# Math – Axioms and Proofs

If mathematics is created by women/men, why do we sometimes feel that mathematical truths are objective facts about the world rather than something constructed by human beings?

We sometimes feel that mathematical truths are objective facts about the world rather than being something constructed by human beings because of the axioms that exist. Since axioms are accepted facts without proof, they can give us insight on facts about the world since there is no proof so see whether they are true or not, and even though there are people trying to prove them to be true, they are still simply accepted and understood the way they are without needing an explanation. Even though mathematics is something that is created by human beings, we have grown and learned to use our deductive reasoning to find evidence for claims, hence justifying whether they’re true or false, therefore implement them into our daily lives as an underlying order that makes us sometimes feel that mathematical truths are objective facts about the world.

# Mathematics – Scope and Application

Definition of Math: Mathematics can be considered pure, where it includes abstract concepts such as space or the abstract science of number, but can also be applied to other disciplines such as physics and engineering.

Adding to the definition: Mathematics can be considered pure, where it includes abstract concepts such as space or the abstract science of number, but can also be applied to other disciplines such as physics and engineering. However, there is this underlying idea of patterns within math, it can act as a pair of conceptual spectacles that allow us to see the similarities and differences between two phenomena that may seem quite different at first glance.

Change in Definition: Mathematics can be considered pure, where it includes abstract concepts such as space or the abstract science of number, and have an underlying idea of patterns, as it can act as a pair of conceptual spectacles that allow us to see the similarities and differences between two phenomena that may seem quite different at first glance. It can also be applied to other disciplines such as physics and engineering through pure and applied math, where the basics of mathematics can be transferred and implemented.

# The Arts – WOKs and Knowledge Framework

Take a picture of your diagram and explain it in your blog.

In The Arts, I believe the acquisition of knowledge comes from four ways of knowing working together. We took the specific example of Salvador Dali’s The Persistence of Memory, and decided that Sense Perception, Imagination, Emotion, and Reason work together. Firstly, when you view an artwork, you would have to view it through active sense perception in order to see the colours, the techniques, what objects are presented within the work; then this can be taken into two different strands: Imagination and Emotion. Imagination can be used when taking your personal perspective to thinking about what the artwork is trying to represent, and what the symbols show. On the other hand, emotion can be used when depicting the symbolism of the colours used. These two WOKs can also work together as emotion can influence imagination, as a certain colour may cause you to imagine certain things when viewing the artwork. After imagination and emotion, Reason comes in to try and explain what you have come up with using imagination and emotion, and to see whether they fit within the context of the artwork and/or the artist’s intention. These four WOKs work in a cycle, with sense perception starting it off, and they all work together in the acquisition of knowledge in The Arts.

# The Arts – Knowledge, Method, Historical Development

What is the methodology behind the lightsaber as a piece of Art?

In the method of creating the lightsaber, the creator was creative by using personal knowledge of having swords from films that included chivalry to represent some kind of honour when fighting, along with imagination to develop this idea further in order to create the lightsaber. This creation also used the relationship between art and technology, as the lightsaber’s intention was to be some type of sword that allowed the Jedi to protect themselves, but at the same time it was created to be more futuristic compared to the traditional swords we are used to seeing. When creating the lightsaber in Star Wars, they were like torches, and through the use of reason in technology, the light ray was able to be created and used in the fight scenes along with other digital effects such as blocking rays.

Does Deadmau5 give you knowledge that goes beyond language.

I think Deadmau5 gives you knowledge to some extent because when I was listening to the song and walking around the classroom, at certain parts throughout I felt the urge to move and dance. I think that in this case it does give me knowledge that goes beyond language as the feeling of wanting to move cannot fully be expressed in words in order to allow other people to feel the same way, as they actually have to feel and experience listening to the song in order to understand the sensation.

# The Arts – Scope and Application

Write your own definition of art based on the dictionary definition.

The Arts is a broad variety of branches such as painting, music, literature and dance. These branches typically use creativity and imagination, where these branches create a form of visual expression with emotion, and can be intended for an audience. Art is rather subjective, as people have different views on what they consider is art, and these views may not necessarily be the same way the artist themselves think.

# Natural Science – WOKs, Language and Concepts

Write about two separate networks that use the ways of knowing. The first network uses the ways of knowing to produce knowledge in the natural sciences while the second network uses the ways of knowing to acquire knowledge in the natural sciences. Each network should have a minimum of two ways of knowing in it.

In the production of knowledge, it requires a network that uses the ways of knowing in order to create a certain pieces of knowledge in the natural sciences. In this network, it can use several ways of knowing such as Sense Perception, Imagination, and Reason. These three WOKs work together in a network as imagination is used when coming up with a hypothesis out of the blue, and sense perception steps in to help test that hypothesis in an active way in order to make some sort of judgement about the hypothesis that came from the imagination. Reason then can come in when trying to explain why these observations through sense perception happen, and can be done through inductive reasoning. However, reason can also falsify the observations that happen with sense perception, thus can further contrast from the hypotheses created using imagination. Therefore, Sense Perception, Imagination, and Reason are three ways of knowing that can be used to produce knowledge in the natural sciences.

In the acquisition of knowledge, it requires a network that uses the ways of knowing in order to learn and understand knowledge in the natural sciences. In this network, it uses different ways of knowing than in the production of knowledge such as Language, Faith, and Memory. These WOKs work together in a network as language is used to deliver and communicate the knowledge through definitions and explanations, and faith is involved in the acquisition of knowledge due to whether people believe and trust the information they are receiving. Memory then can come in when trying to remember the information that has been communicated, as remembering the information is important during the acquisition of knowledge. This is important because it requires the more effective verbal communication in language as well as believing and trusting the information in faith in order to remember it and recall it in the future in order to apply it to daily life. Therefore, Language, Faith, and Memory are three different ways of knowing that can be used to acquire knowledge in the natural sciences.

Why is it important for the Natural Sciences to have their measurements found in nature and not created by humans? How is measurement the language of Natural Science?

I believe it is important for the Natural Sciences to have their measurements found in nature because it is less likely for it to be manipulated or changed compared to measurements created by humans. Measurements are crucial in the Natural Sciences as many concepts and ideas require numerical values and quantification in observations in order to support hypotheses and to come up with appropriate conclusions using that data; therefore, using nature could allow these quantities to fluctuate less due to less modification in them, hence making these measurements more reliable. This is different from measurements created by humans because they have the tendency to fluctuate and change overtime, and it could be less accurate due to wanting to modify the values in order to justify the hypotheses and observations being made, thus making these measurements less reliable than measurements found in nature.

# Natural Science – Historical Development

What were the five key events in the Historical Development of the Natural Science?

1. Ancient people who discovered facts through sense perception and trial and error. This is a historical development because back then people did not record what they discovered, for example by touching fire and knowing that it is hot.
2. China and India using their religion and beliefs to discover more aspects about the natural world. This is a historical development because this is when the Chinese did alchemy, which was early Chemistry and discovered answers through the elements and yin yang. It is important because it was one of the starting points to discovering more about the natural world.
3. Galileo discovery of the microscope and telescope because it was different from religion, which was what people mainly depended on when reasoning the observations in the natural world.
4. Creation of the printer because it allowed people to share their knowledge through publications.
5. Isaac Newton who discovered the scientific method because it allowed there to be a more structured way to create theories, concepts and ideas about the Natural Sciences.

Is it inevitable that the Historical Development of the Natural Science’s has led us to our current way of doing Natural Science? Why or why not?

I think it is inevitable to a certain extent that the Historical Development of the Natural Science’s had led us to our current way of doing Natural Sciences because without previous inventions and theories that have been discovered by people who may not even be scientists, there would no be base that starts off the development of Natural Science. Currently, we stick to concepts such as the scientific method, but the study of Natural Sciences is a continuation of developing ideas that have been created in the past, but at the same time there are some that try to disprove theories and ideas, showing that the historical development of Natural Science’s has led us to our current way of doing it. This contrasts from what has been done before in Natural Science, as people used ideas from religion and intuition. However, it may not be inevitable to a certain extent as well because without the Historical Development of Natural Science, there could be new methods that have been developed now that lead to the current way of doing Natural Science. For example, the Scientific Method is a method that can be used in Natural Science but some can deviate from it as they believe that shouldn’t be the way of doing Natural Science.

# Natural Science – Methodology

In what ways does this quote help us understand the methodology in Natural Science?

This quote mentions that in science, there is an essential balance between two contradictory attitudes, one where there is an openness to new ideas, no matter how bizarre they may appear, and secondly, the most ruthless skeptical scrutiny of all ideas, old and new; and through this is how deep truths are created from deep nonsense. This helps us understand the methodology in Natural Science because when someone first observes an area of the natural world, they have to approach it with an open mind in order to fully comprehend and start to make hypotheses about it before conducting experiments. Furthermore, one would have to take account all old and new ideas and theories in order to critically observe and examine the area of the natural world, thus working towards developing conclusions after looking at all areas that need to be covered.

What is Karl Popper’s theory of Falsification?

Karl Popper’s theory of Falsification disagrees with what people usually think, he suggested that bold hypotheses should be made and can be falsified by evidence. He believes that scientists should go out of their way to find evidence that falsifies their hypotheses in order to refute them and not to find confirmation to support them. For example, scientists may come up with a hypothesis saying that all swans are white, then continue to look for evidence that supports that. However in Popper’s theory, these scientists would have to go looking for black swans, and not to continue looking for white swans.

How is it different from the way most people view Natural Science?

Most people view Natural Science because most people believe that new theories and ideas are created by building upon old theories and ideas, and creating new ones that support and confirm the ones made before. However, Popper states that ‘Science is all about Falsification, not confirmation”, as it is a series of conjectures and refutations, and he believes that the best that scientists can do is to try and prove their hypotheses wrong and fail, thus making Popper’s theory of Falsification different from the way most people view Natural Science.

# Natural Science – Scope and Application

Create your own definition of the term Natural Science based on the TOK questions and dictionary definitions.

Natural Science is a system of knowledge that involves the study of the physical world and its phenomena, and include areas such as physics, chemistry, biology, or geology, but excludes social sciences, and abstract or theoretical sciences. This involves observing objects or processes in nature and using the Ways of Knowing working together, such as reason and imagination to create a prediction. Then through the process of understanding, generalized statements, principles or scientific laws can be developed about the natural world that can be shared amongst individuals to create shared knowledge.

Who is the Natural Sciences map metaphor for?

The Natural Sciences map metaphor is for those who interact the natural world, which helps them understand and have a sense of the physical world around us, which could allow them to create generalized statements, principles or scientific laws about the natural world. It can also be for those who want to manipulate the natural world, as the map metaphor would help them understand and comprehend the natural world, allowing them to develop methods to change it to perhaps fit a concept or rule.

What questions in Natural Sciences is it answering?

The Natural Sciences map metaphor can answer questions such as:

How is our natural world like?

How is our natural world viewed? Can it be viewed in one perspective?

What hypotheses, generalized statements, principles or scientific laws can be developed about the natural and physical world?

How is the map skewed in Natural Science to help us answer its questions?

I believe that map is skewed in Natural Science in the way that it gives us a limited view on how the natural world is actually like, as different people have different opinions and come up with various contrasting theories that allow one to question how they see the natural world. It allows us to realize that we cannot really view our natural world through one viewpoint, as there are copious amounts of statements, principles or laws that can be generated from the map to help us answer questions about our natural world.

# Intuition

What is intuition?

Intuition can be seen as the unconscious processing the brain undergoes when it first sees something. This can be the first instinct that comes to mind, and this initial thought can come easier through prior knowledge, beliefs, and experiences. Intuition can be thought of as more personal knowledge, as what one might think is accurate through the way they perceive the instinct, it may not be the same amongst a shared community.

What is System 1 and System 2 thinking?

System 1 and System 2 thinking are two contrasting modes of thought. System 1 thinking is your brain’s first instincts, and the mode of this thought can be automatic, effortless, fast and ineffable; whereas System 2 thinking is when your brain takes more time to think about the instinct, and this mode of thought is more controlled, effortful, slow and effable.

How could you incorporate System 2 thinking into TOK?

System 2 thinking can be incorporated into TOK because a lot of the knowledge questions we get require some thinking in order to come up with a conclusion. We might initially have an answer to the question, but we have to take more time to understand and process the question to come up with a suitable response. Additionally, System 2 thinking can also be used when coming up with knowledge questions from the knowledge claims, as knowledge claims can be more of a System 1 type thinking, as it is taking claims from the real life situation, however, when creating knowledge questions, the thought is more controlled, effortful, and slow in order to ask a question that leads to the bigger picture.

Do you trust your own intuitions? Why or why not? If your answer is “It depends”, then on what does it depend?

I believe that I can only trust my own intuitions at certain times. When it comes to expert intuition, it is something I have experience and am familiar with, allowing me to be more knowledgeable in that area, thus making my intuitions more trustworthy. Even though intuition is typically the first instinct that comes to mind, and it should be automatic and effortless, if it is expert intuition, I would know more about this area of knowledge, therefore my intuitions would be more reliable to a certain extent. However, when it comes to situations where I am not that familiar or have less experience with, it would be better if my intuitions were not trusted, as I am less knowledgeable in that area.

Is intuition a convincing justification for shared knowledge?

Similar to the previous question, I believe it depends on whether the shared knowledge is in an area where the whole group is an expert in because if this group were all experts in a specific area, their intuitions would be more reliable and trustworthy, thus making it a convincing justification for the shared knowledge. However, if the shared knowledge is in an area where the whole group is not an expert in, it could be moral intuition rather than expert intuition. This is where beliefs are formed through the influence of different environments, and instead of having their intuitions based on what is accurate in that area, their intuitions could be based on the different combinations of moral values each individual has, thus suggesting that the intuition is not fully a convincing justification for shared knowledge.