles stand for is just fundamental components or ideas on any visual work. They certainly are not a set of guidelines or rules for an artist to follow in order to create an appealing work of art. People can still form their own preferences to what they consider aesthetic within the elements and principles. For an easy example, some people prefer blue over red. Some may like the use of dominance, while others think that a repetitive artwork is nicer to look at. Because people can form their own biases and opinions within the elements and principles of art, beauty remains in the eye of the beholder.

TOK #13: What is Art?

Unlike The Arts, Science tells us something valuable about the world.
 Outline a clear argument in support (claim, explain, evidence)
  Outline a clear counter-argument ((claim, explain, evidence)

The arts is only able to produce conceptual knowledge about humanity, whereas Science actually provides us with useful information about the world we live in. In comparison to the factual aspect of scientific knowledge, what we can obtain from art is very limited and would not be of any significant value. The information we gain from science is invaluable, because without science human civilization would not have been able to advance very far from primitive cavebeings.  On another note, any knowledge gained from the arts is difficult to trust because what is being conveyed depends on the creator. Everything is subjective, so the information gained from art has the possibility of being inaccurate. It’s based on personal experience, affected by a myriad of factors, whereas science is subjective. Scientific knowledge is empirical and testable – having been explored and verified by scientists all over the world to become widely accepted. Thus, science is so much more valuable because we’re actually able to take that information and use it to further develop our understanding of the world, to advance technology. The things you can do with the conceptual knowledge gained from art is limited. Perhaps this is why IB allows students to take double sciences without an art, but does not allow them to take double arts without a science subject.

Conceptual knowledge about humanity is valuable as well, because it gives insight into human nature. Information about “the world” is not limited to only the physical, natural world but rather is an all-encompassing term that is very broad. What can be considered valuable is subjective, and different to everyone. The type of knowledge generated from science and arts is very different –  while science deals with the natural world, art provides us with insight into humanity. It could be argued that one is more valuable than another, but both are definitely valuable. For example, cave paintings and artifacts allow us to glimpse into the past, for historians to gain more knowledge of how life and culture was like in another era. To develop an understanding of the past is valuable, as it allows us to make more informed decisions about the future (history repeats itself). Comic strips and graffiti drawings are examples of how art can allow us to see harsh realities that are covered up or unspoken of, as artists commonly use these mediums to express their opinions on politics or society.

TOK #12: Science vs Pseudoscience

It is unsurprising when we hear that experts in Art can’t always agree what ‘is’ and ‘is not’ Art. We might say that the distinction between what ‘is’, and what ‘is not’ art, is not always clear. Similar to the question of what is art, the distinction between science and pseudoscience is also not clear. Analyze this claim.

On the surface, the distinction between science and pseudoscience seems clear, if we follow Karl Popper’s approach. According to him, only theories that can be falsified (proven false) can be considered scientific. Pseudoscience, on the other hand, deals with practices that can’t be proven false. For example, in the case of chinese medicine, many believe that acupuncture can help to treat various health related issues. While there is no compelling scientific evidence to prove why or if it works, you can’t say that it doesn’t, as it’s a well-known treatment used by many. Even if you were to find a person that claimed to not feel any difference after a treatment, the acupuncturist can just argue that Chinese medicine works differently on everyone, and that the same results can’t be created every time.

Popper’s deceivingly simple way to identify what is science is not perfect, and has a few flaws. The first problem is that Popper grew up with experience in physics, which may have influenced his philosophy on science. Physics is a branch of science that deals with exact laws and precise theories. When you get to topics such as human evolution in biology, the degree of falsifiability declines, in other words theory of human evolution is less falsifiable than quantum mechanics, for example. While you may be able to find evidence to go against human evolution, because it happened so long time ago no one can say for sure if the evidence is able to disprove it – there are myriads of other variables or possible reasons for why said evidence exists. As human evolution falls within biology (which is an accepted science), but is too vague to be outright falsifiable, there is a problem with Popper’s criterion.

If everyone in the scientific community followed Popper’s theory of falsification, we would be in a lot of trouble. Should scientists throw away their work just because it doesn’t deal with testable predictions? Most theories are accepted when the findings are backed up from experiments conducted by scientists all over the world, and even when there is something to disprove it, the theory is not completely useless or disregarded immediately. In conclusion, testability is a flawed criterion that is too limited in definition.



TOK #10: Intro to Natural Sciences

Reflecting on our discussions in class, and with inspiration from the TED video, what distinguishes Natural Science from other AOKs?
Identify any potential issues or questions that may arise when you consider your definitions.

Firstly, it may seem quite obvious to state but Natural Science is unique from other AOKs in that it limited only to the natural world. This means mechanisms or concepts related to how our physical world works, and not the supernatural world (things that are unproven). Practical problems that can be solved through applying this AOK for example, could be answering how the digestive system works, or identifying how far away the earth is from the sun. It is important as discoveries in natural science has helped to shape the world we live in today, from the invention of planes to breakthroughs in prosthetic limbs. Science is not always fair, and one aspect of this is the question of ethics. Quite often, ethical considerations can limit the scope of inquiry into certain areas, such as research into stem cells. The use of stem cells is controversial because it involves the death of embryos, which some consider to be unjust.

Knowledge is gained through the formulation of a hypothesis or prediction, which is then verified by experiments. Natural sciences is also based on theories, which can be backed up by sold evidence. The more pieces of evidence from different lines there is to back up a theory, the stronger the credibility of said theory. This area of knowledge seeks to understand, but does not seek the truth – as scientists are always trying to disprove existing theories for further comprehension of the natural world. While scientists come up with laws and theories, none of them are final, as science is simply an attempt in finding the best explanation for how things work. Nothing is certain, and nothing can be proven or disproven indefinitely. Over the years, existing ideas has been built upon, refined, or debunked in the search for understanding. What the general public accepts as a widely known fact today can be proven wrong tomorrow.

The natural sciences is baised.  This statement refers to the subjective nature of scientists, in that as humans they are bound to be influenced by various factors, be it gender, culture, background, or interest. It is possible that scientists who expect a certain outcome in an investigation may unconsciously alter the data to achieve their desired results. Therefore, every scientist has the responsibility to minimize any type of subjectivity in order to present reliable and valid findings.