Philosophy of mathematics

In his Meditations on First Philosophy, Rene Descartes proposes the argument: “Nothing further now remains but to inquire whether material things exist. And certainly I at least know that these may exist insofar as they are considered as the objects of pure mathematics, since in this aspect I perceive them clearly and distinctly” (451) Essentially Descartes is putting forth the assertion that only the mathematical characteristics of objects can be clearly and distinctly perceived as being manifest of the true nature of them. The first premise of his claim is that I can infer mathematical qualities exhibited by objects are existent due to our systematic and regular perception and I cannot conclude that the non-mathematical properties I perceive…

Even his friends shook their heads regretfully in sympathy for my misery. The conversation appeared ready to move on to another topic, but there was a sudden inspiration rising up in me which was triggered by a recent lecture in our Ancient Greek Philosophy course. The pre-Socratic philosopher Zeno had claimed that change and motion were illusions and he attempted to demonstrate this by presenting a set of apparent contradictions utilizing the concept of infinity. His paradox of the arrow can…

G.E. Moore addresses the idea of philosophical skepticism. His counter argument implements the use of common sense and the idea of a premise that requires no proof as it is "known" to be true. However this means that Moore begs the question when he arrives at his conclusion. Moore explains he can rigorously prove the existence of two hands, by simply holding up his two hands. He mentions that as he makes a certain gesture saying "Here is one hand" (G.E Moore 197) and then by simply mentioning…

Are Mathematics and Christianity related at all? For some, mathematics is simply rules, laws, and axioms that are used to make sense of problems. For others mathematics is the language God used to create universe in its entirety. Either way, certain questions continue to puzzle mathematicians such as: are mathematics invented by human minds to unlock the many mysteries of the world, or are these mathematical truths embedded in God’s nature and henceforth used in the creation of the world?…

What does it mean to have knowledge with absolute certainty? Is there any? Though might seem very simple to answer, they can be very difficult to ponder upon critically. To reason such inquiries, one must go into deep thought of what it is questioning and that it exactly what philosophy is. Author in his book examines each of the famous opinions raised by the fathers of modern philosophy and some of the most sophisticated thinkers. Before presenting his own, author states his view toward each…

I wander through the palace, trying to think of something to do. Queenstrial is tomorrow and today is a declared day of rest for all the Queenstrial participants. How do they expect me to relax with Queenstrial approaching? It seems impossible. I’d rather be at training. It would be something to do to distract myself from. All of my nerves are standing on edge. It’s almost like I should be controlling the electricity in the air instead of metal. But that’s impossible anyway. No one has that…

Descartes’ journey through the realm of his mind and his internal exploration of all the things he previously thought to be certainly true, brings him to the subject of the existence of God in his Third Meditation. Before he touches on the existence of God, he concludes that there are three different types of ideas. There are fictional and adventitious ideas which Descartes’ creates on his own and finally there are innate ideas which are present in the mind at birth. With these types of ideas in…

My Philosophy of Education The American Heritage Dictionary defines philosophy as the “love and pursuit of wisdom by intellectual means and moral self-discipline” (para 1 2005). The second definition in the American Heritage Dictionary states that philosophy is an “investigation of the nature, causes, or principles of reality, knowledge, or values, based on logical reasoning rather than empirical methods”(para 1 2005). Philosophy of education means that I love education and that I am in search…

Descartes and Galileo were two the leading figures in the transition from natural philosophy to modern science and philosophy. They were some of the first modern thinkers who looked at the world and said that the laws of nature are indeed mathematical. One of Galileo’s goals was to take the studies of science and separate them from the ideologies of philosophy. Studying philosophy and mathematics Galileo was able to gain a clear understand of what separates the mathematics from the ideas of…

At six, he suffered from (suffering from muscle and joint pain) fever. Although he recovered from this too, he became convinced that his heart had been damaged permanently. Kurt Friedrich Gödel was an Austrian-American logician, mathematician, and philosopher, born in the Austro-Hungarian city of Brno. He was a bright and inquisitive child, who had interest in various subjects. Although he entered the University of Vienna with physics, he continued attending mathematics and philosophy classes…