Mathematics explained.. and concluded

So mathematics and logic have been around since time bagan but over time philosophers have come up with new theories to explain numbers and their origins. In Ancient Greece philosophers such as Plato believed that Greek numbers were derived from geometry and the art of music and the first number that existed was the number two. For example, the number three has its origins from a triangle which is a three sided geometric shape. You can count the sides of a triangle and the answer is three. This is known as the Platonic theory of numbers and Plato also continues to argue in his writings that all numbers are related to each other through ratios. Using the example of a piano all the keys are in ratio to each other from the note C.The note C is almost the base note which determines the other notes as note E is a specific ratio of C and so is B. Each ratio equates to a certain number which is then used to describe mathematics. Therefore, the one way in which numbers can be understood are in relation to others otherwise mathematics canot be interpreted properly. You need to understand a whole system before you are able to analyse individual parts within a system.
One crucial part of the Greek numerical system is that it did not contain the number zero. The number zero was first used in India by the religion of Islam. Aristotle argued that it was not possible to have the number zero as the definition of zero was that zero was nothing, for example if there are no apples on a table you say "there were no apples on the table". But the number zero was something otherwise it cannot mean nothing. A number cannot be nothing and also something, therefore zero does not exist.

Giuseppe Peano
(27 August 1858 – 20 April 1932)

However, modern philosophers such as Guiseppe Peano and Bertrand Russell believe that zero can be regarded as a natural number. Peano was an italian mathematician who argued that zero was a real number that could be used to count objects and could also be used in mathematical operations such as addition and multiplication. He also believed that there were numbers that were lower than zero (negative numbers) but these cannot be used for counting as it was impossible to have minus objects. For example, you cannot have minus 2 bananas and then add 3 bananas as you do not have anything to start off with with. Russell had similar theories to those of Peano and used analytical philosophy to explain mathematics. He argued that mathematics was a form of language and each number had its own individual class. For example, the number 5 is a word to describe a class that contains all classes that have 5 objects and we know this through the method of counting. Counting creates a group or category that can be described using natural numbers such as 4 or 7. As human beings we are able to instinctively count up to seven objects before actually physically counting them as 1...2...3..4...5. There is a process that we undertake to calculate numbers:

Natural number + process (known as a syntax)= predicate (outcome which can be a larger or smaller number depending on the process)

These predicates can be analysed by applying mathematical operations such as square roots and division. For example, the number 5 can be multiplied by 10 to make the answer 50 but the number 50 can be divided by 10 to get the answer 5.  Therefore, mathematics could be applied to all fields such as physics and even mechanics and played an important part in everyday life even if it was simply counting schoolchildren.

Existentialism concluded

The second lecture of the semester concluded the topic of existentialism and we looked at key figures of the movement including Nietzsche, Heidegger, Sartre and Fanon. Heidegger believed that reality revolved around a concept that there is no certainty in our lives and that philosophy is no longer relevant as we are now able to think freely for ourselves. Society has developed almost through the stages of childhood as children are told what to think but now humanity has matured into adulthood where it has the capability to think independently. There are new and different moralities which give the right to kill and oppress fellow human beings should it be thought necessary. This opposes John Locke’s natural rights as Locke believed that every human being should be guided by a God like figure who represented authority and violence was not permitted under any circumstances as it is a sin. In Nietzsche’s world there was no God as he coined the famous phrase “God is dead!”  He also stated in his philosophy that every human being can be described as an “overman” where he must create his own place and identity in the world and defines himself by the choices he makes.

Heidegger wrote his famous book “Being and Time” which was obsessed with human existence and asked the question what is it to be a human being?  and what does it mean to physically exist in the world. He concluded that all beings and creatures are Dasein (they just exist in the world for a period of time until they die). We are stuck in our minds and we can never be totally sure of what is around us. For example, we may believe that we can see a computer screen but we can never be 100% sure that the screen is actually real or just a product of our imagination.  We are defined by our engagement and involvement in the world and when we are asked to describe ourselves we do not speak about our true selves only the social aspects of our selves.  The future is the only time that matters as it gives beings an opportunity to make choices that will affect the rest of their lives, the past has been and gone and you cannot make choices about the past.  The philosophy of Heidegger is in direct contrast with that of Rene Descartes who believed that “I think, therefore I am”. We can only be sure of our existence because we have the ability to think which shows that we are living beings.

Sartre believed that humans cannot escape choice, everybody has to make choices in order to progress with their lives but you can hide away from it.  However this is bad as you should not follow society but be your own individual person.  Each person should take responsibility for their own actions and not place the blame on anybody else or lie to escape punishment.  Authority is the “other” in us and should be ignored and overcome as it stops human beings from being their real selves.  Fanon developed Sartre’s ideas further and believed that society should use direct violence against its oppressors and kill everybody who is associated with a violent regime not just the boss.  Non-violence is just collaborating with the enemy and is an acceptance of the oppressor’s power. Fanon’s book “The Wretched of the Earth” has been used worldwide especially in the Black Power movement and Malcolm X in the USA in the 1960’s. This idea can be closely linked with Fanon’s personal life as he was a soldier who fought in the Algerian War of Independence and saw the torture and violence that was targeted at the Algerians who were fighting to become a free nation away from France.  

Following on from Fanon’s idea of violence the group watched a film “The Battle of Algiers” which was released in 1966 to show the struggle and violence which took place between the French army and Algerian nationals during the War of Independence from 1954 to 1962. The film highlighted the realities of Existentialism as the both the French troops and Algerians were using every form of violence they could think of in order to kill the other including makeshift bombs and walk by shootings.

This video is a trailer for the film but highlights the violence that is used by both the French forces and the Algerian nationals. It is well worth a watch