Pt. 7 – The Areas of Knowledge:
Mathematics, the Natural Sciences, The Human Sciences and History

What are the Areas of Knowledge

The Areas of Knowledge are a bit different, these are about what we know. There are 8 Areas of Knowledge, these are: Mathematics, the Natural Sciences, the Human Sciences, History, The Arts, Ethics, Religious Knowledge and Indigenous Knowledge.

Each Area of Knowledge is a system. Within each AoK system there are agreed ways to investigate things. There are also agreed standards of proof and argument that are different in each Area of Knowledge. So we can think of an Area of Knowledge as a body of knowledge that seems to fit together in one system.

The Areas of Knowledge are the ways we categorise the knowledge that we have. In this post we’re going to run through the first four of the Areas of Knowledge and talk about the features of each of these systems.


Mathematics is a fascinating topic to think about, largely because it works differently than many other areas of human reasoning. For example, in mathematics we start from a set of axioms that we all agree on. An axiom is a basic fact or idea that we say cannot be changed. You might have also heard of the work premise. This is similar to an axiom as both are starting points for an argument. In mathematics, the idea that the addition of two positive whole numbers can only ever lead to a positive whole numbers is axiomatic. No matter what positive whole numbers we add together they will always produce a positive whole number.

Mathematics is unusual because it is founded on axioms which are more or less universally accepted. This means that across time and culture mathematics seems to be universal. One discussion that surrounds this is the debate over whether mathematics is discovered or invented. Whilst some claim that it is the product of human thinking and thus must by definition be an invention, others refute this perspective. It can be argued that mathematics is simply a description of the real world. The area of a circle is equal to pi times the radius squared. This is a description, not an invention, some would argue. What do you think? Click here for an excellent video on this topic!

We should also link this Area of Knowledge to reason as a Way of Knowing. Indeed, part of the universal nature of math is due to the fact that it works according to deductive reasoning (see our previous post on the ways of knowing if you aren’t sure what deductive reasoning is). This means that many people from very different backgrounds are able to follow mathematical arguments, as they possess this deductive ability. If you’re thinking about discussing mathematics in your work you can use this feature to begin an argument about whether all people possess the same reasoning ability in the same degrees. Some might argue that our resoning ability fundamentally differentiates us from the rest of the animal kingdom. They might point to the clever things people have done using reason. But you could point to people who have a diminished capacity for reasoning, such as the mentally disabled, and ask if they are not human. An interesting debate is sure to follow!

Another discussion that can be had with regards to mathematics is about its relation to reality. After all if we accept that mathematics is discovered rather than created we have to deal with an awkward fact. Pure mathematics does not rely on any prior sense perception! Isn’t it strange to think that something can be discovered entirely without the senses? How might we explain this? You could contrast this with the appliance of mathematics to the real world.

This typically happens in the natural and human sciences.

Homer in a relative world

Remember: If you want to talk about mathematics consider whether it is invented or discovered, whether it is certain or true (or both!), and whether mathematics is independent of culture.

The Natural Sciences

The natural sciences want to investigate the natural world around us. Their methods include observation and testing of hypothesis. This is the scientific method. One of the most interesting questions in this field is about the removal of the human element. Scientists try to design experiments to reduce the effect that the human observer has on the outcome. Asking how possible this is in different fields can tell us something about the strengths and weaknesses of the natural sciences.

Science is different from mathematics in that it combines sense perception and deductive reasoning. Reasoning must be present in relevant argumentation, but theories must also be able to survive the test of real life experiment or observation. This combination allows us to open up interesting questions about what a science is. The line between the human and natural sciences is a thin one, and is often debated. Indeed the very name ‘natural sciences’ contains an implication that human beings are outside of nature. Does this make sense to you? Do you think that this assumption is an objective one or has cultural roots? If science contains cultural assumptions do these impact its supposedly objective work? Thinking about these questions will help you form an argument in your ToK essay or presentation. You can even think about how the different AoKs interact with each other. If science is non-human, because it is objective, then should it be constrained by ethics? What justifies a scientific experiment and what ethical concerns might stop such an experiment?

Human Sciences

For IB students the human sciences include many of your group 3 subjects. The human sciences are meant to study the reality of being human. That means that human sciences look at things like the social aspects of human life and how people live together. They also explore culture and human thinking. Subjects like sociology, politics, anthropology and psychology fall into this category.

So what are the differences between human science and social science? Well, one of the big differences is what we mean when we use the word ‘science’. In a way human sciences do count as science because they use the scientific method. That is, they create a hypothesis and then test it against reality. A psychologist might hypothesise that classical music tends to make people perform better in IQ tests. They could devise an experiment, try this out and find that indeed, if people listen to Mozart before a test they tend to score a higher mark. The use of hypothesis and experiment might remind you of the natural sciences. There are some differences from the natural sciences though. For example, the psychologist would struggle to call this a ‘law’ as in the law of gravitational attraction. This is partly because the psychologist could not reliably show that all people were affected the same way by this music. Then there would be questions of which cultures responded in this way, and whether responses changed over time. The predictive accuracy of the human sciences tends to be lower than in the natural sciences – although this is a controversial topic and one you could certainly explore.

You might also want to consider what constitutes proof in the human sciences. Often we find that the human sciences will rely on statistical probability. In the natural sciences there may be more times where that probability approaches one hundred percent. Do you think there are any problems involved in using statistics in the human sciences?


History as an area of knowledge does not simply refer to everything that has ever happened. Instead it is about the past that has been recorded by human beings. One of the major debates that you should consider in history is interested in the idea of the ‘historical fact’. At first it might seem obvious what this is – a fact telling us something that has happened. But think about it, there is a lot of human involvement in defining the past when it comes to history. You might have heard about the notion that the winners of a war write the history books. What do we think they are likely to record. Should it be called a fact? You should ask yourself whether it is possible to be objective when writing about history. The historian Max Weber thought that it was not. He argued that in every situation there were endless things that could be described. The fact of having to choose which ones to discuss already stopped one from being objective. After all, focussing on role of one person rather than another will affect how the past is perceived.

Max Weber
Max Weber

We can also draw attention to another interesting debate in history. Rather than considering which facts are being described, we might consider whether we can have any facts at all. If we think of an historical event, such as a great war, we might think we know much about that war. But ToK invites you to ask how we know such things. Did you see the war, using your own senses? If not, how did you find out about it? Perhaps you heard from a friend or a family member, but how reliable is their knowledge? Maybe you read about the war in a text book? But who wrote that book and for what reason. Do you think that text books in North Korea will write much about the mass starvations that have happened to their people? Are your text books more reliable? Why? These are sort the questions that show you are reflecting critically in subjects like ToK.

Well Done!

If you’ve read and understood each of these Areas of Knowledge then you are not far off mastering this area of ToK. By thinking about some of the questions involved here, you should be able to start developing your own perspective on these subjects. It is now your job to defend and grow your perspective throughout ToK essary and presentations. The things you have learned here should be a first step in mastering ToK and acing those assessments.

Read Part 8: The Areas of Knowledge – The Arts, Ethics, Religious Knowledge, Indigenous Knowledge