To what extent can a person believe that an area of knowledge is discovered or invented? The question allows me to interpret the definition of discovered as a theory that people have realized and learned about through out time and invented as an uncertain theory that has been created by humans from thought and imagination. For years many thinkers have argued about whether various areas of knowledge are discovered or invented. Through my essay I will approve that some areas of knowledge such as mathematics, arts, and ethics are both discovered and invented as they rely and depend on each other.
If we define knowledge as a justified true belief, then invented knowledge means knowledge that essentially formulated from one’s self instead of the outside world. John Polkinghorne once said, “Mathematics is the abstract key which turn the lock of the physical universe. ” In my own experiences of at studying the subject I always felt like it is a discovery rather than invention of information, as I only had to prove statements and calculate numbers. However, I believe that my first impression is wrong and that Mathematics does not come under the category of discovered knowledge.
Consider a circle. A circle is a geometric shape with points in a plane that are equidistant from given point, the centre. This would mean that the circumference is infinitely thin and smooth. The problem with that is that such a design cannot physically exist. So what do we benefit from the theorems about circles? One theorem is the Tangent C, the angle between a tangent and a chord is equal to one half the subtended angle on the opposite side of the chord. Where does all of this knowledge come from, if these shapes do not and cannot exist?
One possible answer is that these perfect shapes exist in a non-physical form in another dimension. This idea is based on Plato’s beliefs, the ancient Greek philosopher. However this answer is unlikely to be accepted without any justification. The other solution is that perfect shapes do not exist, and just a creation of out mind – invention. This means that mathematics is a fiction, and just exists in our mind. Then how come we can apply math in the real world? It is simple, mathematical systems are invented, but the way these systems apply to the physical world is a discovery.
The reason for that is that sometimes we are influenced by the physical world without us realizing, and at times it is just a coincidence. Let us take Pythagorean theorem as an example, it states that the shorter two sides of a triangle squared are he same length as the longer side squared. Although the theorem is named after the Greek mathematician Pythagoras, many historians claim that the Babylonians ‘discovered’ the idea first. Although they had knowledge that there is a relationship between the sides of a right triangle, they didn’t have any proof.
It was Pythagoras and his students that ‘invented’ the theory and proved it with some deductive system. It could be argued that Pythagoras and his students discovered some sort of triangle shape in the real world and then invented the theorem, or invented the theorem and then discovered how it applies to the real world. This shows that invention and discovery of knowledge rely and depend on each other. A fellow classmate argued that mathematics is discovered because you just can’t invent such things as ‘1 + 1 = 2’ because “it just is.
” Well it is on the contrary, ‘1 + 1 = 2’ is statement that is invented, because the numbers and symbols used are concepts created in the mind. On the other hand, ‘by picking up an orange and then picking up another orange, you will end up with two oranges’, is discovered because it is based on observation and experience rather than pure logic. We cannot observe ‘2’, but we can observe objects with ‘2’ as a property such as a pair of chairs. So unless we are willing to accept Plato’s theory, we have to accept that ‘1 + 1 = 2’ is an invented knowledge.
You could ‘invent’ a new formal mathematical system in which ‘1 + 1 = 5’ but unless you discover a way in which the system applies to the world we live in, nobody will accept it as it will be considered useless. At the end of the day mathematicians try to separate them from the philosophical realm and get on with proving and disproving theorems, not caring they are discovered or invented. Oscar Wilde once said, “Life imitates art more than art imitates life. ” Before we discuss whether the arts are invented or discovered, it is important to differentiate between the work of art and what the art is trying to communicate.
Work of art is things such as songs, paintings, films, photographs, sculptures, and other visual media. On the other hand what art tries to convey is a discovery by the artist himself or by other humans. Let us take the ‘Mona Lisa’ by Leonardo da Vinci as an example. It is a half-length portrait of Lisa Gherardini that is considered the most famous work of art. It is an invention because da Vinci created something for the very first time and there is nothing like it in the state it exists in. The way the Mona Lisa smiles, her hand gestures, and her eyes are expressions that we discover with time.
The feelings we get when we look at the painting are not invented, as they are just our perceptual abilities. Another art form is music. Music, as a subject, is discovered because nobody invented it and it is essentially different sounds put together whether it is sounds of the ocean or a piano. The evolution in music results into an invention. Lets us take the song ‘Shake It Out’ by Florence + the Machine, the tempo, texture, articulation, rhythm, and the other elements are all invented and the song itself is also invented because it is the first time that a person put these elements together to create a song in this state.
The genres in music are invented and it is developed and improved in time. The final area of knowledge I shall examine is ethics. Ethics and morals are an area of knowledge that relate to each individual personally. So where do morals and ethics come from? Are you born as a ‘good’ person? Personally, I have formed my ethical values through my experiences as I grow older. For instance my friends, family members, and the media have all influenced me to act in a certain way that is considered ‘correct’ in my society.
In this example ethics, as an area of knowledge, is discovered by each individual. It can also be argued that ethics is invented. When a person is told to act in a certain way from a young age, that person did not discover ethics by himself. The ethics have been passed on from generation to generation, thus being invented by people to co-operate with each other. If people discovered in themselves the idea of being polite then it could mean that this idea existed in the mind of a higher being.
In conclusion, examining the nature of the areas of knowledge has showed that our assumptions about them may be completely false. Whether the area of knowledge is invented, discovered, or both, overtime is can be appreciated and understood. We also have to accept that invention and discovery rely on each other and at times create each other.
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