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Are “vagueness” and “ambiguity” shortcomings of language or can they be viewed as positive aspects of language?

The ambiguity or vagueness of language can often cause misunderstandings.  These misunderstandings can sometimes lead to embarassment, inconvenience, or even accidents.  On the other hand, I feel that it is the ambiguity of language that drives the possibility for creativity within language.  Humor is often dependent on the ambiguousness of language, such as in puns.  In literature, especially poetry, the words used may have been chosen purely because of their ambiguity.  Thus different people may respond to a piece of poetry in different ways according to their own experiences.  Those ways may be unintended by the author, but in the end still enhance the value of the poem.  So even though the vagueness or ambiguity of language are often seen as shortcomings, they can definitely be viewed as positive aspects of language.

Are “vagueness” and “ambiguity” shortcomings of language can they be viewed as positive aspects of language?

I think that we often see the vagueness or ambiguity of language as having a negative effect.  It results in miscommunication since people can interpret the same word differently and the connotations of each word could vary within a group of people.  This ambiguity could hinder one’s quest for knowledge because the value claims associated with particular words do not have a consistent meaning for everyone.  Of course, dictionaries are supposed to be exact definitions yet the trouble with ambiguity comes with the connotations of each word.  Vagueness enables us to get a way with “lies”, such as in advertising.  I once did a project observing the effects of Hairdye, on the box it said that if you use their particular Keratin serum it’ll make your hair “stronger” yet it doesn’t specify what your hair will be stronger than.  Sure the serum makes your hair stronger after you dye it, but your hair is strongest left untreated.

However, the vagueness and ambiguity of language can also be seen as a positive aspect because the numerous intrepretations that result from a single word or sentence makes up the beauty in literature.  In English class, we often analyze poems or novels; coming up with explanations that can seem to be from two ends of a spectrum.  In this case, the ambiguity of language is good because it allows for us to think creatively and create our own meaning from a text.  As we go around the room during the Socratic Seminar sharing our different interpretations, we can all appreciate and learn from each other’s ideas.  Creative forms of language is a result from this vagueness and ambiguity, thus illustrating how it can be viewed as a positive aspect.


  • more creative
  • allows for multiple interpretation
  • allows you to tell white lies to avoid “hurting” someone


  • when it is not intended –> can offend people
  • not good for the sciences, when you are trying to be exact
  • can be used for manipulative purposes
  • religious and political conflicts

Vagueness & Amibiguity

Are “vagueness” and “ambiguity” shortcomings of language or can they be viewed as positive aspects of language? Explain.

There are a number of benefits and shortcomings to vagueness and ambiguity. Without ambiguity, students would be unable to analyze and deconstruct abstract concepts such as poetry and art. Ambiguity is also necessary for humor, such as puns. However, ambiguity can oftentimes cause many problems and can lead to misunderstandings. An example would be the Madagascar clip that was played in class, where one ambiguous instruction that was given to the crew led to a disaster. Similarly, the lack of specificity in vagueness can be problematic when there are situations that require very detailed instructions with very little room for error. Launching  a shuttle into space requires a high degree of accuracy, so a vague instruction could result in fatalities. Additionally if a business hired a group programmers to develop a system for them and gave them vague requirements and an unsuitable program was developed, the operation would have been both costly and useless.  However, too much specificity would prevent people from making creative interpretations, thereby restricting their thinking.

Are ‘ambiguity’ and ‘vagueness’ shortcomings of language or can they be viewed as positive aspectes of language?

Ambiguity and vagueness both can be viewed as positive and negative aspects of language; in other words they both have their separate uses. Ambiguity and vagueness can be positive aspects of language by allowing the reader, listener, etc to come up with their own opinion of what has been said. This allows for creativity in everyday life; the arts, English, and other areas of knowledge are very ambiguous. Poems, books, abstract art are all examples of ambiguity; what would life be like is there was only one correct perspective of a poem? So, ambiguity allows for multiple perspectives, which allows for an interesting life; however, multiple perspectives can also be negative. Image an engineer designing the engine of a plane, having ambiguity in his designs would be a very negative outcome, most probably resulting in the death of many people. So, ambiguity in areas where specifics are vital can be very dangerous, the sciences are an example of this. So, having different perspectives (i.e. having ambiguity) in some cases is certainly a negative aspect of language and is critical that in some cases specificity is crutial. It can be seen that ambiguity and vagueness can both be positive and negative aspects and they both have their separate roles in language.

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Are “vagueness” and “ambiguity” shortcomings of language or can they be viewed as positive aspects of language? Explain.

I think that vagueness and ambiguity are limitations of being able to communicate because if language lacks clarity it is not efficient in passing along information and leaves people with unanswered questions.  It is definitely not a positive aspect of language because language is our main method of communication and used to pass on messages to one another or to a large group of people and if a single message is not clear and easily understandable, many different interpretations of a message could be perceived.  Different interpretations of something are not efficient in using our language skills to communicate if the other person or group does not understand or has questions for clarity.  Ambiguity specifically can leave open many different interpretations of one thing.  Vagueness specifically leaves someone confused and unclear as to what someone or something wishes for them to understand.  Overall both are negative aspects of language and can sometimes have a negative effect on an individual or even a society.

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Are vagueness and ambiguity shortcomings of language or can they be viewed as positive aspects?

Vagueness and ambiguity have always been the “enemy” of philosophers and others on the search for truth.Vagueness and ambiguity can allow for deliberate misinformation in order to exploit individuals and influence to take certain actions. However, it should be honestly considered that perhaps vagueness and ambiguity serve a purpose as well in the search for truth. The positive aspect of vagueness is that it allows one to be truthful or express something truthfully in a general sense. What is meant by this is that for example if one felt that it was quite hot outside it would in all likelihood be more truthful to say that it simply was hot outside instead of trying to attach a specific temperature (like 78 degrees) to one’s experience of hotness. Precision is prized in the sciences and in general however if one does not possess the capacity to be precise to a degree then it would be more untruthful to presume that degree of precision instead of being vague. In this case intentional vagueness becomes a tool to communicate the most accurate information that is known to the individual at a time. Ambiguity works in a different more complex way as it manifests itself as metonymy or zen koans. In this regard ambiguity is used to allow the listener to interpret something their own way, an indirect form of communication which allows the listener or reader to use their own WoKs (other than direct language) to acquire truth.

TOK Essay 2

What is the value of learning to distinguish between valid and invalid arguments? Discuss this relative to at least two AOKs.

This question is specifically for deductive reasoning, this type of reasoning is where you go from general to specific. The basic format of deductive reasoning is that it is trying to prove, or validate a conclusion. To validate this conclusion one must have two true premises and a true conclusion. So the basic format is shown below.
Premise one, Premise two, conclusion
For an argument to be valid is if the premises are true than the conclusion must be true. The main value of being able to distinguish between a valid and invalid argument is very important and I believe that it applies to all the AOKs. Even though it applies to all the areas of knowledge there are two main AOKs that it is very important the first is Ethics. The next important AOK in the natural sciences
The overall benefit of being able to tell a valid argument from an invalid argument is big. The first major thing is that when an argument that is presented to you that is invalid then you would first be able to spot it. Then you would be able to act upon being presented an invalid argument and realize the flaws that were presented to you. Then you would be able to choose the more valid side of the argument because you can tell the differences between valid and invalid. The next thing is that is you see that it is a valid argument while others around you may not. The overall benefit of this is that you will gain greater amounts of knowledge. The reason I think this is because you will be able to see when an argument is invalid and you will be able to see all the possibilities in the world around you. This is not easy because there are many things that play a factor in to it. The biggest one that plays an important part as why people cannot see the validity is confirmation bias. They may just say that I believe that the conclusion is true so the premises they must be true, and this can also lead to hasty generalizations because there may be an insufficient amount of data.
The first AOK is Ethics. Ethics is one an AOK that is based more on emotion even though it is not as certain as the others there are still reasons to have arguments on what to do. For ethics specifically it is more that you act upon something and you are arguing what to do in a situation. The way most people support their arguments is from memory, like when I was a child did I get in trouble for doing this or not. When a person who cannot tell the validity of what they are doing it is very relevant. A person who cannot distinguish the validity is normally acting too severely on a situation for example, if pushing is a crime, and a crime should have consequences, then I should kill him. So if we look at this we can tell that it is not valid because it is over exaggerated. The first and second premise are true, but the conclusion of killing him is over the top because if someone pushes me I am not going to chase after him and try and kill him. Someone who cannot tell the validity and they think that it should have consequences then something that is exaggerated may seem a perfect conclusion to come to. The reason that I think this is over exaggerated is because not every crime should be punished with death. This is where this uncertainty is made in the ethics because some people cannot make the same argument because each person has their own experience.
The next AOK that I think it is very valuable to distinguish between a valid or invalid argument is in the natural sciences. The natural sciences focus on proving the truth of a conclusions premise to make an argument that, that certain conclusion is valid. To do this scientists conduct large numbers of experiments to that one or both of the premises are true.
Another thing that the natural science does is generally they use deductive reasoning to come up with a hypothesis, and then they try to prove if the reasoning behind their logic is valid or invalid. So if your hypothesis is not valid and you do not see this then your entire process would be flawed and you would not collect the correct sets of data that you need. With the assumption being that a valid argument automatically is true. An example of this is, if fear increases heart rate of a person, and john gets scared, then John’s heart rate increases. Now if we look at this the natural sciences are not trying to prove if the conclusion is true because if they collected sufficient data it should prove itself. Now what scientist normally do is look at why. So then they get more specific, if fear causes the production of adrenaline, and adrenaline causes an increased heart rate, then when someone is scared there heart rate increases.
If a person cannot distinguish this there are many costs because change is inevitable and if you ignore the change, even if it is completely valid, you will be left behind .An example of the costs of not being able to distinguish the validity of an argument is during scientific revolutions being able to see that an argument for operating in a different paradigm is valid means that you may gain a deeper understanding in more area of the sciences rather than just focusing on one and when everyone else realizes that it is valid, and the scientist that did not see it as a valid argument would have wasted there life operating under this paradigm. The assumptions here being that there is only one possible paradigm to operate under and there cannot be more than one in your specific field.
So overall the benefit of being able to distinguish the validity of an argument is vast. The reason for this is because there are so many arguments to be had and if you choose one side or another the argument you have should be valid if you want to use it as proof. And when an argument is presented to you that is completely valid and you ignore it because you do not believe it is true then you are missing out on something and you will be left behind in this world where change, big or small, is inevitable.
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Mr. Macky’s Non-Euclidean Geometry

First, I would like to thank Mr. Macky for taking the time to give us a presentation that was both informative and interesting. The presentation puzzled me at first because Mr. Macky explained about laws, constitutions, and congress. And then the volley ball rules…… At some point I had to ask my self, “what does this have to do with Math?” However, all the pieces of the puzzle came together as the presentation progressed. I felt that Mr. Macky’s presentation skills were superb, and it showed how much of a great speaker he is, considering the abstract stuff he was explaining to us.

The concept of Non-Eucleadian geometry was actually very familiar to me. This was because I always thought, how can we say something is a straight line, or that something is always the exact value? I believe that Non-Eucleadian geometry such questions into concern in their constitution for governing mathematics. Then, maybe the main difference between Euclidean Geometry and Non- Euclidean geometry can be the question of certainty. From what I understand, Hyperbolic Geometry states that there is no sum of angles in a triangle. This is because we can never be sure if anything does equal 180 degrees in the real world. In this sense, I can see why Non- Euclidean Geometry is used in the real world, in a bigger scale, and thus by Albert Einstein. The fact is that, nothing in the world is 10+ certain, not even mathematics. We only state that mathematics is 10+ certainty because it is theoretically stated to be in the constitution that Euclid constructed. However, if we get to the specifics of Euclid’s axioms, there are still spaces for questioning.

Towards the end of the presentation, I was both surprised and motivated. First, I was surprised by the fact that people were able to come up with such abstract concepts as Non Euclidean Geometry, and gave me a new vision the human possibilities. Second, I knew that such concepts were out of my realm of mental capacity, which made me want to expand on my mathematical studies until I someday come close to understanding such concepts.

Picture source:,r:27,s:0&biw=1600&bih=775

Thank You Mr. Macky

Mr. Macky, thank you very much for your presentation, it was truly enlightening and very interesting. Many moments of the presentation were very confusing at first but then slowly the mystery became unraveled only to become more tangled than before. At first when I heard of the presentation on “Non -Euclidean Geometry” I was surprised that such geometry even existed and at first thought nothing of it. After the presentation, I realized the implications of this new geometry to the Theory of Knowledge and to the other Areas of Knowledge. Initially as I entered the room I had believed that math was the only Area of Knowledge where 100% certainty could be attained, and I felt sure that it was “impossible” for it not to be provable. As you concluded the presentation, I realized the implications of my initial assumptions that math had 100% certainty, for right there in front of me I had been proved false. The implications of providing this information is tremendous in that it will dispel knowledge about maths and demote it to belief. The presentation showed me that the term “proved” and “certainty” should be avoided in ToK for however certain we are about a given idea, that idea can be dispelled as belief in the future, and thus it is in our best interest to see to what extent we can be certain. My 4th grade mathematics teacher used to teach me that math was “100% true with only 1 answer ever possible”, at that time I believed it and followed the saying fully, but now the question arises, is it? Is there anything we can take as certain? The realization then occurred to me that it was not the certainty that mattered, but what one assumed, because to gain any ground, to make any progress one needs a foundation or a basis, but if that foundation is shattered, if the foundations of modern math were dispelled as belief yet it was still pragmatic, would it still be considered true?

Mr. Macky’s Presentation

Thank you Mr. Macky for you presentation on the non-Euclidean mathematics.

What I could’ve understood from the presentation are the follows. First of all, I clearly understood that mathematicians are bound to this contitutions of mathematics, just like the monarchs are bound by the contitutions of parliaments. Another thing is that as these contitution changes, like the rules of the volleyball. These contitution or laws are based on the mathematical axioms that though we can’t prove, is the starting point of all mathematical concepts. Without them, we can’t go anywhere in mathematics.

So to what extent is certainty attainable in mathematics?

To what extent is certainty attainable within Mathematics?

Hi Mr. Macky!!! Thank-you very much for opening my eyes—I never know that there is such thing as Non-Euclidean geometry. To be honest, you shattered my belief that there is an absolute certainty in Math, which is what I’m going to talk about in this essay. The knowledge issue I’m going to explore is to what extent is certainty attainable within Mathematics?

To answer this knowledge issue, I’m going to quote Einstein when he said, “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

I think certainty of a mathematics axiom depends on the real-life situation. Laws of mathematics are invented so they are not certain; however,  the axiom would be consider certain if scientists can discover something  new that can be applied to the real world. For example, Riemannian geometry is the product of nineteenth century mathematician Riemann’s invention. Of course, we can prove the Riemannian geometry axiom by inventing any formal system and using theorems but how could we applies the system to the real world? Riemannian geometry applies to real world situation because it describes physical space. So, Riemannian geometry would be considered to be certain.

However, Godel was able to prove that formal mathematical system is free from contradiction in his incompleteness theorm. Godel did not prove that mathematics actually contains contradictions but that we cannot be certain that it doesn’t. So, mathematic, at an abstract level is uncertain. For some reason when I was listening to your presentation about Non-Euclidean, I kind of think about the conjecture that states that every even integer greater than 2 can be expressed in the sum of two primes. But how could mathematicians test that since the numbers are infinite and they need to stop at some point, right? Since they stop at one point, how could they be sure that the next two prime numbers will be able to express an integer greater than 2—there is still a possibility that it might not work!

In conclusion, math, like other areas of knowledge does not have absolute certainty. Although it can be argued that math is the subject that has the most certainty compared to other subjects. It is a good thing that non-Euclidean geometry is useful in describing physical stages. However, I don’t think I will become comfortable with that geometry because I have learned Euclidean geometry since when I was very young.

Mr. Macky’s Presentation on Non-Euclidian Geometry

First and foremost, I’d like to say thanks to Mr. Macky for a superb presentation. The use of metaphor/simile really helped to put it into laymen’s term and drive a very good point home. I thought it was very thought provoking and was shocked by the implications of this kind of mathematics. I’m sure it took quite some time to make and I know Mr. Macky has many duties in addition to teaching, so I’m very grateful for the splendid presentation. It certainly was an eye-opener for the measly math student.

As far as the knowledge issues concerned go, I feel some of the bigger ones involved were definitely “What does it mean to say that mathematics is an axiomatic system?” and “How do we choose the axioms underlying mathematics? Is this an act of faith?”. These two issues connect largely with Mr. Macky’s point that math is like a game or a government: everything changes when the rules are altered. To the first issue, we can say that math is entirely DEFINED by the axioms. Without a set of axioms, you have no basis for the reasoning and logic that takes place. To the second issue, we can say that these axioms are selected since they are “self-evident”, or “blindingly obvious”. In other words, they are so and intuitive and obvious that they are beyond question. To some degree, these axioms may be based on the established paradigms of mathematics, however it is possible to have different axioms as demonstrated by hyperbolic and elliptical geometry. While they share several similar axioms, a change in one axiom (which still makes sense in context) allows for the nature of mathematics to change drastically. However, I assume that we adopted our set of axioms since they work well with the Euclidian geometric model, the model of geometry which has proved most useful to people at a local level.

If I had one question, though, it would be the practical application of these types of mathematics aside from Einsteinian relativity as mentioned. I can use Euclidian geometry to find the area of a square in a town, I can calculate the height of a pole using its and my shadow, etc. I suppose that elliptical geometry (if I understood correctly) involves circular/round surfaces, I can see the practical applications of this in geometry involving spheres (planets, stars, balls, etc.) and understand it may be useful for engineering or astronomy. However, I don’t see where the usage of hyperbolic geometry comes into play. If it works on the basis of a “curved plane”, how can we realistically use that to solve real world problems or make useful knowledge claims in theoretical physics?

CAS – Badminton

My primary goal in this activity was to have fun and enjoy Badminton, which I did. I found it to be quite a relaxing experience, especially due to all the stress from school.  Badminton every Tuesday helped my relieve that stress.  One of the challenges that I faced was that I have not practiced Badminton much, and thus I am not very good at it. However, I think sportsmanship and trying your best is more important. I also feel that I have improved in the sport through CAS Badminton. I would like to continue playing Badminton in my next school, where I am moving to.

Probably my favorite part of the activity was the teamwork involved, because often we played in doubles, and I usually teamed up with my classmates. I learned that a sport like Badminton requires good co-ordination and movement, especially when playing in a team.

Mr. Macky’s Presentation

Firstly, I would like to begin by thanking Mr. Macky for dedicating his time after school to teaching the TOK classes about non-euclidean geometry and sharing his understandings about certainty in mathematics. I greatly enjoyed how he put the lesson into perspectives that he would understand. Math is not my strongest subject, and therefore I was appreciative of the way that he used the analogy of the United State’s Constitution as the basis for the government, similar to axioms being the basis of all mathematical laws. When feeling lost during multiple parts of the presentation, the constitution and volleyball metaphor helped me to relate to the lesson and provided as an aid to better understanding the topic as I could apply it to a practical, real life situation.

The topic of non-euclidean geometry lends into the question, to what extent is certainty attainable within mathematics? Mathematics is the only area of knowledge that can be regarded with +10 certainty. However, there is a difference between absolute certainty and +10 certainty. In Godel’s incompleteness theorem, it was proven that it is impossible to prove that a formal mathematical system is free from contradiction. Therefore, the possibility of finding a contradiction, while is possible and therefore, at an abstract level, mathematics is not certain meaning that we cannot say that mathematics gives us absolute certainty. Non-euclidean geometry sounds abstract and strange, however, it is still a part of mathematics, just different. This shows that finding contradictions or revelations in mathematics is possible, and therefore it cannot be regarded with absolute certainty.

While absolute certainty is not attainable in mathematics, we still regard certainty in mathematics very highly as it is still +10 certainty.  We base our knowledge in everyday situations off of the assumption that mathematics is certain. For example, in my biology class, while completing an individual research project, the qualitative data such as age and gender collected about the subjects in my experiment was very important, but in order to analyze the results, I used quantitative data, or mathematics to determine the significance and importance because I rely on mathematics with certainty.  Therefore, while mathematics may not have absolute certainty, it is regarded as sufficient certainty in most aspects of our lives.

Mr. Macky’s Presentation- TWE is certainty attainable in Mathematics?

I would like to begin by saying how thankful I am for the presentation done by Mr. Macky on non-Euclidian geometry. Although I was unable to attend the presentation because of the fact that my exams took precedence, the videos I watched on YouTube were very informative. So, thank you for posting the videos on YouTube.  To me, the idea that math is a sure thing and a hard fact is almost inherently known; I grew up believing in the simple facts like, 2+2=4 and that if you subtract 7 from 10 you get three. However, this video really opened my to the abductively reasoned abstract idea that math is not always a sure thing and that math can be a field that is more conceptualized rather than actually performed in reality. This idea is really more aligned with my way of reasoning when it comes to math because it is hard for me to think that math is a sure thing that only has one answer and that the background reasoning for that answer is not always needed. I always need a reason for why something is the way it is, and when math presents a formula that is to be plugged into a calculator and then an answer is found, I think to myself ‘why must it always be like this and how did it come to be’. The analytical philosopher Bertrand Russell once said, ‘Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.’ (Russell), this statement to me is a reflection of my own ideas on math and it also really presents to the reader the idea that math can be a mysterious unknown entity. I learned of an entirely new concept while watching the presentation, a concept that demonstrated to me the idea that in a mathematical system, the term axiom can be both logical and non-logical and that axioms are followed by the theorems and that the laws of the mathematical system must agree with the axioms. Math like all other fields of knowledge works with paradigms and paradigm shift, when a theorem is in agreement with an axiom a possible paradigm shift could occur and cause the previous ‘fact’ to become invalid.

It was learnt during the presentation that:

 -There should be as few axioms as possible

-These axioms should be simple

-There should be no overlap between axioms

-The axioms should be self-evident and not provable using other axioms

-The axioms should use as few undefined terms as possible

Euclid was a Greek mathematician, who is often referred to as the Father of Geometry.  He was the first person to conceptualize the idea of the ‘axiom’ the total number of axioms he worked with were five axioms. With these five axioms Euclidian-geometry was created. Axioms provide a sort of support for mathematical theories because they produce simple justifications that do not cause fallacies.

Non-Euclidean Geometry Reflection

Mr.Macky’s Presentation

Dear Mr. Macky,

Thank you very much for your presentation about math and how it relates to TOK. I wasnt able to attend the presentation because of an IB exam however i was able to watch the youtube video and i was still really impressed. One thing i learned form your presentation was that in math, the laws are called theorems, and the constitution are referred to as axioms, similarly, laws of the system must also agree with the axioms. I also liked your real life example of the volleyball team and how they worked together. Thanks again!

One thing i learned from your presentation about math was that there are 5  basic requirements of an axiom:

  • 1)  The axioms should be as simple as possible
  • 2)The smallest amount of axioms should be used
  • 3) Axioms must not overlap
  • 4) There should be fewest amount of undefined terms as possible
  • 5)Axioms must be self-evident

Axioms should only be established if it is both simple while still being able to prove its point. If an argument is reduced multiple times only the undecipherable facts remain of that argument. This often results to the significance of the argument being lost.  However this does not mean that the concept of reductionism is useless but rather, humans need to know when to stop reducing an issue before it loses its significance.

Therefore although mathematics shows complete certainty at first  if one analysis the basics of math there is a chance of uncertainty. This means that although math is the only Area of knowledge that can have a +10 certainty there are also examples of how math does not always show 100% certainty.This is an example of an axiom.

Mathematics: Mr. Macky’s Presentation

How do we choose the axioms underlying mathematics? Is this an act of faith?

Mr. Macky began the presentation with a short story about changing rules of volleyball and the consequences that follow. He explained to us how changing the rules changes the way the game is played, and can also change the outcome of the game. On a larger scale, congresses come up with laws instead of rules, and these laws must agree with the constitution (foundational set of laws). In math, the laws are called theorems, and the constitution are referred to as axioms, similarly, laws of the system must also agree with set of axioms.

There are basic requirements of an axiom system:

1) The smallest amount of axioms should be used

2) The axioms should be as simple as possible

3) Axioms must not overlap

4) Axioms must be self-evident

5) There should be fewest amount of undefined terms as possible

We then learned that the geometry  we had learned in school was actually Euclid’s geometry, and shockingly, other types of geometries exist. Euclid came up with five axioms, which are easy to understand. One statement, the parallel postulate, was not self evident because it was long, lacked simplicity, wasn’t obvious therefore many mathematicians objected to this fifth axiom and tried to disprove it. People then tried to disprove this statement by using theorems based on the other four axioms, but all efforts failed. As a result of the best mathematicians attempts, other types of geometry (non-euclidian geometry) was developed.

Everyone in the room had thought that they had mastered geometry but when Mr. Macky started to show us parallel lines from hyperbolic and elliptic geometry, we were all a little bit confused. I had never thought outside the paradigm of euclid’s geometry, and had never even considered that there was a complete other type of geometry. I used to be completely certain (10+) about math, but the presentation raised some questions. I think an important reason that I never questioned the certainty of euclidian geometry was because all the math problems I tried could be solved, therefore this method passed the pragmatic test. Just sitting and listening to Mr. Macky talk about the complex non-Euclidian geometry was already confusing me, and I couldn’t even imagine what it would be like if we had to actually learn how to solve problems using non-euclidian geometry. Therefore, even if we can never prove whether the theorems we follow are correct or incorrect, we must to a large extent rely on our faith. Although the different types of geometry caused me to wonder about the certainty of math,  I remembered that in the end, Euclid’s 5th postulate was not disproven and is still true and continues to be.  Therefore I think that we still have +10 certainty, in math just not absolute certainty.

Thank You Mr. Macky for the Non-Euclidean Geometry Presentation

‘Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.’ Bertrand Russell (1917)

Mr. Macky,

First off I would like to say how thankful I am that you took the time out of what I am sure is an extremely busy schedule, to give us the presentation on non-Euclidean geometry. I gained many interesting facts about math, concepts that I had never thought of, or probably would have ever come across without you. Many things in the world have to do with the set of rules that society follows, that the foundations must follow for things to run in the system properly. During the presentation, I found that the basis of a mathematical system ‘axioms’ are followed by the ‘theorems’ and that the laws of the mathematical system must agree with the axioms. For me this understanding of how the building blocks that define specific focuses was helpful to prove that systems in the world work, and how they function in a connecting network. Such as in everyday situations, at school there is a school mission statement which can be seen as the axiom, we follow a set of rules and guidelines provided, what to wear, when to arrive at each class, what time school ends, all these rules are put into the system as laws or theorems which agree with the axiom in order to prove that the system is beneficial.

How do we choose the axioms underlying mathematics? Is this an act of faith?

– small amount of them

– simple as possible

– no overlap

– self-evident

– few undefined terms as possible

Faith is when we as knowers have complete trust or confidence in something or someone. All our knowledge apart from that of our core sensory experiences is based on faith, if we personally believe in something that cannot be logically obtained than we gain this personal knowledge from faith. Our deepest core, most inner-knowledge is not certain truths, but what we prove to ourselves by believing. Faith is the basis of the system of knowledge and to an extent the building blocks to understand which axiom system is the ‘best’ or how to choose what order to put them in, or if they should even be axioms in the first place. We state the axiom clearly before we use them in order, but to get the axiom in the first place we need to be able to identify what needs to be stated from an observed, missing link in a system, using the axiom to change that. In math, the axioms that are underlying the system are picked on the basis that they proved inductive/deductive reason that give the laws of math. They also produce simple justifiable points that do not cause fallacies.

Non-Euclidian Mathematics

TWE is certainty attainable within Mathematics?

Ahhhh!  NON-Euclidian math?! What?!?  My bubble of 10+ certainty in mathematics has been abruptly burst.  So I’ve always thought that this is parallel..

But apparently…

.. this is too.

And likewise, this as well.

The presentation that Mr. Macky gave on non-Euclidian geometry introduced to me a totally new paradigm of mathematics.  I used to think that math was the only area of knowledge that allowed for 10+ certainty; however now, I’m not so sure.

Euclid, born sometime in the 300 BC was the genius that established the axiomatic approach to geometry.  He came up with 5 axioms which could be used to explain and prove through logic, mathematical propositions.  Today, Euclidian geometry is taught to young children because it is simple and coherent with the physical reality we live in and are familiar with.  Even now, as an HL math student, I have a hard time grasping the concepts of non-Euclidian geometry.  And so far, pragmatic-wise, Euclidian geometry is providing us with all the answers we need to our mathematical problems.  Learning non-Euclidian math probably won’t be useful to people unless they’re into the crazy, Darkside of ultra high level physics, which most people such as myself am not :)

So to what extent is certainty attainable in math? I think it depends on the context.  Of the 5 axioms Euclid proposed, all were accepted except, the 5th one, the parallel postulate.  It was challenge by many people; resulting in the introduction of non-Euclidian geometry.  Elliptic geometry was coherent with Einstein’s theory of relativity, demonstrating that indeed, light does not travel in a straight line.  With just a small alteration in the parallel postulate, emerges 2 completely new whole paradigms of geometry.  In their respective frameworks, each of the paradigms exists with equal certainty and truth.

And I’m wondering.. why are there only 5 axioms? Is it all we need? Is that all that exists out there? What if there was a 6th axiom?  Much like how the change in the 5th axiom lead to the discoveries of 2 new types of geometry, a creation of a 6th axiom will rock the mathematical world.  Wouldn’t that also lead to discovers that could potentially further increase the level of certainty in math?

Mr. Macky’s Non-Euclidean Geometry Presentation

Date: 19 May 2011

Location: Web 2.0 Room, Library

Mr. Macky’s presentation on Non-Euclidean Geometry left many of us baffled and dumbstruck, but nonetheless fascinated (: To start off, Mr. Macky showed us a picture of the English Royal Wedding, and compared the laws of mathematics to the laws of a country. He said that similarly to how the laws of a country must follow the constitution, the laws in mathematics must follow the “constitution of mathematics”, which are called axioms. Axioms are self-evident, non-provable statements that are held as the ‘truth’. Axioms cannot be proved using other axioms, although theorems can be proved using the axioms.

Mr. Macky said that Euclid, who basically founded geometry, defined 5 axioms. The 5 axioms act as the ‘paradigms’ for Euclidean geometry, which is the geometry that we are most familiar with. Mr. Macky went through each axiom and axioms 1~4 did make sense. However, the controversial axiom 5, known as the Parallel Postulate, was not as self-evident as were the others. In the past 2000 years, some of the smartest people tried to prove Euclid’s 5th axiom wrong. Some people who had other perspectives entirely dismissed the Parallel Postulate, and instead used axioms 1 ~ 4 and other newly made axiom to create new areas of geometry, such as Hyperbolic geometry and Elliptic geometry. Using different axioms resulted in an entirely new ‘type’ of geometry, which was almost too obscure for us Euclidean-trained students to understand.

In the end, Mr. Macky said that Euclid was right; the Parallel Postulate could not be proved wrong after 2000 years of endeavor. One thing that Mr. Macky mentioned which I thought was particularly important was that had the Parallel Postulate been proven wrong and changed (Paradigm shift!), it would have changed the geometry we know entirely. Logically, this makes sense, because if the building foundation is changed, so will everything that is based on that foundation.

Now relating to the knowledge issue “To what extent is certainty attainable within Mathematics?”, I think the highest degree of certainty can be attained in Mathematics compared to other areas of knowledge, especially Ethics and the Arts, which are subjective and value-based. Mathematics gets close to +10 certainty but does not attain +10 certainty because of the unquestionable nature of axioms. As Mr. Macky explained, axioms cannot be proven true, but are nevertheless accepted without question (for most people) as ‘the truth’. This is problematic because these axioms serve as paradigms and if we cannot prove or disprove axioms, how can we know that these axioms are “The Axioms”? Did Euclid know that the axioms were “The” correct axioms?  We learned in ToK that if a paradigm is shown to be false, everything that is built within that paradigm collapses and is not regarded as true. Despite this fundamental uncertainty, math is more certain than other areas of knowledge because some things do not have to be proven in order for us to know that it is true (e.g. no one will deny that 1+1=2; we all know this intuitively).

The presentation really helped in my understanding of Mathematics as an area of knowledge, and it helped me relate the ideas that we learnt in ToK to “real” math concepts. Thank you Mr. Macky for giving us a taste on Non-Euclidean Geometry, and for delivering an awesome presentation! (:

credits to

Blog Post #5

Thank you, Mr. Macky for your presentation about certainty in Mathematics. It gave me a new insight towards mathematics which I always thought +10 certainty (no biases,no issues with different ways of interpretation) on the belief-knowledge continuum. I always thought if something could be proven with mathematics, (a couple of mathematic symbols, a few numbers and an equal sign), it was the “truth”. However, this presentation helps me realize that even mathematical rules I abide by like there are 180 degres in a triangle, parallel lines never touch may not be “the truth”.

Firstly, I could relate to your example about volleyball in the introduction of the presentation. It is one of my experiences as a math student. In middle school, I was only taught when looking at circles to define the angles using degrees, however starting in high school I was introduced to a new way of defining the angles: Radians. I struggled a lot in familiarizing with this method, from my perspective the method of solving problems with radians was extremely burdensome. However, the question  raised during the presentation,”Which set of rules is “better”?” made me start to wonder whether radians is by nature more complex like I always thought, or is it just because I was taught how to use degrees first?

Secondly, with the reference to Isaac Newton and Albert Einstein and their perspectives towards the description of “space”, I learnt that the quote we were introduced to “context is all” seems to apply to the area of knowledge of mathematics too not just ethics.  This suggests that there is no real certainty in mathematics, because it depends upon the assumptions the arguments are based on. In my classes, my teachers remind me of making my assumptions clear, and I think the last part of the presentation about the difference between non-Euclidean geometry and Euclidean geometry is the epitome of why explaining assumptions in arguments is so vital.

Mr. Macky’s Presentation

How do we choose the axioms underlying mathematics? Is this an act of faith?

If math were to be compared with a nation, then the constitutions of a country would be equivalent to axioms (a set of rules are the foundation of math).  When the governing body decides on laws, these implemented laws will not go against the constitution as it is based off of it.  Similarly, theorems must agree with the axioms provided or else the whole basis of mathematics would fall apart.   Greek mathematician Euclid was the first to introduce axioms that are commonly known today as “Euclid’s elements”, being the base for geometry that we are taught in school every day.  There are several requirements for an axiom:

1. We should use the fewest axioms as possible

2. When an axiom is created it must be in the simplest version as possible

3. There must be no overlap between axioms

4. Each axiom must be self-evident

5. Undefined terms should be kept at a minimal level

Regarding the decisions to choose the axioms that are underlying in mathematics, reductionism is used as each mathematical theorem must be able to be reduced to its core components, or in other words, its axioms. Reductionism seeks to explain one subject in terms of another, and in math the reductionist approach is used to justify the statements that we agree upon as axioms.  Euclid’s axioms are a very basic set of rules that seem to make sense for us as they pass the pragmatic truth test (it is useful in application) and the coherence truth test (it fits in with our current paradigm and what we are taught in school).  For example, I remember back in the 9th grade when I took geometry, I had a conjecture book with all the theorems I ever needed to solve a geometric problem.  Looking back, I realized that what these theorems all shared were several core assumptions (or in math terms, axioms) that must be true in order for the theorem to make sense.  If I was looking at my conjecture book today, I would be able to break down the geometric theories that had once seemed so complicated  into Euclid’s elements that are associated with it which help prove the theory to be true.  However, I cannot prove the axioms to be true because one of the requirements is that they are self evident.  Additionally, if I were able to prove an “axiom”, it would no longer be an “axiom” because I would be able to reduce it even further which means that the axiom is not the simplest version of a claim.  Thus, the process of choosing the axiom underlying mathematics starts off as an act of faith.  In the case of Euclid’s 5th postulate, the Parallel Postulate, many mathematicians were skeptical of it not truly being an axiom due to the wordiness of the rule, but even with thousands of attempts to disprove it, no one was able to show how the Parallel Postulate was an overlap or uncover simpler axioms beneath it.  Perhaps Euclid started off choosing the axioms as an act of faith, but with the inability of the mathematics community to refute or refine it, these set of rules we deem as axioms become clearer and more certain to us than the act of faith that had brought the set of rules together in the first place.

Non-Euclidian Geometry: Thank You

The presentation was very interesting for me as I like to learn about new ways of looking at a problem.  I would be interested in learning more if the math itself is not too difficult (I understand that conceptually it would be hard).  I had never been taught about the axioms before aside from being told those things were true and have often wondered how math got started.  This helped me to understand how our current math came to be.   I am also confused about some things, like how rectangles don’t exist, but I imagine that if I looked at this in more depth that I would understand more (as well as probably have more questions). I am choosing to try and write about:  How do we choose the axioms underlying mathematics? Is this an act of faith? Here are the five requirements for an axiom according to Mr. Macky:

“1) We should use as few axioms as possible.

2) Each axiom should be as simple as possible.

3) There should be no “overlap” between axioms.

4) Each axiom should be self-evident, and not provable using the other axioms.

5) We should have as few undefined terms as possible”

Therefore the ways of choosing an axiom can be seen above, however the question regarding faith is a little harder to answer.  I think that to answer this question the fourth requirement is the most applicable for addressing the faith issue.  By being self evident according to our reason and/or our sense perception the only faith really needed is the faith that our reason and/or our senses are not flawed.  If I have one chocolate chip cookie and my brother has another, and I take his, then according to my observation I obviously have two cookies.  However as we are dealing with ways of knowing there are problems.  My brother, for example, may not say that he has zero cookies, but rather that he is missing a cookie and thus has minus one cookie. This would then mean, using traditional math, that there is one cookie as I have two cookies and my brother has -1 cookie. So now there is a problem because we can both agree that really there are only two cookies.  From this it can be seen that by changing the perspective of the “obvious fact” the final result is different using math.  Now I notice that this logic is not the most reasonable, however it can be seen that choosing the axioms for math could be slightly subjective.   This can be seen by looking at geometry in different ways.  (If I have understood the theories incorrectly then please call me out and I will try to correct my thinking).  By changing ones point of view of the world, ones’ view of whether rectangles exist changes.  Seeing planes as parabolic instead of flat causes drastic changes to the way that math is understood.  In conclusion it would seem as if the axioms are based upon the perspectives of the maker of the axioms and thus we must place faith in his ability to reason and perceive.  However due to the number of people that look at the axioms and try to prove them false, an appropriate amount of certainty can be placed in the axioms and that they most likely represent the perceived world.

Mr. Mackey Presentation: TWE is certainty attainable within Mathematics?

Let me begin this post by thanking Mr. Mackey for making non-Euclidean geometry somewhat understandable. Even if I was not able to completely visualize and comprehend non-Euclidean geometry, the way you presented helped me understand the reason for the possibility of uncertainty in mathematics.

TWE is certainty attainable within Mathematics?

Mathematics seems to be able to attain certainty to some extent.

At first glance mathematics seems removed from any type of emotion, bias, intuition, etc. It seems to be based only on sound reasoning. As the uncertainties arising from the sciences and history seem to be largely due to emotion, bias, etc (found in sense perception and possibly in logical fallacies), its seems valid to say that the subject mathematics contains a very high certainty. When asked to prove a mathematical equation through induction there are three logical steps leading to a final conclusion: (below is a simplified version)

  1. Show that the statement is true for n=1
  2. Assume that the statement is true for n=K
  3. Show that the statement is true for n=k+1
  4. Thus, the statement is true for all values of n, n

I am pretty sure there is no bias found in this process as it seems to leave no room for emotional interpretation. Thus, mathematics can be said to some extent, to be certain.

However, when we consider the axioms in which mathematics are based on, the amount of certainty applied mathematics is questionable. The math presently taught in most schools is Euclidean geometry. It is based on 5 axioms which are supposed to be self-evident and easy to understand. However, the fifth axiom concerning parallel lines, which states that

“if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles”,

is not self-evident (as no one can see onto infinity and know that two parallel lines will not pass) or easy to understand (difficult wording).

Not only this, the decision on which axiom to choose is based, to some degree, on intuition (although it is also chosen to some extent using reason as there are rules). Intuition is not precisely reliable. For example, when the axiom concerning parallel lines is replaced with another axiom, a new type of mathematics was “invented”: non-Euclidean geometry. As I do not understand non-Euclidean geometry to the extent that I can discuss it without too much uncertainty, I will only state that non-Euclidean geometry completely changes the way we view the world and geometrical mathematics if we use Euclidean geometry.

To conclude, although mathematics seems to have attained complete certainty at first glance, further analysis of the basis of mathematics illustrates the possibility of uncertainty in mathematics, leading to the conclusion that mathematics contains, to some extent, certainty.


It is quite interesting how little sense non-euclidean geometries make. Because we have grown up our whole lives observing euclidean geometries on a human scale, we find it incredibly difficult to work in other geometries. Of course, pictures of the planes that exist in other geometries help considerably, but those planes only help to understand the 2-D properties of these geometries. In the same way trying to visualize a 4-D object makes no sense, trying to visualize a three dimensional version of these geometries does not either, as our brains are so encoded to the pragmatic euclidean model of the world that we work with every day, that we cannot really use any examples or experiences to deal with other geometries.

How do we choose the axioms underlying mathematics? Is this an act of faith?

Math is a juxtaposition between the complete certainty of theorems proved using axioms, and the absolute faith in and uncertainty of axioms used. While it is true that mathematicians try to simplify and boil down sets  of axioms to as few short axioms as possible, it is impossible to prove any of the axioms as true.

But then how do we decide on axioms? Of course guidelines exist in choosing axioms, but where on earth do they come from? The most basic and original set of axioms, Euclid’s axioms, are the first ones we learn in school for a reason. They are the ones that govern the human-scaled, human-observable world. They are so easily understandable and evident in ordinary life that they remained the only axioms used for a very long time. In different situations, it seems to be pragmatically true that different axioms apply, such as is evident when using Euclidian geometry in physics, or hyperbolic geometry in Einstein’s relativity. However, proving that a set of axioms apply to a certain situation may be close to impossible. This is because, to prove anything to be true using deductive reasoning, premises are required. Axioms of a system are the most basic premises by which absolutely anything else in the system may be proven, but trying to prove the axioms themselves is pointless, as more premises (or axioms) would have to be created to prove them, and those would instead be the axioms of the system. This is where the concept of trying to get the most basic and few as possible premises in a system as possible comes into play, a significant part of which includes langauge, as something simple in one language may actually be very complicated to describe in another. The real confict here must be proving that axioms apply to a situation. There are an infinite number of axioms, and systems based on sets of axioms, with a infinite number of theorems in them, all of which are true, but the systems have no significance until they are applied to a situation. Demonstrating that an axiom applies can be a very uncertain process, just look at how, before Einstein, it was thought that space was simply governed by Euclidean geometry. This is because, again, t0 prove anything, a prerequisite premise is necessary, and the process must stop somewhere. Where we stop proving, and start assuming, it is simply an act of faith.

TOK: Mr.Macky’s Mathematics Presentation

First off, I would like to thank Mr.Macky for spending his spare time in order to educate our young minds about the wonders of Euclidean Geometry in such understandable and intriguing ways. He provided analogies leading into his non-Euclidean geometry topic which consisted of contemporary examples that proved helpful in enabling us to grasp the key ideas. There was the historical progression of volleyball game rules, which he used to lead into the foundations and axioms of mathematics that was a very intriguing start to the presentation. He said that when the rules changed through out history, it affects the way the game is played, and sometimes affects the outcome of the game.

This leads onto a Knowledge Issue want to discuss, which is: To what extent is certainty attainable within Mathematics?

Mathematics can in the realm of TOK, be referred to with +10 certainty. Considering that mathematical systems have the foundation which is a set of axioms, where mathematical laws are called theorems and these laws must agree with the set of axioms previously established. Mr. Macky said that there were rules to the creation of these axioms and laid them out for us as follows:

1) We should use as few axioms as possible.
2) Each axiom should be as simple as possible.
3) There should be no “overlap” between axioms.
4) Each axiom should be self-evident, and
not provable using the other axioms.
5) We should have as few undefined terms as possible.

The underlined words show that these axioms seem to be put through multitudes of thorough reductionism to get to the most raw and logical postulate, and the axioms that Mr.Macky brought to light were Euclid’s five axioms which are actually the back bone for euclidean geometry us students learn in maths today. He conveyed Euclid’s axioms to us in a way that us ‘normal humans’ would understand, which was basically a re-cap of simple geometry lessons. However, although four out of the five axioms were simple and resolute to understand. The fifth axiom known as the parallel postulate was much more hard to grasp and ‘wordy’ than the others. It was not easily understood nor pictured and as a result Euclid was criticized for it, thus he said no proof was possible. For thousands of years the smartest mathematicians tried to disprove this parallel postulate. Others simply discarded the parallel postulate and as a result hyperbolic geometry and elliptical geometry were created leading to many theories, such as to support which shape our universe is actually in the form of.

Towards the end however, Mr. Macky told us about how Euclid was right after all, citing the source of Eugenio Beltrami. Then it occurred to me that Euclid’s axioms are still the being held thousands of years after his contribution to mathematics. This supports the suggestion that mathematics can truly lead to definite certainty. Due to one mathematical claim, being able to get proven thousands of years after its establishment as a law. The level of thought and refinement put into mathematical postulates are an important example of certainty within humans capability to use our logic. There may be no ‘absolute’ and completeness in mathematics, but without the +10 certainty, why would humans even bother to try and utilize mathematics to derive such things as the shape of the universe?


Non-Euclidean Geometry

First of all, I would like to thank Mr. Macky for taking the time to get our neurons fired with an engaging presentation.

TWE is certainty attainable within Mathematics?

I walked into the Web 2.0 thinking that Mathematics is the only subject where +10 certainty is attainable for all its aspects. I walked out of the Web 2.0 telling myself that I should never use the word ‘all’ so loosely again.

In order for something to be a foundation of a mathematical system, the following conditions need to be met:

1) We should use as few axioms as possible.

2) Each axiom should be as simple as possible.

3) There should be no “overlap” between axioms.

4) Each axiom should be self-evident, and not provable using the other axioms.

5) We should have as few undefined terms as possible.

Euclidean geometry was used as a model of knowledge because it seemed ‘certain and informative’. However, issue of language comes into play when people began to find the ambiguity in the axiom of parallels, because it was neither simple nor self-evident. Because it is a violation of two of the conditions, mathematicians tried to prove that the axiom of parallels was a theorem rather than an axiom, and non-Euclidean geometry was born.

As one of the many people who had their brains programmed to Euclidean geometry, non-Euclidean geometry was challenging for me to grasp and I found it to be absurd. However, I could not say that non-Euclidean geometry is wrong.

At the beginning of his presentation, Mr. Macky presented two sets of volleyball rules to us: the rules from before 1999 and the rules today. When he asked us which set of rules is ‘better’, all of us hesitated for a few seconds before saying, ‘neither’. There is not one rule that is ‘better’ than the other, because they are both purely different approaches to playing the same game. This is analogous to how Euclidean geometry and non-Euclidean geometry cannot be compared with one another, as they are both effective in their own rights and both contributed to great scientific breakthroughs. This may be one of the reasons why +10 certainty is not always attainable in Mathematics, because the correctness of one approach over another becomes more open to debate as complexity grows.

Thank You Mr.Macky!

First off I would like to thank you, Mr.Macky for your time.  I really enjoyed your presentation on Non-Euclidian Geometry.  I liked the way you started off your presentation about something current and relevant like the royal wedding and then spoke about the rules of volleyball and how they’ve changed over the years.  And then you transitioned nicely from talking about volleyball to talking about axioms and other fundamentals of non-Euclidian geometry.

To what extent is certainty attainable within Mathematics?

I believe that certainty and ultimate truth do not exist; therefore I do not believe that certainty can be fully attainable within mathematics.  Although, I do believe that mathematics is a crucial area of knowledge that allows a limited amount of certainty to be achievable.  There are thousands of theorems, rules, formulas and postulates that have been discovered in the world of mathematics over thousands of years of scholars working to develop these.  I believe that the scholars and mathematician’s discoveries, that can now be found in any math book around the world that is taught in school, does attain a high level of certainty.  I believe that the theorems I am taught in school are correct because by me demonstrating my understanding and use of the theorems allows me to earn a good grade in the class.  My opinion, however, is bias because I choose to believe authority; I choose to believe what the teacher teaches me.  For example, I do not have the same skills, abilities and logical thinking that Pythagoras had when he formulated the Pythagorean Theorem, thus I do not have the knowledge to provide evidence that his theory may be ‘correct’ (correct based on mathematical world).  I always trust and rely on Pythagoras that his theorem is accurate and if I use it correctly that I will get good grades on my tests.  Overall, regarding the non-Euclidian geometry controversy, once people learned to accept the postulate and other branches of Non-Euclidian Geometry, other doors were opened up and Albert Einstein was able to develop his theory of relativity.  In my perspective, it is difficult for me to imagine how people could accuse the possibility of non-Euclidian geometry because never before in my life have I questioned what I was taught in school, I choose to believe the authority.

Euclidean vs. Non-Euclidean Geometry – by Mr. Macky

The previous Thursday during ToK flextime, Mr, Macky gave us a very fascinating presentation about the uncertainty in math. I would like to thank Mr. Macky for sharing to us, the ‘other’ side of math. I’ve always thought mathematics had a very high certainty in the justification of true belief, however, I never knew that such a counterclaim in geometry would exist. Math, to me, had proofs for everything, equations, graphs, etc, unlike the sciences which had a theory/model but other uncontrollable facts affecting it. Math is just the math, nothing about the environment or nature of the earth’s gravity affecting our calculations. Mr. Macy presented us with a very interesting and opposite view of what I expected in math and now I see, I learned that math is definitely not 100% certain.

So..the widely held question is?..To What Extent is certainty attainablewithin Mathematics?

I would say, to a certain extent. In my perspective, I think it also depends on the language. For example the definition of a plane. A plane is a two-dimensional surface most of the time containing a line or shapes. This definition of a plane does not state specifically if the plane is curved or on a flat surface. However, humans do not notice that the meaning of ‘flat’ is not actually really flat, on Earth. Our earth is in the shape of a sphere, and it could be said to not have any flat surface, only curved; therefore, the claimed-to-be flat plane, is curved- disproving many rules/theories in mathematics, just like those theories in physics, biology or chemistry. Say for example, I was to calculate the right-triangular area of a certain farm in rural Thailand. The measurements for two sides were given to me, and I was to find the remaining side by using the pythagorean theorem. My answer however, will contain errors in it, for, I neglected the curving shape of the Earth’s surface by assuming this farm was on a flat 2D plane (which in real life cannot exist on the surface of the Earth). In conclusion, I think the uncertainty in mathematics is caused by a human error by not explaining all possible characteristics of natural things, which we think do not have an effect, but actually do, on mathematics.

(The 3D sphere is like the shape of the Earth, so the triangular farm I was referring to would appear similar to the triangle on the middle object with a positive curvature)

Mathematics Presentation by Mr. Macky

I think the most important and noticeable thing which I learned is that space-time is curved, not straight. While obviously I don’t fully understand it, it seems like a very astounding fact, because it means that lines are not really straight; they instead curve. Mr. Macky’s analogy of a person walking in a straight line on earth, and thinking he is going straight when he is actually traveling on a curved path, was helpful. It make me understand a little that the lines and rectangles we see may seem straight, but in the bigger picture, they are actually not, because the Universe in three-dimensions curves.

KI: How do we choose the axioms underlying mathematics? Is it an act of faith?

We choose the axioms underlying mathematics in context of how we want to use it, and its application. For example, in our Geometry class, we all learned about math based on Euclid’s axioms. This works perfectly fine for the high-school level, because it is only used to solve problems over small distances. Also, in the context of the classroom, we only need to learn enough Geometry to get a good grade. Thus, we choose Euclid’s axioms in this case, because its application is only for teaching a high-school level course.

However, when considering broader applications, we need to choose a different set of axioms, such as those in Non-Euclidean Geometry. For example, if scientists are launching a satellite into space, they will need to make calculations according to Non-Euclidean Geometry (according to Mr. Macky), because it operates over large distances. Also, when studying the Theory of Relativity, we need to choose Non-Euclidean Axioms, because the geometry of the space is curved, so Euclidean axioms won’t really apply. When trying to study the Universe, Einstein chose Non-Euclidean axioms, because they are true over large distances.

Thus, I think that we choose mathematical axioms based on what their application and use is, not based on our faith.

Euclid, what’s the deal?

Although non-Euclidian geometry isn’t necessarily as highly regarded and Euclidian geometry (standard high school geometry), it surely offers a different, viable perspective on geometry. Geometry that we were once taught is still correct (well, that’s what we hope at least), but non-Euclidian geometry was generated by a group of scientists who refused to agree with one of Euclid’s five geometric axioms for they believed it didn’t belong. For thousands of years, scientists attempted to base their geometric theorems and axioms without the use of Euclid’s fifth axiom, which was proven to be quite difficult. However, after years of sweat and complexity, an awkward group of ideas united to form a convoluted set of ideas known as non-Euclidian geometry.

Interestingly, in mathematics in general certain words are left definition-less. For example, take the word “point”; undoubtedly it is difficult to define, and yet we know exactly what “a point on the line” means; these ambiguous terms exist in both mathematical ways of thinking.

Nevertheless, there must be some distinction between Euclidian and non-Euclidian geometry. In actuality, there are some major differences, some disturbing ones for that matter. Non-Euclidian mathematicians actually began to redefine certain words to fit their logical cognition. For instance, the term “parallel” to a student like myself means something dissimilar than to a non-Euclidian mathematician. Parallel lines were redefined to be simply lines that never intersect, for non-Euclidian geometry is not planar but spherical and relates to the three-dimensional shape of the world. Modifications like these are what in actuality cause a great difference between regular geometry, and “abstract” geometry.

From more of a philosophical perspective, it seems as if certainty is difficult to obtain in mathematics. On one hand, solving for variable x in a complex equation can provide you with a rather high certainty of what x is. However, on the other hand, as proven by the multiple geometric aspects, there could be many ways to interpret the same “subject”. Neither geometry is incorrect (again, we believe), however one is simply more favored than another, most likely because it is more simplistic and facile to understand. However, since both perspectives are viable in the sense that neither is incorrect, we could conclude that certainty is difficult to obtain in mathematics at times like this, when many perspectives could provide you with different answers to similar problems.

Mr. Macky’s Presentation: TWE is certainty attainable within Mathematics?

To begin, Mr. Macky used the analogy of a constitution before jumping into the abstract mathematics. He explained that like the laws of a government must follow the constitution (example of the United States) all mathematical laws must follow the basic axioms. These axioms are used to prove all of the theories, laws, and other theorems about mathematics. There are a few rules to these axioms:

-There should be as few axioms as possible

-These axioms should be simple

-There should be no overlap between axioms

-The axioms should be self-evident and not provable using other axioms

-The axioms should use as few undefined terms as possible

Euclid was the first person to actually write the axioms. In total he had five axioms. With these five axioms Euclid’s geometry was created, which is the geometry that as Mr. Macky put it “normal humans can understand”.  However, there was one axiom that did not quite ‘fit’ with the rest or with the rules. This other axiom, known as the parallel postulate was much more complex and ‘wordy’ than the others. It was not easily understood nor pictured and as a result he was ridiculed for it. For thousands of years the smartest mathematicians tried to disprove this parallel postulate. Others simply discarded the parallel postulate and as a result hyperbolic geometry and elliptical geometry were created. These geometries do not accept the parallel postulate and as a result the whole of Euclid’s geometry is changed and new types of geometry, altogether, are born. Mr. Macky gave the analogy of when the rules of volleyball changed; how the game is played is changed as a result of just a few changes in the rules. This example shows that when there are a few changes to the rules, not only does the outcome change, but how something is done as a whole changes as well.

To address the knowledge issue, I believe that there can be certainly to a degree, in mathematics. The highest level of certainty of all the areas of knowledge can be achieved in mathematics. It is much more accurate than chemistry, history, and especially ethics. However, there is some uncertainty in mathematics and this is why it cannot reach +10 certainty, but gets very close.  The aspect of mathematics that makes it uncertain is the axioms. Firstly, these axioms must be assumed to be true as they cannot be proven; but how can we be sure that these are the correct axioms? We cannot because they cannot be proven and since we cannot be sure, mathematics cannot reach +10 certainties. Regardless, it is still very certain because we can be quite sure that the axioms are correct, simply not +10 sure. This leads us to the second point. As a result of not being able to be sure that the axioms (specifically the parallel postulate) are correct we cannot be sure whether Euclid’s, hyperbolic, or elliptical geometry is correct. Therefore there are multiple possibilities and with this there cannot be +10 certainties. In mathematics, usually only one answer or possibility exists which is why math is usually said to be +10 certain. However, because there are multiple possibilities for the axioms and the related geometries, there cannot be +10 certainties in mathematics. Regardless, math is very uncertain, much more so than any other area of knowledge, which is why we rely so heavily on it to run numerous aspects of our lives.

In conclusion, if there is just one aspect of Mr. Macky’s presentation that stands above all else, I believe that it should be that we should all be grateful for Euclid and thankful that we are not required to understand, let alone learn, hyperbolic and elliptical geometry.

These pictures from:,

To what extent do our senses give us knowledge of the world as it really is?

How do we define ‘reality’? Would you define reality as the sensual experiences that our senses can perceive? Like the smell of a flower, shape of a building , sound of a bus moving along the road. These ‘sensual experiences’ could be categorized as empirical evidences which our senses can perceive directly. I believe that knowledge is ultimately based on our perceptual experiences. People might argue that reason is the best way in expanding our knowledge, however I support the argument of empiricism because without our sense perception our reason is less likely usable. Using a computer as an analogy, let’s say that the microchip is the brain of person or in this case it represents our ability to reason; and the computer inputs such as the keyboard, mouse, monitor and etc. are our senses where we get the information to be processed. Like a computer’s microchip that is dependent on the inputs from the keyboard and other devices; our ability to reason  also relies on how we gather ‘inputs’ in this case sensory inputs for our brain to process.

In contradictory,  our sense perception might give us first-hand knowledge based on our ‘sensual experiences’ however, due to biological limitations and personal biases sense perception is often placed below against reason. For instance, our sense of sight can only perceive limited amount of light wavelengths. Humans are not capable of seeing very and very low frequency wavelengths such as infrared and electromagnetic fields.  However, with the help of technology our ability to perceive is extended to some extent.

To conclude, since the definition of what ‘reality’ is  relative to everyone. Since our personal ‘sensual experiences’ is private knowledge and is not available to everyone and is subjective depending on our own personal biases. I would say that sense perception can give us 1st -hand knowledge to great extent but is problematic due to the biological limitations and personal biases.

Compare the Role of Reason in the Natural Sciences and Human Sciences

Compare the Role of Reason in the Natural Sciences and Human Sciences

Just stumbled upon…


Fallacy: appeal to believe

Fallacy: appeal to believe -“Osama Bin Laden died eight years ago during the battle for Tora Bora in Afghanistan, either from a US bomb or from a serious kidney disease.”

The most common theory about Osama Bin Laden is that he died. This is a theory that developed since the terrorist attack of 9/11. There is nothing that can prove that Osama Bin Laden is dead but it is a common believe that most of us have. This article date back to January 9, 2010 and few days ago, May 1st of 2011 finally U.S.A army confirms the death of Osama Bin Laden. This confirm that the article below contains fallacies on what many people based their believes, supposing that Bin Laden was actually dead long time ago. There are different prospective about Osama’s dead. People used to think that he died long time ago, during the war between U.S.A and Iraq during the battle for Tora Bora in Afghanistan. His dead should be caused by a US bomb or from a disease. Other thought that he successfully escape from the U.S army radar hiding in caves of the deserts around Middle East for long time sill directing Al-Qaida and their terrorist attacks. But then the news of Bin Laden dead few days ago made new prospective. Now some people finally believe surely that Osama Bin Laden is passed away, but others still do not believe in this fact, they think that it is just another fallacy that the US government and Obama made up to reassure the US population.

Bias Samples:

Numerous audio and video statements purporting to be from Bin Laden have been released, but their authenticity has been continually questioned.”

There are many videos that prove that Osama Bin Laden was still alive but their authenticity is often questioned. There is no real evidence and real prove that confirm that the most wanted man in the world is still alive. In fact most of Bin Laden statements are only audio recorded and only two actually show Osama speaking since 2001. So the audience is still split in two sides and the new cannot prove yet what the truth is.

“I think those conspiracy theories that he is dead are pretty much laughable”

This is a quote from Art Keller, an agent from CIA. He thinks that Osama Bin Laden is still dead, and the theory that he is dead is just ridiculous conspiracy. Could be that Osama Bin Laden decided to fake his dead so that he would not be wanted anymore because considered dead.

Reason Artifact


“The officials pointed to “double standards” in the west’s response. “What’s the difference between the Libyan rebels and the IRA?” asked one. “The IRA were armed rebels who wanted their independence. The British – the legitimate government – fought them, and anyone who gave [the IRA] support was considered an enemy. Now the British are doing the same with the Libyan rebels.”’

This is an example of the straw man fallacy. The straw man fallacy occurs when a position is confirmed or denied based upon the truth or falsity of another claim that is similar to the first.  When the rebellion in Libya started Gaddafi cracked down hard.  The Libyan army attacked the rebels and backed them into a corner; however the UN sent air strikes to help the rebels.  The rebels since then have neither retreated nor gained any ground.  Recently there was an airstrike on Gaddaffi’s house, his youngest son and three of his grandchildren were killed.  Gaddafi and many of his officials were very angry and felt betrayed, especially by France and Britain.    In the above quote the official tried to justify their position of killing and imprisoning the rebels by comparing it to Britain justifying destroying the IRA.  This is an example of straw man fallacy because they are supporting their claim on the justification of a twisted version of their idea.  The killings in Libya and defeating the IRA are two different situations that cannot be used as justification for one another.  First of all, the targets for the two rebel groups are different.  The IRA bombed busses and buildings, killing many civilians in their struggle for freedom.  The Libyan rebels on the other hand are only fighting the Libyan army, and the Libyan army has probably killed many more civilians than the rebel army.  Also their organization is different.  The IRA was an organized army with trained combatants and was decently armed, with planned missions.  The Libyan rebels on the other hand, are a disorganized, poorly armed, haphazard group of people who want to change their government.  Neither group like their government and both groups are rebels; however the groups are different enough that the straw man fallacy is introduced.  The official probably is offended by England, and chose this example as a message to the English because they might have an emotional attachment to the idea of the IRA.  This could cause someone who was affected negatively by the IRA to subconsciously condemn their governments for helping the Libyan “IRA” rebels.  However, to an Irishman this may be, to them, an example of the British government choosing the right side for once and helping the Libyan “IRA” rebels where they originally fought the IRA.  Since I have Irish roots and I did a project on the IRA I am more inclined to think like the Irishman.


‘”If I were a president, my fate would be like the fates of the presidents of Tunisia and Egypt,” Gaddafi said.”’

First Premise: Gaddafi is a theoretical president

Second Premise: The same thing would happen to the president of Libya as the president of Tunisia or Egypt

Conclusion: The theoretical Gaddafi president would have the same thing done to him as the presidents of Tunisia and Egypt.

The first premise is true due to the nature of a theoretical claim.  Theoretically anything can happen to anyone if there is the imagination to think up the situation.  However the second premise is not true as a president is originally elected and has specified amount of time to rule.  Thus if the president were originally elected then he originally had the favor of the majority of the population.  This favor would most likely not decrease so much as to make the president step down unless they did something drastic.  Since the rebellion in Libya is mostly due to people becoming fed up with Gaddafi’s long reign, if he had been in power for just a short time most likely people would not have rebelled.  This leads to the final conclusion also being false as Gaddafi did not do anything super drastic to start the initial rebellion. It was merely Gaddafi’s 42 years of oppression that caused the rebellions.  One big assumption that this argument makes is that if the people felt the same about Gaddafi as the Egyptians felt about Hosni Mubarak, then they would be able to over through Gaddafi.  This claim might appeal to Gaddafi because it implies that due to the fact that he is not a president, he doesn’t have to step down and the people of Libya won’t try to take all of his power.  This also might appeal to the people of Libya because it does imply that the people of Libya have the power to rout Gaddafi if they wanted to.  For me, this seems to suggest the extent to which the people of Libya want Gaddafi out of power by saying that if he were in a position of power then the people would make him get out.  Being a dictator, one might assume that he had power, however he says right before the quote that ‘”I don’t have any function or post,”  which means that for him he has no power.


The authors of both articles make it seem as if NATO was in the wrong for bombing Gaddafi’s house.  Also both articles examine both sides of the story and both articles seem to present their NATO/British spokesperson in a bad light.  This seems to suggest that the authors of the articles believe that NATO was unjustified in their attacks on Gaddafi.  From my point of view, I don’t think that it was right to target Gaddafi’s life with a bomb due to the fact that it was a “violation of international law” according to the author.  However, I do think that an attack on Gaddafi’s life follows the intent of the attacks as “all its targets are military in nature,” due to the probability that Gaddafi is the one behind the attacks on the rebels and as such is part of the war.  Therefore attacking Gaddafi would be a military operation against the Libyan army in an indirect manner.

Reason Artifact: Post Hoc Ergo Propter Hoc

“Adding some deep breathing to your daily routine can actually help to boost your metabolism.”

This post hoc ergo propter hoc fallacy states that deep breathing can actually help a person lose weight. This article failed to mention evidence or reference to a test or experiment that was done to support the statement that deep breathing causes weight loss.  The article goes on to give different causes of weight loss but fails to make a clear distinction that deep breathing routines result in the actions that cause weight loss.  The article continues to make other premises,

“Deep breathing reduces stress which in return keeps that waistline slim.”

The above statement consists of another premise that continues on to convince the reader that deep breathing directly alters whether a person loses with or not.  The second premise says that deep breathing reduces stress and then because of the stress reduction, that is what causes the weight loss.  Similar with the first premise,

Deep breather helps boost your metabolism,

Increasing your metabolism burns more calories,

Therefore, deep breathing causes weight loss.

This article can be classified as post hoc ergo propter because the author is confusing a correlation with a causal connection; assuming that because one event precedes another it caused it.  Just because there might be a correlation between deep breathing and weight loss does not mean that deep breathing directly affects a person’s weight.

Considering the author’s perspective, the author I would guess is someone who has experienced weight loss and perhaps had a routine of exercise and other supported weight loss techniques.  The author could have connected with the deep breathing that is part of their routine with weight loss and convinced themselves that deep breathing somehow influenced their weight loss.  It also sounds as if they may have searched on the internet the causes of weight loss and also what deep breathing can do to benefit your body and connected the two directly.  The writer’s audience probably is a person who would like to lose weight and is looking for tips to lose weight.  The simple and easy appearance of this “exercise” will most likely be appealing to the reader.  An advertiser or corporate owner may not view this method of weight loss as reliable because there is no source listed on the article and no reference to an actual test or experiment that can be used to support this claim.  In my perspective, I do not support this claim because of the knowledge I have gained through school.

Post hoc ergo propter hoc

Post hoc ergo propter hoc

Article Used:

Before I start to analyze through the article that I chose, I would like to define what is post hoc ergo propter hoc. “Post hoc ergo propter hoc” means after this, therefore because of this in Latin. This basically means that event followed by this one must have been caused by this one. In other words, correlation not causation. For example, Koreans eat kimchi, therefore kimchi must make Koreans good in math.

The article that I chose is about an IQ test testing the ability of intelligence and motivation. The article states, “Researchers from Pennsylvania found that a high IQ score required both high intelligence and high motivation but a low IQ score could be the result of a lack of either factor.” This is yet another post hoc ergo propter hoc. Therefore it concluded, “IQ tests measures motivation, not just intelligence”.


Premise 1: High IQ scores shows higher individual intelligence

Premise 2: Individuals with higher intelligence motivate themselves more

Conclusion: IQ score reflects on motivation

As stated in the statement, IQ tests relations to motivation too. The conclusion itself is valid because it is a derived from the 2 premises. However, is the conclusion true? To know if a conclusion or an argument is true, we must look upon the certainty level of the assumption, which are the premises.

“The higher IQ shows higher individual intelligence” is hard to test because IQ test itself is a test based on intelligence (that is what most people on Earth agree upon). There may be bias and perspective differences; however, a test cannot be perfect, so to make it simple and to not to go too into a deep analysis of such an acknowledged test, I will assume that it is true.

The problem that lies in the conclusion is premises 2. “Individuals with higher intelligence motivate themselves more”. That statement itself can be countered very easily. I have a friend named Seo Ji Hun who had a low IQ level then mine (we were all tested at the same time, so I got to see his score), but he always worked harder and was more enthusiastic about learning than any students in my class. This example shows that motivation is not a result from his high intelligence as the article states.

Another funny aspect of this article is that it made two sided comments on that page. I see that people are commenting that goes against this article such as many people tell me I’m very intelligent, but I don’t really have a lot of motivation and that IQ test can be prepared for.

Before concluding the article’s post hoc ergo propter, I personally think that perspective plays a huge role in this. Most of the reader of this article with high intelligence, motivation, and IQ scores will probably accept this research as it is before even looking at the fallacy in the premises because it is favorable to them; however, that situation may not be for a person who has high motivation, but lacks others. Also this article’s argument’s truthfulness and fallacy is  heavily dependent on a person’s perspective of the IQ test because it is part of the premises.

Logical Fallacy

Title: Lower IQ ‘a heart disease risk’

Heart and circulatory disease is the UK’s biggest killer

This article presents a new finding of a medical research team from the University of Glasdow and the University of Edinburgh who believed there’s an undiscovered factor that causes heart disease. After years of research, this European team came to conclusion that “having a lower than average IQ is in itself a risk factor for heart disease”.

This claim that lower IQ causes heart disease is a clear post hoc ergo propter hoc fallacy. The reason is that just because two things (in this case, the low IQ and the number of heart disease) correlate together, it doesn’t mean one is the cause of the other. For example, there’s a positive relationship between my height and S. Korea’s GDP. However, it doesn’t mean that S. Korea’s GDP was increased by my height. There are other reasons for the growth in S. Korea’s GDP such as increased overseas trade, thriving industries, and political stability. Likewise, there are many alternative reasons for the increase in heart disease, such as high fat diet, natural genetic formation, and smoking.

This argument can be made into a syllogism. The first premise is that socio-economically disadvantaged people have worse health and tend to die earlier from heart disease. The second premise is that these socio-economically disadvantaged people tend to have lower IQ. Thus, lower IQ increases the chance of having a heart disease.

In my perspective, the first premise that lower IQ leads to socially or economically lower positioned jobs is false, because one’s effort to be successful, one’s social relationship with other people, and one’s EQ also play large roles in determining one’s socio-economic status. The second premise that socio-economically disadvantaged people tend to have lower IQ is also false, because many rich people too, suffer from coronary heart disease, which comes from intake of high fat-orientated diets.

One clear assumption here is that the higher one’s socio-economical status is the better health care one is going to get. It also assumes that better health care means prevention or treatment of the heart diseases.
On the other hand, from the writer’s perspective, (who needs something shocking to attract readers) it may not so. To satisfy the appetite of the readers who’re tired to seeing mundane articles, the writer even mentions explanations to make the argument more plausible.

The writer’s argument is quite tied to Darwin’s theory of natural selection. It seems quite plausible at the first sight that people with low mental capacity may not prosper as they aren’t certainly the fittest ones. However, past studies show that people with mental problem do go off living a long life and that some even manage to get married. This shows that God has unique plan for each and every one of us no matter what handicap we might possess and that no one is born as weaklings or by mistakes.

Post hoc ergo propter hoc


Post hoc ergo propter hoc is defined as “the logical fallacy of believing that temporal succession implies a causal relation”. People often presume that just because two variables correlate with each other, it must mean that one is a direct cause of the other. This misconception is understandable, as situations with cause-and-effect relationships always correlate with each other. However, situations that correlate with each other do not mean that one is a direct cause of the other. For instance, consider the Philips Curve, shown below.

The Philips Curve indicates that there is an inverse relationship between the inflation rate and unemployment rate. While the correlation is negative between the two variables, it is not to say that inflation causes unemployment or vice versa. The relationship exists through common factors which happen to drive both of them.


The article that I chose concerns the recent ‘hot topic’ of the marriage of Prince William and Kate Middleton.

According to the article, one premise is that the event could cause as much as a quarter of a percent loss of British economic growth due to the lack of economic activity from the extra holiday. Furthermore, the event falls on a week that Britons already have multiple holidays. Therefore, Britons have the opportunity to have an 11-day holiday, by using only three days of vacation. This would then mean that, for the last two weeks of the month, Britain businesses would close – all because of the royal wedding. This can be represented through deductive reasoning:

Long holidays hurt a country’s economy.

The wedding creates a long holiday.

Therefore, the wedding will hurt Britain’s economy.

While their argument appears to be logically sound, there are still other factors that could contribute to the decline in the economy. It was mentioned in the article that Britain’s economy “isn’t in great health already”, so the economy has already slowed down without the wedding. This means that it would not be justified to blame the wedding for a potential economic decline because there seems to be other forces at work.

One major issue in this argument is the apparent bias that is displayed. Since this article is more of a commentary, the author would be inclined to make arguments that twist or exaggerate the truth and attract attention. He could be compiling a bunch of facts and figures together to support his argument, regardless of whether they are valid or not. Simply adding an extra holiday would probably not cause as huge a decline in the economy as the article suggests it would.

This article was found in a website that was dedicated to Prince William and Kate Middleton’s wedding, so it is aimed at an audience that is highly interested in the event. It is understandable that the author is trying to set the article apart by focusing on the negative aspects of the wedding rather than the typical supportive remarks.

I think that perspectives play a large role in this situation. The author seems to avoid talking about the positive impacts of the royal wedding. If the author were more supportive of this event, he would be focusing on the beneficial rather than the detrimental effects. Instead of saying that the wedding would hurt the economy, he may put more emphasis on the argument that the economy could benefit from the wedding, due to an increase in tourism and wedding memorabilia. Also, he would point out the benefits of a long vacation, such as creating opportunities for people to spend more money. Through a change in perspective, the title, “Royal wedding to hurt Britain’s economy” can easily become “Royal wedding to lift Britain’s economy”.

Because I am impartial to the event, it would be easier for me to analyze the situation from an unbiased view. At this point, the impact of the royal wedding to the British economy is unclear. There are clearly both positive and negative aspects, but it is also possible that the wedding may have no effect on the economy at all.

False Dilemma

False Dilemma: No Other Choices

‘False Dilemma’

“Prosperity can be a tool in our hands — used to build and better our country. Or it can be a drug in our system –dulling our sense of urgency, of empathy, of duty.” (George Bush Acceptance Speech)

A false dilemma is a fallacy which occurs when it is assumed that there are only two alternatives exist, i.e. good or evil, black or white, happy or sad, etc. In George Bush’s acceptance speech he assumed that there were only two consequences of prosperity. These were:

1. A “tool” to “build and better our country” (good)

2. A “drug” that dulls “our sense of urgency, of empathy, of duty” (evil)

In employing this tactic, Bush could persuade his listeners to agree with his future action. When a person first listens to the argument, the person may not identify the fallacy, perhaps the person is not listening for a fallacy, and thus think Bush’s logic is solid. The person may then react in outrage at the present president, if they believe that prosperity has not been used to build and better our country, which Bush seems to advocate during the rest of his speech. However, it is also possible that the listener believes that the present government is handling “prosperity” well. Nonetheless, both types of listeners will probably support Bush’s actions as he uses this argument as the basis to the justification of his future plans.

It is probably true that Bush did not write the speech. However, he probably approved of the ideas in the speech. From this, it could be true that Bush believes that there are only two alternatives of prosperity and does not see the fallacy in his logic. However, it is just as possible that Bush is aware of the alternatives and is merely using this argument to get what he wants (we are assuming that he wants American citizens to support his ideas). As can be seen from the previous argument, if his listeners were American citizens, this alternative perspective is possible.

As I am aware of the fallacy in the argument, it seems to me that there are other options for prosperity, for example, prosperity could be used to help other nations or help solve global issues(although this is probably not the primary concern of a government, it probably is one of their concerns). Thus, as I believe that Bush did believe that his argument was sound, Bush’s intelligence is questionable.

For people who are aware of the fallacy in the argument, but believe that Bush knew that his argument was not sound and was using it to gain the support of the people, may end up supporting Bush still. This is because they may admire the ‘smartness’ of the argument. However, they may also end up not supporting Bush as they view him as manipulative and dangerous because he could convince American citizens of something that may be false.

“America has a strong economy and a surplus. We have the public resources and the public will–even the bipartisan opportunities–to strengthen Social Security and repair Medicare.

But this administration (the Clinton/Gore administration)–during eight years of increasing need–did nothing.

They had their moment. They have not led. We will.”


America has a strong economy and a surplus. We have the public resources and the public will–even the bipartisan opportunities–to strengthen Social Security and repair Medicare.

But this administration (the Clinton/Gore administration)–during eight years of increasing need–did nothing.


They had their moment. They have not led.

An assumption not stated in the argument, but stated previously in the speech is “Prosperity can be a tool in our hands — used to build and better our country. Or it can be a drug in our system –dulling our sense of urgency, of empathy, of duty.” As the Clinton/Gore administration “did nothing” when “America has a strong economy and a surplus”(prosperous nation) it seems to lead to the conclusion that during the time Clinton/Gore administration was in power, prosperity was a drug in the system. When Bush concludes that “They have not led. We will.”, it seems to hint that during Bush’s time as president, prosperity will not be a drug(like during Clinton/Gore administration) but be a tool used to build and better the country.

Also, it is assumed the listener should probably have a pretty good idea of how American politics were at the time (who “we”, “they”, “administration” stands for), the state of the nation (prosperous), and have feelings, probably negative, concerning the present administration. It is also assumed that strengthening Social Security and repairing Medicare is important to most of the listeners.

The purpose of this argument is probably to convince listeners to support the Bush administration. It is probably written for people who do not support the Clinton/Gore administration as if they did, they may not agree with the second premise. This brings to question the truthfulness of the conclusion. If the implicit or hidden assumptions are taken into account, this argument can be considered valid as:

1. America is a prosperous nation

2. Prosperity either can be a tool or a drug

3. Clinton/Gore administration is in charge of America

4. Clinton/Gore administration did nothing

Thus: Clinton/Gore administration is not a good choice for leading a prosperous nation like America.

However, it is probably true that the conclusion can be declared false as its premises are not all true. The 2nd premise: prosperity either can be a tool or a drug, has been proven to contain fallacies in the first few paragraphs of this blog.

The various perspectives present for this argument is similar to those stated at the begining/middle of the blog post.


A fallacy refers to an error in reasoning in an argument. The error in reasoning arises due to the conclusion of the argument not having sufficient support from the premises or the argument being invalid.

Post hoc ergo propter hoc: ” Those with no religious affiliation have been found to be younger, mostly male, with higher levels of education and income, more liberal, but also more unhappy and more alienated from wider society. “

The argument mentions multiple premises stating the relationship between people with no religious affiliation and different types of people (education, income, liberal, social etc). The conclusion is that the people with no religious affiliation have specific characteristics like being younger, male, higher education and income etc. The argument is based on a periodic data collected in the 20th Century by surveying people of high IQs or those affiliated with Sciences. As the writer is from America (where Christianity is dominant), he has a different view towards people with no religious affiliations. He is culturally influenced and assumes that people with no religious affiliations are a minority and have some special characteristics. However, if a reader from China reads this same argument, he/she may consider it to be faulty as a large population of China have no religious affiliation and quite apparently have different behavioral norms than those mentioned in the argument. The second assumption made is that the “characteristic patterns” that models an approximately 5000 population of high IQ society will also work with the general population. As there is not enough evidence to support that people with no religious affiliation have specific traits, the argument is a fallacy.

The argument may  be valid for the 5000 group of people that were surveyed. However, there might not be a causal relationship between the conclusion and all the premises. For example, although the relationship between income and religious affiliation can be argued through statistical data, the relationship between happiness and religious affiliation can not be directly shown. This is because happiness of a person is subjective to the person at a given time and is a value statement.

The argument cannot work for the general population as it is based on the data for a limited group of people. The argument is thus, an inductive fallacy as there is not enough evidence to support the conclusion and the conclusion is only limited to a certain number (minority) of people.

Logical Fallacy: False Dilemma

Over the past few years, there has been a lot of pressure amongst parents to enroll their children into a good pre-school that will guarantee their child on a path to success.  One of the questions brought up in this article is what is more important the development of their beloved 4-year old, education or play?  I think this article illustrates the logical fallacy of false dilemma, which is when one assumes that only two alternatives are available when in fact there are more.  In this case, the author is presenting the topic as if only one answer, education or play, is “correct” and will promise a successful future for their children.  However, it is possible that both education and play are important towards creating a positive learning environment for young children and fostering a healthy academic atmosphere which will help them develop a love for learning in the future.

Describing herself as “a disciple of the power of play”, the author of this article is clearly a proponent of play-based schools and she even ventures to say that studies have shown “children who attend academic preschools are more anxious and have lower self-esteem”.  It is possible that the fact that her children are enrolled in play-based preschools has contributed to her bias towards why she firmly believes that “the joys of dressing up and building block castles” will be more beneficial towards a child’s future academic career.  The use of the word “or” in the title of the article implies that there are only two options.  However, it is possible that parents shouldn’t be making the decision between having their children attend play-based or education-based school but rather schools that offer a mix of both.  In fact, most pre-schools do emphasize the importance of learning and play time as both of these aspects need to be present in order for a child to receive the full, well-rounded experience (, we can see from these two websites that preschools do have a mix of work and play).  The article demonstrates a logical fallacy in trying to polarize pre-school education into two distinct sides.  It is easy to note the dichotomy that can be embedded in the readers’ minds when reading the article.  In English class, we once touched upon the idea that our society tries to manifest the idea that things must be “either/or” when in truth, everything more or less lies on a spectrum going from one end to the other because there are very few cases where there is 100% absolute certainty (as we have learned to question pretty much every single thing in TOK!).

The argument in this article is that “play is the best context in which children learn”.  The two premises and the conclusion that follow this argument can be summarized as the following:

  1. Children will be more academically successful in the future with the foundations of a play-based preschools
  2. Education-based preschools do not provide the same foundations as play-based preschools
  3. Education-based preschools do not make children as academically successful in the future as play-based preschools

The first premise is false because the evidence that arguably “justifies” this premise could suggest ad populum fallacy because the author states:

Much of Europe has shifted gears, from academics in early childhood education to play. In Russia and Germany and Scandinavia, reading is not introduced until age 6 or 7. Even in academic powerhouses such as China and South Korea, where The Power of Play has been translated into the local tongue, there is budding recognition that play fosters creativity and curiosity.

The second premise is also false for the reasons that pre-schools, whether play-based or education-based would most likely share the same objectives in creating a positive learning atmosphere and encouraging a love for discovery in children.  The second premise is also an enthymeme, in that although it is not stated in the article, the emphasis on education versus play implies that the author believes education-based preschools do not provide the same platform for children as play-based preschools.  Thus the two false premises lead to a false conclusion.  Another important fallacy relevant to the argument is the underlying assumption (another enthymeme) is that preschool education is a main determinant of how successful a child is in his or her future academic career.  This falls under the slippery slope fallacy as the article quotes someone stating:

“The suit charges that preschool education is critical to a child’s success in life…it is no secret that getting a child into the Ivy League starts in nursery school”.

Although the article later criticizes the quote, the fact that the article is debating whether education or play matters more in preschool in itself implies the idea that preschool education does play an important role in developing the child’s academic intelligence in the future.  It is a hasty generalization to say that preschool education is critical to a child’s success as this can be determined by a variety of factors.  Preschool is a relatively small portion of one’s life, thus the great consequences such as the higher amount of income resulting from attending good nursery school as the article suggests exemplifies a slippery slope.

From my personal perspective, I feel as if the author should not have polarized these two sides of education and play but rather note the importance of achieving a balance in both.  Being a student, I realize that getting a head start in learning how to count or read well can provide the basis for future growth but I also believe that discovering one’s passion for learning simply stems from having fun.  However, readers that appeal to the argument such as mothers whom are desperate to give their child the best possible education system may overlook this logical fallacy and reading this article may make her side with one argument or the other.

From this TOK assignment, I learned that is important for us as readers to be critical thinkers and not believe everything presented to us so easily.  For someone who is very gullible, this blog post taught me to really sit and think about the truth and validity within a claim.

Fallacies: Appeals to fear, biased samples etc.–dimanno-no-rest-for-japan-quake-victims

Appeal to Fear –

In this article, one observes the authors general intent to relate the death and destruction caused by Japan’s recent 9.0 earthquake to the devastation wrought at the Fukushima Nuclear power plants. Although the title suggests a lack of respite for the victims of the recent earthquake, quotes such as,

[Perhaps the real lesson here is that the nuclear reactors should never have been built on an island geographically vulnerable to earthquakes… How unreasonable of Mother Nature to knock off a 9.0 earthquake instead.]

suggest that the discomfort experienced by the people located in the vicinity of the quake affected region are to blame the foolishness of nuclear power plant construction in an area as seismically active as Japan.

Biased samples –

[“We could have power restored on Friday,” another TEPCO technocrat opined optimistically, making it sound as easy as flipping on a switch. No one in Japan believes any of this babble. Those who are able, and have the wherewithal, are moving as far away from nuclear ground zero as possible, way beyond the 20-kilometre exclusion zone that’s been evacuated.]

The generalization here exists in the authors false understanding of the Japanese peoples opinions regarding TEPCOs handeling of the nuclear crisis. Although, a large sum of people have expressed dissatisfaction and even disgust at TEPCO for another one of it’s blunder; Many people have supported TEPCO and the workers, examples being family, friends, and the portions of the Japanese media. Also, the ignorance of a 10km recommended evacuation zone OUTSIDE the 20km exclusion zone emphasizes the authors lack of knowledge regarding this issue. An actual measurement of Fukushima city, which is 65km away from the power plant itself shows little more than 13.9µsv/hour.

Perspective –

The author may have been trying to protest the usage of nuclear power plants, as seen with her rather vicious comments calling the TEPCO Fukushima power plant operators a ‘technocrat’ and suggesting that the people rather than the earthquake should be blamed for the catastrophe at Fukushima. Also, the over-sensationalization of the events in Japan can be attributed to the necessity of the article writer to provide an interest in the reader; taking into account the other vast amount of hyped-up news outlets that exist.

The reader, in any case, should be able to recognize the obvious fear-mongering and ignorance of the truly occurring events. However, this article seems to be directed far more towards western readers; Many of whom, have seemed to have been easily influenced by the torrent of false information coming from sensationalist western news sources.


Reason Artifact

Ad Hominem Fallacy
The fallacy that I decided to choose was ad hominem. This fallacy is when you target the person instead of the ideas or speeches they put forth. So I looked into real examples of these and found that it is a very common thing in politics. The reason this might be is because politicians are in a way voted on their appearance to the public so if a politician is attacked verbally and called out they may not do as well when it comes to voting. So it can be a tool used by politicians to attack the representative of an idea rather than the idea itself. If they want to strengthen their argument in the opinion of the voters.

On former Liberal Party Leader and Shadow Treasurer, Andrew Peacock:
“…if this gutless spiv, and I refer to him as a gutless spiv…” “…the Leader of the Opposition’s inane stupidities.” “He could not rise above his own opportunism or his incapacity to lead.” “I suppose that the Honorable Gentleman’s hair, like his intellect, will recede into the darkness.” “The Leader of the Opposition is more to be pitied than despised, the poor old thing.” “The Liberal Party ought to put him down like a faithful dog because he is of no use to it and of no use to the nation.” “We’re not interested in the views of painted, perfumed gigolos.” “It is the first time the Honorable Gentleman has got out from under the sunlamp.” “…a fop such as the present Leader of the Opposition.”
I think that this is ad hominem because if you look at all these different quotes you can see that they are all personal attacks. Also not only this he focuses on the facts that he is old, and his inability to lead. And these may be things that the voters may not see as the best thing for their leader. So the speaker used these to create an undesirable image for the voters. The next thing I noticed that could have supported that this is ad hominem is the highlight that is blue it says “We’re not interested in the views” this is interesting because it is what ad hominem is sort of about that we do not focus on the ideas but instead we look at the weird parts about him which is stated right after that.
2. Argument
The argument that he is trying to prove is that old outdated politicians are not capable of being good leaders. The premises and conclusion is
That He is right and the opposition is wrong
Voters vote for the person who is correct- Assumption
He should win the votes
But the actual way that he is doing this is like this:
He is Right because he is awesome and the opposition is wrong because they are old
Voters vote for the person who is more correct (Awesome) – Assumption
He should win the next election

3. Perspective
The person delivering the speech obviously is trying to persuade and he is trying to do this by making his competition look bad. The person delivering the speech must also see it as something. I think that he sees it as something that could possibly get him the votes he needs he may also see it as true because what he says is very strong and he can only deliver this if he thinks it is true because if he is questioned, the media may be able to tell that it was just an attempt to lower the image of his opponents party.
The next perspective is the audience that he is delivering it to his audience. The audience would probably see this as an attack on the other political party this might be because it is a common tactic used by political parties.
The final group is the media they may see this a bit different then the intended audience because they have to go more in depth into the story, because it is their job. They may see the same things but they might also see the motives behind it rather than degrade another party but instead see it as a way for the voters to create an image that the party is just a bunch of old guys and hope the voters jump to hasty conclusions and think that since one acts this way all the others must act that way to.

Reason Artifact

“Now, I’ve worked in this community for 13 years, and I just never see people standing on street corners with their hands wide open, palms open to the sky, with bags of marijuana sitting in their hand,” she said. “It’s nonsensical. Everybody knows it’s not true.” – Robin Steinberg

-From an article on cops in NYC allegedly illegally performing random body searches and arresting people for publicly displaying marijuana, even though they had it inside pockets or jackets on their person. In NYC possession of small amounts of marijuana is a violation, with a fine and ticket, as long as it is not ‘publicly displayed,’ which is a misdemeanor.

This is an example of argument ad populum. Steinberg makes a personal anecdote from her experience that people rarely display marijuana publicly in NYC (which is low-certainty evidence by itself). She then says “everybody knows it’s not true [that people publicly display marijuana],” using an ambiguous yet large source to support her argument. This argument ad populum makes it seem to the reader like Steinberg has many supporters, evidence and people who agree with her opinion, while in reality she has not given the reader any way to verify her claim. A reader who agrees with Steinberg would be inclined to agree with her statement that “everyone knows” as evident from their own experiences, however someone who disagrees would likely criticize that Steinberg’s “everyone” is probably limited to a friend or two who’s opinions she has generalized.


“First, for a police officer to stop someone, he needs reasonable suspicion the person is committing a crime. These men say there wasn’t any reasonable suspicion in their cases – they were just walking down the street.”

This argument takes the form of two premises, with the actual conclusion assumed. The first premise is that police officers may legally stop and search someone if there is reasonable suspicion that they are committing a crime. The second is that these men were not reasonable suspicious. These two premises are presented as more evidence for the argument of the whole article, not mentioned in this paragraph, that these men were being illegally searched by police. The argument is valid in a deductive sense, the certainty or uncertainty of the conclusion will come from the truth of the premises. The first premise appears relatively easy to show true with high uncertainty, just reading the law, however this law may not be enforced or may be interpreted differently on the inside of the police force, and it may actually be normal routine for police officers to stop people on the street at their discretion for any reason. The second premise is harder to show true, in that it is just the testimony of individuals. Also, these individuals may have a motive to lie about their behavior, and what is suspicious to one person may not be suspicious to another. The problem with this premise is that it is also a low-certainty value claim. From the perspective of the police, one would likely deny the second premise, and claim the opposite to those they arrested, saying that there was some suspicious behavior whether illegal activities were actually taking place or not. Clearly, the questionable certainty of the premises causes the argument to not be particularly solid in showing the truth of the desired conclusion.

To wrap it up, some perspectives on the whole article:

From the writer: The writer is siding with what she deems the ‘victims’ in this situation, speaking out for people who have been unjustly arrested. Her motives for this argument may include a moral desire for justice or fairness, a personal experience related to those she is arguing for, or an opinion aligned with the progression of marijuana legalization.

From the cops: The police have a job to do, to prevent illegal activities as deemed by the government. They would be likely to deny any claims of their alleged own illegal activities, as would anyone in their position. As for the reason these alleged illegal searches are taking place, it may again be a moral desire to ensure everyone is following the law, with an overzealous and hypocritical application, but it may also be a matter of abuse of power.

From the ‘victims’: Just like the police, the victims have a motive to deny any claims of their illegal activities. They could also be lying.

From me/the reader: Notice in this case, as the reader, we tend to side with the victims. This is possibly from bias in the article (the article is definitely biased towards the victims), or it could be a David and Goliath effect where we root for the underdog, the everyday normal guy. It could also be because we may identify more easily with the ‘rough around the edges,’ ‘make a few mistakes’ position that the victims are in.

Special Pleading – Fallacies


Sheen ended up with a police escort worthy of a head of state—complete with blasting sirens, flashing lights and street closings—from Dulles International Airport to the downtown venue where he was scheduled to perform on Tuesday.

Special Pleading: While running an hour late, after getting off his private jet coming from a L.A. courtroom, Charlie Sheen ended up with a private police escorts even though it is clearly stated in the policies that police escorts are for providing security for the President and the Vice President (and other visiting heads of State) only. He was trying to make it back in time for his Violent Torpedo of Truth Hour. Because he is a star and has the money and accessibility to use his ways of getting what he wants, Charlie Sheen most likely feels that he deserves these ‘special protective measures’, no matter if they are allowed or not. (

This case presents a clear example of an individual’s use of double standards to get his own way. Charlie Sheen was willing to bend the rules for himself to get what he wanted. Just as a common ‘special pleading’; fallacy were a person applies certain standards, rules and principles while they exempt themselves from the situation, without clear indication and adequate justification to why they are being excused from the situation. People who feel superior to others may try to take advantage because they feel that they are better than everyone else.  The writer’s perspective on Charlie Sheen is show to be that of which he is a joke, from the language and tone of voice used in the article, there is no evidence to show the audience that the fallacy was appropriate. My personal views of this fallacy are that Charlie Sheen used his stardom to take advantage of privileges not made for him, and by doing so proving errors in his reasoning, providing more evidence for people to make negative judgments on him. However, it could be seen that these measures were taken not to give Charlie Sheen VIP escorts, but to protect the people on the road from him, given his past with reckless driving. Another way the writer could have intended the reader to view this, was as a tool to provoke emotions and for us to question society today and how they handle issues like this. If they are going to let Charlie Sheen get away with using special pleading then others may do the same, how will these repercussions change the hierarchy in the advancing world.


Sheen probably thinks he qualifies for “extraordinary protective measures,” there are probably a few cops—not to mention a few tax payers—who will disagree. Enough people think Charlie Sheen is a person who should have these privileges. Therefore, support him, giving him the motivation to keep doing what he wants to further him in life. But there are also those opposed to what this ‘star’ is exploiting the world to, and his assumptions that what he is doing is the ‘correct’ thing has effects on the audience. This balancing act on which side you will support is what the writer is trying to get us to decide, using evidence and reason to support that it was wrong by the police quotes, the writer is trying to sway the reader. Maybe Congress should rename it the “District of Charlie.” Shows evidence that the writer of this article is making fun of the situation, and how it is inappropriate given the consequences Charlie Sheen is in, to be expecting people to agree that he should be exempt for partaking in normal activities like the rest of the world. He gets his way with so much that, laws should not be applied to him as he uses double standards for so much.  And for some reason he wound up with the VIP escort—which, in typical winning warlock fashion, he took to Twitter to brag about. This example shows validity that Charlie Sheen consciously knew that he was using ‘special pleading’. Tweeting it to the world, trying to get a reaction, this evidence supports that title of the article Charlie Sheen’s Latest Cop Trouble: D.C. Metro Probing His Police Escort, that this man is seeking attention, the conclusion of the piece is stated in the title. “It is not our practice to utilize emergency equipment for non emergency situations,” Supporting evidence that this is a special pleading fallacy, as it is not in ‘practice’, with what normally goes on we can see this as an authority figure retells this information. The premises of what Charlie Sheen committed was unsupported and therefore a double standard. Charlie Sheen clearly has errors in his reasoning.

Reason Artifact

My fallacies come from the Church of the Flying Spaghetti Monster’s Home website.

The Church of the Flying Spaghetti Monster is a satirical organization dedicated to ridiculing religion through the use, specifically, of logical fallacies which can often be found in the context of religion. By blatantly pointing out the flaws in religious beliefs and metaphysical claims, the Church of the Flying Spaghetti Monster (silly as it may be) does succeed in making one think. Why do I believe what I believe? How can I confirm or validate it?

For example, one of the Church’s most famous claims is that global warming is the result of their deity (the Flying Spaghetti Monster) being displeased with the decrease in the number of pirates worldwide. This is a good example of a post hoc ergo propter hoc fallacy. By showing a graph with global temperatures on one axis and pirates on the other, they create a linear correlation which appears to corroborate their claim, however this is obviously coincidental and has no evidence to support it other than the metaphysical claim itself.

Another example of the fallacies they use to insult religion is ad ignorantiam. They claim that their deity exists and that their is scientific evidence, however this evidence is never provided. “Many people around the world hold the belief that the universe was created by a Flying Spaghetti Monster; It was He who created all that we see and all that we feel. We feel strongly that the overwhelming scientific evidence pointing towards evolutionary processes is nothing but a coincidence, put in place by Him.” these claims say they have evidence, however never give it. This is much like in many religions where there is no evidence but written materials.

Although there are a good many other examples they use, I will lastly point out the use of Ad hominem. They satirize the use of famous people to publicize religion by listing “Smart People Who Agree With Us”, all of whom have PhD.s and none of whom make sense. However, the purpose of these fictional people is to use professional opinion as evidence instead of actual evidence. In the context of a more serious piece, readers’ opinions of the material could greatly be altered by seeing educated individuals praise this viewpoint.

The Church also argues against the use of science to disprove the existence of the diety is illogical because their diety can alter the laws of science themselves. They claim that since:

The Flying Spaghetti Monster is Omnipotent, invisible, and intangible.
Scientists cannot perceive invisible/intangible beings.
Therefore, if the Flying Spaghetti Monster interferes in their experiments, they will not be able to perceive it.

This is, of course, based on the assumption that the Flying Spaghetti Monster exists, is tangible, and that it would have some desire to interfere in scientific experiments. Once again, this is an example of ad ignorantium: they provide a premise however the premise is not widely accepted and has no prior evidence to support it. Therefore, the argument itself is flawed in that it has a false premise.

the audience of this website is, just as much as atheists and those who ridicule religion, practitioners of religion as well. By pointing out some of the logical flaws in certain beliefs, they are trying to persuade the reader to abandon the concept of organized religion, ironically enough through the use of organized religion. They even contradict themselves by saying “Our only dogma is in that we attempt to abandon and ignore dogma”. This is most likely the goal of the writers: to get the reader to abandon dogma and use reason to come to sensible conclusions.

This image presents another syllogism, which is once again false. The first premise has no evidence and calls something perfect which is virtually unknown. The second premise says existence is perfection, which is not necessarily true. Some may argue that all existence is flawed, so this statement is controversial at best. Perfection is also a value judgement: what may be perfect to one person is imperfect to another. Finally, they conclude that since the Flying Spaghetti Monster is perfect, it must exist. However, both premises used are false or not proven to be true, so even if the argument is valid, the final result is not conclusively true.

Post hoc ergo propter hoc Fallacy

“New York City Council member Leroy G. Comrie Jr. of Queens is leading the charge to ban kid-friendly toys from any fast-food meal that doesn’t meet certain nutritional standards, arguing that the plastic playthings serve to reward children for making poor food choices and undermine parents’ attempts to steer kids toward healthful options.” – Post hoc ergo propter hoc Fallacy
The fallacy of Post hoc ergo propter hoc is when one assumes something is the cause of another event. This reasoning is risky because there is a lack of a strong relationship between two events, and there may be other reasons for the event to happen. Such fallacies are often used in the tobacco industry, when business men claim that although there may be a correlation between smoking and lung cancer, smoking cannot be stated as the “cause” of lung cancer. New York City Council member Leroy G. Comrie Jr. strongly detests the including of little toys in Happy Meals from the well know fast food company McDonald’s, which lure children to choose unhealthy meals over others. This accusation displays false reasoning, especially the post hoc ergo propter hoc fallacy because it assumes that children choose to eat Happy Meals because of the toys. There are various reasons why Mr. Comrie’s claim falls in to the category of Post hoc ergo propter hoc fallacy. First, he does not show much evidence(perhaps statistical), or expert claim about the actions that children take in regards to happy meal toys. Second, there can be many other reasons Children choose to eat happy meals. For example, Happy meals consist of food that fit the needs of the young. For example, Children may choose to eat Happy meals because they simply taste good. Compared to a healthy salad, it is much more probable that Children will favor a Happy meal with a juicy burger with crispy French fires. Furthermore, fast food provides benefits such as low cost and availability, which may meet the needs of not only the child but its parents.
The main argument that exists in this article is that Children tend to eat more fast foods due to there liking of little toys. The following argument can be organized as a syllogism, which includes 2 premises and a conclusion
1) Children love Happy Meal toys. (Premise1)
2) Happy Meals include Happy Meal toys and children buy happy meals.(Premise2)
3) Therefore, Children choose unhealthy meals over healthy meals.(Conclusion)
The assumption that this syllogism contains is located in Premise 2. It is assumed that children buy more happy meals due to the fact that Happy Meals contain toys. This assumption therefore allows the reader to believe that the syllogism is true. However, the syllogism is valid at the most, and the truth of the statements cannot be displayed before further research. In this sense, the syllogism is also an enthymeme. An enthymeme assumes some premises as obvious, and does not bother to explicitly explain them. The argument assumes that children love toys, without stating the specifics, so it is an informally stated syllogism. Such an argument can affect a variety of readers. To the government members, the argument will have a strong effect because it correlates the problem of Children choosing unhealthy meals to the presensce of toys, which will help in passing Mr. Comrie’s ban against Happy Meal toys. In the perspective of parents, or the readers of the article, the argument may seem sound, and they may support the ban of Happy Meal toys. Children who enjoy Happy Meals for the sake of their taste may disagree with the argument, and point out the assumptions made about children buying Happy Meals just for the toys.

Reason Artifact; Pacers defense fuels survival

1) The NBA’s Indiana Pacers fought hard on Sunday to stay alive in the playoffs against the Chicago Bulls. Find this article here.

Fallacy: “A Carlos Boozer three-point attempt — his first in more than three years — drew iron and was rebounded by Danny Granger, clinching the Pacers’ 89-84 victory that sends the series back to Chicago for Game 5 on Tuesday night.” (post hoc ergo propter hoc)

Currently, the NBA playoffs are underway, which are debatably the most important months of the year for these basketball athletes. Chicago, who finished the regular season with the number one seed, are playing Indiana, who barely clinched a playoff spot, finishing the season in 8th place in the eastern conference. Chicago cruised past Indiana in the first three games, however Indiana outplayed the Bulls in the fourth game and managed to extend their season. The post hoc ergo propter hoc fallacy in the article states that because Chicago’s center failed to tie the game with few seconds left, the bulls lost the game, which is false. The article failed to mention that Derrick Rose, Chicago’s star player, had sprained his ankle the game before and was thus playing on an injury, which in turn worsened his performance compared to his other games, leading them to their loss against Indiana. Boozer, Chicago’s center who missed an open look to tie the game, is being scolded for his missed attempt in the article. Derrick Rose, who led the bulls to victory in the previous games, couldn’t step up due to his injury, which actually led the bulls to an away loss in Indiana.

2) ‘‘I have to go up stronger and get fouled,’’ he said. ‘‘I easily could have laid it up with my left hand. But I thought he was going to foul me, so I tried my right. And that’s how he hit the ball.’’

The above statement, said by Chicago’s injured Derrick Rose, consists of a premise, a missing premise and a conclusion. Initially, Rose states that he could have gone up stronger and drawn contact in order to achieve a foul, which is the first premise. An assumption exists in this argument by Rose; he assumes that by obtaining a foul, the course of the game would be altered. Therefore this leads to Rose’s conclusion, that had he gone in harder to the basket and drawn contact, it is possible that the Bulls would take the lead of the game and thus come forth victorious. Rose’s first premise is assuming that had Rose gone up for contact in attempt to claim a foul, a foul would have definitely been retrieved; this is false. A wide range of possibilities could have occurred had Rose drawn contact from the opposing defender; for example, Rose could have further injured his already unstable ankle. Not only would his presence on the court be missed after injuring himself furthermore, but also his teammate’s morals could be impacted as their key player is off the court. Therefore, it is possible that by Rose drawing contact on the described play, his team could have been worsened, not bettered. Thus, Rose’s conclusion that drawing contact on that play would benefit his team is in essence false.

3) It is vital we consider different perspectives when analyzing this article. Initially, we must interpret the writers perspective. The writer of the article fails to mention at any point that the key player on the Bulls team is injured and thus caused their loss to Indiana. It is almost as if the writer didn’t want to admit that Rose was injured which could hinder their chances of winning the championship; this subsequently could have provoked the writer to throw the blame of their loss on a less significant player of the team. In turn, this caused the writer to fabricate a false conclusion regarding the loss of the bulls. We can extrapolate here, and come to the assumption that the majority of Bulls fans reading the article would agree with the author, for they would also not want to admit that their most prized player is injured in any way. Therefore, the author shares the perspective of majority of the Chicago fans when reading this article, who would agree with his false conclusion of the games turnout.

Another perspective possible is that of someone with no bias, unlike the Chicago Bulls supporters; this includes myself. Since I show no particular affection towards which team wins in this round for I am neither a Bulls or Indiana supporter, I would analyze the situation, observe through use of empirical evidence and come to a logic argument as to what caused the Bull’s loss.

Post hoc ergo propter hoc

Part I: Post hoc ergo propter hoc (False cause)

Title of Article: Diet of fish “can prevent” teen violence


This article argues that having more fish in a child’s diet can decrease chances of him/her engaging in criminal behavior in the future. It suggests that the causes of criminal behavior may be attributed more to biological factors (genetics and structure of the brain), rather than social factors such as poverty, unemployment, or peer pressure. This is an example of post hoc ergo propter hoc because there are many confounding variables in this study that were ignored. Even though there may be a correlation between children who eat a lot of fish and lower crime rate, doesn’t always mean these 2 variables have any cause-and-effect relationship. For example, : The programme devised by Raine that attempts to decrease chances of children committing crimes by giving them an “enriched diet, exercise and cognitive stimulation, which included being read to and involved in conversation”. However the main conclusion “diet of fish “can prevent” teen violence” does not take into consideration how the “cognitive stimulation” or “exercise” may have contributed to the decrease in crime rate among the children. Also, the validity of this can be judged using common sense, and how it does not cohere with theories learnt in psychology class about human behavior.

Effect on Reader: The title of the article may capture many readers’ attentions as it is a very new knowledge claim. However, it may mislead some readers. For example, many people believe that fish is healthy as it provides protein. So, they may feel that it is logical that eating fish has a positive impact on human behavior. Also, readers may find the knowledge claims to be reliable because the article cites sources of authority such as psychologists in universities.

Part II: Argument

Premises: The conclusion that the article comes to “diet of fish ‘can prevent’ teen violence” is based on 2 assumptions.

Firstly, the authors suggest that “according to research to be announced this week which suggests the root causes of crime may be biological rather than social”. The scientists in this study solve criminal issues by investigating the structures of the brains (biological factors), and they dont really acknowledge the environmental factors that contribute to human behavior. The effect of this on readers is it creates a sense of urgency. For example, they may be in a hurry to increase fish in their children’s diet afraid that it would be too late, and their children’s brains would have already developed. However, according to what we have learnt in psychology this “assumption” may have flaws. For example in the Psychology course companion I found a study done by Bennett and Wright in year 1984, which investigated the whether the burglars have “free will” or are they biologically determined to be burglars. They interviewed the burglars and asked them about what factors they consider before they decide to steal. The results of the study suggested that the 3 main factors were 1. Reward they would get if successful 2. Whether it is easy to get into the house 3. Whether they would be caught. This suggests that burglars go though a decision making process, so they do have a choice. Whether they become a burglar does not seem to be biologically determined. Also, “many studies have clearly indicated a correlation between rates of unemployment and crime” (Crane, page 64) suggests how social factors can influence behavior. What we have studied in psychology this year, about how cognitive, biological, and sociocultural factors all interact to shape an individual’s behavior, challenges the assumption made by the author of this article.

Secondly, the argument that “feeding children a diet rich in fish could prevent violent and anti-social behaviour in their teens” in the opening line of the article is based on the assumption that the children from Mauritius who participated in Professor Raine’s programme represented the general population. The assumption may increase the reader’s confidence in the knowledge claim, as it does use empirical evidence for the generalization. However, the sample size is quite small as only 100 children participated in the programme. There are 6 billion people on Earth and more than 200 countries, the findings from the 100 children in 1 country probably can’t be generalized to all of the children on Earth. In conclusion, there are limitations to this knowledge claim.


From the perspective, of the news agency this title although it has fallacies may serve to capture the attention of the reader in the first place. Often readers only browse through the headlines and click into the articles that interest them, therefore the journalist uses this title to capture the attention of the reader, as the knowledge claim is very shocking and unique.

From my perspective, the title immediately captured my attention, and I couldn’t wait to look through their article. However, when I first read this article it was for a psychology homework assignment, where we had to identify flaws (confounding variables) in knowledge claims and play the devil’s advocate. So, from my perspective as a knower, knowing my assignment I was more skeptical with what I was reading, and often questioned the argument.

From a psychological perspective, this study that led to this conclusion “diet of fish ‘can prevent’ teen violence” may have many confounding variables, such as how exercise and cognitive stimulation could potentially have contributed to “preventing” teen violence. It is unclear how the participants were recruited, but if the participants were volunteers, the data may be less reliable because it may be prone to volunteer bias. One last confounding variable is that some children were malnourished. However, the author doesn’t analyze how the environmental factors such as how being malnourished may potentially affect criminal behavior. In this article, counter-arguments are not acknowledged. For example, there may be another possibility that by giving the malnourished children fish or food of any kind may decrease their criminal behavior, because one of their motivations to commit crimes may be to fill their empty stomachs.

Works Cited

Crane, John, and Jette Hannibal. “An integrative look at criminal behavior.” Psychology Course Companion. Oxford University Press, 2009. Print.

How might our sense perception be a factor in the growth or stagnation of knowledge

How Might Our Sense Perception Be a Factor in the Growth or Stagnation of Scientific Knowledge