# Do numbers exist?

When we talk about numbers, we can say that they are not tangible objects. By this I mean, you can not take number 5 and trow it to the bin, but what you can do is take page number 5 from a book and throw it to the bin.

From this brief introduction we can see that number do exist but they are a mathematical concept used for counting, something the human race created.

However, many mathematicians say that numbers exist but in another different space and time, they are abstract objects. This is called platonism.

Having this two theories in mind, we can now get to a conclusion. Numbers give us knowledge, and because of this the world works in a better way. Actually we can see numbers wherever we look at, although they are not physically there, we must apply formulas or calculations in order to find them.

When we look at our houses, we can also see numbers although in a blurry way. The walls, the microwave, clocks… In conclusion numbers are everywhere.

In my opinion, numbers do exist but I have a lot of arguments against this statement. What we know is that whenever we need to do something or create it, we need mathematics, and the base of mathematics are the numbers.

# To what extent is mathematics discovered by the human being?

According to several mathematicians, philosophers and teachers maths is everywhere. We can find it in daily situations like going to buy a product or in more depth Jobs such as creating an engineering machine.

Wether it solves internal or external problems. Maths allows us to investigate problems containing numbers and the relations between them following patterns and several ways of knowing, not to say all of them.

These types of problems abroad from issues that are purely about matter within natural sciences for example calculating the speed of a car at a certain point or application problems which include how the problems is going to be solve applying different resources.

Many mathematicians argue that the area of mathematics has been discovered thought the centuries and therefore the human being is responsible for solving any kind of problems that maths have.

On the other hand, this affirmation is argued by other mathematicians that respond that maths is linked to the nature and the universe and therefore is not created but yet discovered through the people. In fact, if this second conclusion was not true how could we explain the idea of infinite, the sequences between prime numbers or going further the geometry species found in the universe like the slightly sphere that represents the Earth or the calculations applied to design a balance building.

An example of this could be that through out the pure mathematics, meaning the abstract recesses of the subject, these give very useful techniques for solving problems with maths application whether is for a natural sciences or a life´s situation.

To conclude, we could agree that Plato´s and other philosophers where right and therefore respond that mathematics is outside in the universe but including other views such as that somehow the subjects is built through social reasoning and both ideas are link together to create a structural feature for this area.

Bibliography:

• Ib Tok guide
• Ib Tok reference Book

# Does maths need language to be understood?

I belive math its already a language on its own, that you need to know in order to understand it. So for understanding this language you must be taught how to. I believe math is like any other verbal language that exists. The main reason for a language is to be able to communicate, with maths you can explain many ideas. Maths wouldn’t be able to understand if they didn’t work as a language.

I believe that actually every language in the world contains math, you can explain a language using maths, not in a simple way, but i think language contains math.

# Does all knowledge depend on language?

Language is a system we as humans use to communicate. And although to pass on knowledge from one another we need language, it is also possible that subconsciously expose knowledge without using language, for example through body language.

Take sense perception, one can easily communicate through it, for example, one might wrinkle their face when they smell something which is not pleasant, most times doing this unconsciously, “pairing” it with body language.

Another way we gain knowledge is through visuals and the way we experience things. Although this would be a form of individual knowledge, not shared knowledge, it is also a way of of gaining knowledge.

I personally believe that knowledge does not depend on language, although a big part of it does, there are many other ways of communicating and passing on our knowledge such as body language, expressions etc…

# To what extent is maths knowledge determined by mathematicians?

Maths facts are proven by mathematicians by the use of logic. However, to what extent do we know what they are proving is true?

To be able to answer this question, we should first consider whether maths is an invented science or if it is something that already exists that we are in the process of discovering. Let’s take the platonistic view and consider maths an established non-invented Area of Knowledge. Up until now, every mathematician has proven very axiom by logic. Were we to regard how a second degree equation is solved, for example, we use the formula which has already been proven. However, what if all our maths methodology is wrong because this procedure isn’t exact.

This is exactly the paradigm of the philosopher and mathematician Russel, who came up with an impossible logic problem: the paradigm of catalogues, which represents the different sets of numbers.

In conclusion, I think our current discovered knowledge in mathematics is completely determined by mathematicians since their atoms are constantly used either to solve known problems or to try to expand knowledge. However wether to think this is actual knowledge or an incorrect method human beings have chosen is completely uncertain.

# Do Mathematics really exist?

Mathematics is an Area of Knowledge that studies topics such as quantity, structure, space, and change. This Area has always created controversy among  mathematicians and philosophers, arguing the scope of the subject and how do we gain knowledge from it, is Mathematics dicovered or invented? Do they really exist?

From my point of view, I really think Mathematics is everywhere. I do think they exist. Even in places where we never imagined such as Pollock’s canvases with their fractal structures. That unintentionally try to imitate nature, for example: the branches of trees, whether you zoom in or out, they have the same complexity anyways. I also think that we discovered some parts of Mathematics like Geometry,

# Is Art Influenced by Culture?

The arts are obviously a big part of our culture. Everything we do is related to culture, because unless you are a hermitage, everything we do as humans is influenced by our culture.

Any aspects of our lives are determined by culture, so therefore most works of art are heavily influenced by culture; and nowadays, with the internet so present in out lives, there is a wider understanding and more knowledge about other countries which inspire many artists.

For example, Plato didn´t not call painting, sculpture, pottery or architecture “art” but a skilled craft, calling works of imitations of things in the arts.- “Art is the best possible window into another culture”.

In my opinion art is influenced by culture and culture is influenced by art as it is such a big part of our lives and the arts themselves represent culture and in other cases, culture is creating through the arts.

# To what extent does historical knowledge change over time?

I believe it changes depending on the side you look at it. For example second world war stories, a story told by a jew won’t have nothing to do with a nazi story. So I believe history can be manipulated, it can be changed depending on what side you are looking at. I believe it also depends on technology, now a days we can find much more data than before, and we have found many things that weren’t found before, so hows something going to be true, if a part of it es missing, thats why I think it will always be changing as long as we continue to discover new things. So many things that were believed before, are now proved that couldn’t happen.

It also depends on the part of the world, you’ll see that history events can change in some way depending on the country.

But I believe historical knowledge changes a lot over time, because theres always more thing to discover that can complete the story.

# How does “believing that” and “believing in” differ?

After reading this question, I will use the knowledge gained in class to answer it along with the way of knowing faith, which takes a big part on the state “believe in”. But before we start answering it, we should know what believe means.

The term believe differs from one culture to another but it will always have a really  common definition with knowledge, as Plato stated (ca. 428-ca. 347 BCE) “Knowledge is true, justified belief”.

Although believes are very subjective, faith takes part in this process, working together with the other ways of knowing. Believing is a process that only you, as a person can do. In there, your emotions, your feelings and memories combine and give a result, the fact that you believe.

When someone says ” I believe in…” they are actually saying that they believe in someone or something to get a goal achieved, but that only senses can perceive and this means they have a mass and occupies space. As many people when they are going to take an exam they say to themselves: “I believe in myself” because they “exist”. The preposition “in” means that the existing object the person trusts in is not an idea nor an image.

Meanwhile when we say “I believe that…” means the other way around. Here you can state ideas, images and opinions. Not because they do not exist, but because the speaker thinks that they do. For this statements you wouldn’t need any proof required while in the previous one you would. Continuing with the example of a student taking an exam they can perfectly say “I believe that luck exists”, and you can not snatch the arguments from him, due to the fact that he or she believes that luck exists.

Although these two terms are used mutually they present two different ideas and by discussing the knowledge issues concerned with the two terms one can understand the vital differences between them.

# Can we gain knowledge from a lie?

The answer to the question above is yes. In order to understand this claim, we can look at the following example, which focuses on math.

In many cases mathematical errors provide us information. For example, if we look at a statistical study, because of the  existing inaccuracy caused by sampling, there will always be an error range.

Plato once defined knowledge as ” a justified true belief.”

In the case of  an statistical study, we could consider the error the true belief. We can justify it’s veracity with the following statement.  The error exists due to an inaccuracy in the mathematical results, originated because not all of the possible/available data were  used to do the calculations and obtain the study’s results.

In this example, the error provides us information about the reliability of the study.

At first, we may consider the truth, however we may consider there is a “Lie” or within this truth based on it’s inaccuracy, which would be the error, as the study does not perfectly reflect reality. Nonetheless, the error can provide some truth about this inaccuracy and therefore, the reliability of the study. Hence, yes, we may gain knowledge and information from a lie ( the error).