Theory of Knowledge blog for students and teachers

2013 TOK essay titles

2012-09-22T03:55:00.002-07:00

MAY 2013 ESSAY TITLES

1. In what ways may disagreement aid the pursuit of knowledge in the natural and human sciences?

2. “Only seeing general patterns can give us knowledge. Only seeing particular examples can give us understanding.” To what extent do you agree with these assertions?

3. “The possession of knowledge carries an ethical responsibility.” Evaluate this claim.

4. The traditional TOK diagram indicates four ways of knowing. Propose the inclusion of a fifth way of knowing selected from intuition, memory or imagination, and explore the knowledge issues it may raise in two areas of knowledge.

5. “That which can be asserted without evidence can be dismissed without evidence.” (Christopher Hitchens). Do you agree?

6. Can we know when to trust our emotions in the pursuit of knowledge? Consider history and one other area of knowledge.

Check out TOK Essay Ideas and get a free TOK essay template.

What is Maths?

2007-12-04T02:03:00.000-08:00

Is maths the language of reality?

"Mathematics is the abstract key which turns the lock of the physical universe." This quote by John Polkinghorne captures the most amazing characteristic of maths: that somehow it, better than anything else, can be used to describe and explain natural phenomena.

Much of physics, for example, is written in maths. Newton's F=ma or Einstein's E=mc2 are examples of equations that capture the heart of their theories. Is reality mathematical or is maths an invented 'language' useful for modeling natural phenomena? Is maths discovered or invented?
We may never know the answer and it may not even matter because maths works very well for our purposes. Abstract mathematical explanations make sense and empirical evidence seems to support them. Galileo said "the laws of nature are written in the language of mathematics"... we just do not know who is writing!

What is maths based on?

In early 20th century Bertnard Russell and Alfred Whitehead published The Principia Mathematica which tried to prove that maths was based on logic (maths is reducible to logic). The Principia was celebrated but as it turned out the thesis was unsustainable.

In 1931 Kurt Gödel proved that it was impossible create logical systems that are both consistent and complete.

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete.

This came to be known as Gödel’s Incompleteness Theorem and it meant that there are some mathematical truths that cannot be deduced in any formal system. Maths cannot be reduced to logic. We do not know what maths is based on. This makes maths fascinating and mysterious but it also means we cannot totally trust it. (Gödel's proof is not easy to follow, but in the end it hinges on something like the liar's paradox known since antiquity. Check his proof here).

How many sides?

During the introductory lessons we learned about many marvels of maths such as game theory, chaos, fractals and topology (an area of geometry). Topology studies continuity of space and spatial properties.

An example of topologically interesting object is the Möbius Strip. You can make one by taking a strip of paper, giving it half a twist and joining it into a loop. An object that had two sides now only has one.

In 1882, Felix Klein imagined sewing two Möbius Loops together to create a single sided bottle with no boundary. Its inside is its outside. It contains itself. It is not very useful as a bottle but it is quite beautiful mathematically (you can find one here, scroll down, it is the last picture on the page).

By the way, topologically speaking vests worn under the jacket are not really under the jacket ... if I ever dress like that I will demonstrate that by removing my vest without taking off my jacket first.

The session was taught by Nigel Wheeler, Head of Faculty for Mathematics.

Science and ethics

2007-11-13T03:19:00.000-08:00

Right & wrong in research

Scientists rarely work by themselves, although scientific breakthrough may be credited for a single individual. When a scientist comes up with a new theory, many other scientists will empirically test it. Only after the scientific community accepts the theory, it will become recognized.

Even the most important scientists who have created paradigm shifts have not worked alone. Newton, one of the most brilliant physicists in the history of science, admitted he was only able to create his theory because many other scientists had made discoveries before him. "I was able to see further because I was standing on the shoulder of giants."

Hoping to become famous and make breakthrough discoveries scientists are sometimes tempted to use questionable methods. They may steal someone else's research data and ideas and take the credit. This happened for example in 1953 when James Watson and Francis Crick were credited for discovering the structure of the DNA, when in fact the credit should have gone to a brilliant female biologist Rosalind Franklin.

Franklin came up with the double helix structure based on X-ray images of the DNA. Her supervisor passed her data to Watson and Crick who at the time were also studying the DNA and realized Franklin was on the right track. In 1962 Watson and Crick received the Nobel Prize for 'their' discovery. Franklin on the other hand was already dead. She died at the age of 38 due to radiation exposure she got from taking X-rays as part of her original research.

Right & wrong of new knowledge

Sometimes new knowledge can be misused. In 1905 as part of his research for Special Theory of Relativity Einstein realized that huge amounts of energy could be released from a small amount of matter. This idea is expressed in his famous equation E=mc2 (energy = mass times the speed of light squared). If one could split the nucleus of the atom a huge explosion would follow. A bomb based on this principle would be a devastating weapon.

In 1939 Nazi Germany started WW II and many were afraid Hitler might try to develop the nuclear bomb. Einstein among other German physicists who had escaped from Nazi Germany decided to send the US President Roosevelt a letter asking the USA to build atomic bomb before the Germans.

By 1945 the work was finished and immediately after that it was used against Japan killing around 200 000 people with only two bombs. Einstein was shocked. In 1954 just before he died he said "I made one great mistake in my life... when I signed the letter to President Roosevelt recommending that atom bombs be made." Also J. R. Oppenheimer (both in the picture), who was in charge of the development of the nuclear bomb, regretted he had helped to bring about such a terrible weapon.

Thankfully the world has never experienced a nuclear war but it did experience the Cold War, a power stuggle between the two superpowers the USA and the USSR. The USA alone is estimated to have spent over $ 10 trillion on nuclear arms during the Cold War (1945 - 1990). What could have been achieved if this money would have been spent on infrastructure, health care, education and medical research?

Right & wrong in science today

Genetic research is a modern area of study that raises many ethical questions. For example, for gene therapies it is sometime necessary to harvest stem cells from human embryos. Is it right to harvest these cells, even if it is done to cure someone? The embryo could develop into a healthy baby.

To study human genes researchers have fertilized eggs that contain both human and animal DNA. Is producing hybrid fetuses morally right? Are we playing god when we conduct such experiments? Some hybrid animals that have been created by researches are quite bizarre like a mouse with a human ear. Some genetically manipulated animals are used to produce medicine, for example genetically manipulated cows that produce insulin for diabetics.

Probably the most heated debate is over genetically manipulated crops. Scientists have improved qualities of some plants so that they grow better or produce greater harvests. Nobody knows if eating such foods that uses such plants poses a health risk for humans, and nobody knows for sure how such crops may alter natural evolution. The debate is over if genetically manipulated food should be allowed or not.

However the advancement of genetic research holds much promise. In 2003 researchers managed to map out entire human DNA. We now are at verge of understanding the genetic basis for many diseases, and with genetic manipulation possibly curing them. For example couples could be screened so they know what risk they have to give births to a baby with a hereditary disease. If the risk is great they could opt to have a test tube baby that has been screened not to carry faulty genes, or through genetic manipulation the faulty gene could be replaced by a healthy one before planting the egg in the womb.

The pursuit of new knowledge and technologies forces us to face new ethical questions. Through rational and balanced arguments we may be able to come to wise judgments regarding the use of new knowledge and technologies even when it is impossible to predict all the consequences these may bring about.

The session was taught by Sara Gleeson, Pastoral coordinator and Biology teacher.

How do scientists do science?

2007-11-06T00:09:00.000-08:00

Rules of the game

Scientists try to figure out the rules behind natural phenomena. We simulated this in our "dice experiment" during the lesson. The interesting thing about this experiment was that we came up with different rules to explain the same phenomenon. This often happens in science.

Of course doing real science is more complicated and involves laboratory experiments, measuring devices and teamwork with other scientists. Science is very much a social endeavour.

Bit like trying to figure out the rules for the “dice experiment”, some philosophers have tried to figure out the rules for doing science. They have asked how do scientists think when they do science?

Inductive thinking

The first answer to this question was that scientists think inductively. They observe phenomena and produce generalisations regarding how things seem to work. These generalisations could be called laws of nature.

This theory of science has some problems however. Imagine what you would say if your biology teacher set you this homework “Go to the Khao Sok national park and observe!” Your first question would probably be, “What are we supposed to observe?” It seems therefore that there is no pure observation, but we always think of our observations through some kind of theory. The theory precedes observation.

If you look at this picture you may observe and interpret it according to female face theory or saxophone theory. The mind is actively interprets all our sense perceptions.

There are other problems too. No matter how many observations we have of a particular phenomenon, we can never draw certain conclusions. Inductive thinking never gives us certainty. Even if all swans we have seen were white, it is possible there are black swans, and indeed there are, in Australia!

Hypothetico-deductive thinking

So, if science is not based on inductive thinking what is it based on? Karl Popper was an Austrian philosopher tried to come up with an answer to this question. You know he was a German speaker because his answer was: hypothetico-deductive thinking. (The Germans are famous for their long words).

Popper thinks that scientist first create a hypothesis (a guess what the rules behind observations may be), then conduct empirical tests to see if the hypothesis can be falsified (proved wrong). If the hypothesis cannot be falsified, i.e. results of the test are as the hypothesis predicts them to be, we tentatively accept the hypothesis as a new theory.

According to Popper scientists should try to falsify existing scientific theories as quickly as possible and replace them with theories that explain the phenomena better. This is how science makes progress.

So, why is this called hypothetico-deductive method? Because firstly you create hypothesis (a guess) and then you test and use deductive logic to reach a conclusion. If the did not prove the hypothesis wrong, we accept that hypothesis. Accepting hypothesis because it is not wrong and an example of deductive thinking.

Popper's idea is interesting because we can use it tell apart theories that are truly scientific from those that only look scientific. Any hypothesis or theory that we cannot be proved wrong is not really scientific.

Example 1. A statement ‘metals expand when heated’ is scientific, because we can imagine a situation in which this statement would be falsified (i.e. heating a metal and finding out that it does note expand).

Example 2. A statement ‘human behaviour is caused by unconscious desires’ is unscientific because we cannot imagine a behaviour that would falsify this statement. (This is why Freud’s theories are not really scientific).

Paradigm shifts

When many scientists in a particular field think alike about some important issues, we say that there is a paradigm. Sometimes a brilliant scientist who is an original thinker comes along and proposes a theory that completely revolutionises the way we think.

For example in physics Newton was such a scientist. So wonderful was his theory that for a long time people thought we knew pretty much everything about physics and there was nothing to discover (Newton suggested that mass is constant). That is until Einstein came along and completely revolutionarised our understanding of physics (Einstein suggested that the speed of light is constant). His theory was better than Newton's. It explained more and it matched better with empirical observations.

When scientific revolutions like this happen we call them paradigm shifts. They do not happen very often but when they do science is taking huge leaps forward. There are some philosophers who are trying to figure out how and why these paradigm shifts happen. The first philosopher to introduce the idea of paradigm shifts was Thomas Kuhn. According to him these revolutions are so profound that one paradigm is incommensurable (incompatible) with one another. This means that it is impossible to marry Newton’s and Einstein’s theories, they just do not fit.

There are other interesting thinkers who explain how scientists think and how science progresses but this is already plenty. The main lesson to learn is that scientist do not prove their theories but disprove them and replace them with better one, and that science does not progress steadily but sometimes there are revolutions.

The session was taught by Nico van de Casteele, IB coordinator and the chemistry teacher (in the picture).

What a TOK presentation looks like?

2007-10-24T17:57:00.000-07:00

Check out this video to get an idea of TOK presentation.

This is what the examiners said about it.

Strengths

The “talk show” format works well
It is engaging and allows the presentation of opposing points of view
The topic is relevant to the student
The argument–counter-argument pairing shows some critical thinking
Ways of knowing and areas of knowledge, for example, language, perception, history and ethics, are mentioned

Weaknesses

It is difficult for the knowledge issues to be addressed explicitly, since this might mean stepping out of the role-play
There is no evaluation of relative strengths of the arguments on either side.
There is no consideration of any implications in related areas
Freedom of choice of the individual is given priority without any justification
Ethical judgments are not linked to underlying principleor
Some ideas are not developed

Comments by criterion

A: Identification of knowledge issue

A number of knowledge issues touched upon but not highlighted. How do we know the connection between a stimulus (in this case playing video games) and behaviour? How do we know where to draw the line between individual freedoms and the interests of the community? (3–4 points)

B: Treatment of knowledge issues

There is no real treatment of these issues once they have been identified.
There is no evaluation of claims and counter-claims (1–2 points)

C: Knower’s perspective

The topic is motivated at the beginning and there is a clear personal involvement in the method of presenting the arguments and the examples chosen.
The links with the local situation (for example, the school) demonstrate the significance of the knowledge issues discussed. (3–4 points)

D: Connections

There are tenuous links to history and ethics.
There is an interesting link to language and its role in ethics that is not fully explored.
There is a good connection to reason and the direction of causality, acknowledging that “all killers played video games” is not the same as “all video gamers killed”. (3–4 points)

Total 10–14 points

Hints for future presentations

There must be more treatment of knowledge issues
The presenters should take the time to fully develop the claims and arguments
Some thought could also be given to focusing on a more limited number of knowledge issues, treated in more depth.
There should be a clear evaluation of the arguments presented.
The students need not come to a definitive conclusion but there should be a sense that the presentation has helped the investigation to progress.
Encourage more audience participation

How to do a TOK presentation?

2007-10-13T18:05:00.001-07:00

A TOK presentation is another important component of this course. One third of your final grade is based on the presentation, so you should really try your best.

This year we have to film all our presentations and send the films to the IB for assessment, so it is particularly important that we have high quality presentations. What would a really good presentation be like?

To get an idea of this we will firstly look at the assessment criteria. In my next post I will show you some video samples produced by IBO and comment them. But now let's look at the assessment criteria of presentations.

Your presentation will be assessed using four different criteria:

Identification of knowledge issues

An excellent presentation identifies a knowledge issue that is clearly relevant to the real life situation/contemporary problem

Lets imagine you would want to a presentation on Is globalisation ethical? How could you link such a 'big' topic to a real life situation?

You could start by researching the idea of globalisation and ethical debate around it. In about 2 minutes I was able to find an interesting New York Times article through news.google.com regarding rights and wrongs of globalisation. This contains real life information about globalisation, such as what people in different countries think about it.
Treatment of knowledge issues.

An excellent presentation shows a good understanding of knowledge issues in the context of real life situation/contemporary problem

Does globalisation have anything to do with your life or is it just a big concept?

Let's think about it.

Did you buy ice coffee today in Flintstones? If you did you supported a multinational coffee company which most likely pays peanuts to coffee farmers in Colombia. That was an ethical decision on your part with global impact although you were just wanted to have a cup of ice coffee. Same logic applies to many other products you consume.

Tell me what globalisation and ethics mean for your life. Tell me what they mean to those farmers in Colombia. Tell me what they mean to that big multinational company? Give me your interpretations. Get it?
Knower's perspective

To get an excellent grade you should provide arguments and examples, show an individual approach and demonstrate why your presentation topic is significant.

Again your personal voice is being emphasised. You should actually try to argue something. A presentation that just lists pros and cons of globalisation is unlikely to get a very high grade. What do you think? Are some examples of globalisation you have covered in your presentation, in you mind, right or wrong. Tell me why you think they are right or wrong?

Select examples that are interesting, topical, relevant to you. Talk about a Julio who is a 14 year old boy working on coffee plantation, not only sales figures of Nestle and some fair trade companies. Give a story a face.

So what? What is the significance of me knowing all this about coffee trade? So what if child labour is used in China to produce Nike shoes I am wearing? Can you make a connection? Your purchase may be supporting a company that is expoiting someone somewhere. Does this make you think twice about consuming these products ... how about buying fair trade coffee instead?
Connections

An excellent presentation shows how the question (and I do want your presentation titles to be questions!) could be approached from different perspectives and considered their implications in related area.

The ethics of globalisation topic could, for example, be approached from perspectives of the individual farmer, the consumer, the economic development.

An important part of the connections section is that you link your presentation to knowledge issues i.e. ask yourself: how can we know? is this knowledge reliable? In this case of coffee trade issue ... am I just believing fair trade propaganda, or is there really something to argument that big coffee multinationals are exploiting farmers? Should I instead believe the multinationals when they claim they are providing job opportunities and creating wealth by their investments?

Be critical about the sources of information you use. Tell where you got the information and if in your mind this information is trustworthy.

When you draw your conclusions try to justify your claims as well as you can. Try to make your arugment such that it mostly appeals to reason, i.e. it makes sense to believe what you are saying.

How to write a TOK essay?

2007-10-13T16:28:00.000-07:00

As you know 2/3 of your final TOK grade is based on writing an essay on one of the prescribed topics. You want to get the best possible grade obviously, and therefore it is important to write a killer essay. How do you go about doing that?

The most important thing about TOK essay is personal voice; it really should be your essay, a piece of evidence of your thinking. You should really try to answer the question as honestly as you can. Don't just try to sound smart with complicated words.

IB gives us a lot of hints about what the essay should be like. We will firstly look at the examiners' report. In 2007 report they give us following advice.

An introduction should not reiterate the prescribed title in detail; nor should it spell out in great detail the exact course of an essay. Introductions should, instead, show a sense of what the question is about and provide an indication of the direction chosen.

Some of the more sophisticated essays used a specific example in the introduction to highlight an issue/topic and then returned to the example in the conclusion to show what progress had been made.
The strongest conclusions do not simply reiterate the main points of the essay, but instead put the findings into context and take a broader perspective on the significance of the issue.
Some students had good TOK points in individual paragraphs, but did not manage to make them cohere. Attention to the narrative flow through an essay was often lacking, and further guidance from teachers in this area is advised.
Over-reliance on rhetorical questions is to be avoided.

So now we know it. I have sometimes in the past given advice what the introduction, body and the conclusion should be like, by way of saying that this is what they could look like. Please do not take my examples so seriously that it starts to interfere with you personal voice.

Another important thing about TOK essays is that when you think of examples, taken from different Areas of Knowledge and your own experience; try to think of something that is original and topical. Check out the BBC website for recent scientific discoveries or debates one in a while. Ask your teachers.

The examiners' report made a specific comment that tired old examples of “1+1=2 ”, the flat earth and Guernica and others taken from TOK textbooks may not show the most original thinking. Do some research to find out better, more interesting perspectives, ideas and examples.

I will give you more ideas in class. For now try to see how you could take this advice and improve your essay. There are also sites that offer help with editing. Good luck!

What is TOK?

2007-10-11T19:07:00.001-07:00

What is theory of knowledge programme about?

Well, I told you it would be a combination of critical and creative thinking, but what does that mean?
Critical thinking means you don't take for granted what people tell you, but you ask yourself: Can I believe this idea? Is this a good argument? Should I change my mind?
Creative thinking means that you don't accept the obvious first idea that comes to your mind as a solution to a problem but you brainstorm and look for alternatives.

How will this blog help you to develop this type of thinking?

Time to time I will ask you post your ideas on this blog and sometimes we will post some of your homework too. Maybe you come up with an interesting link or picture ... post them here.

Let's make this blog come alive with your brilliant ideas!