# philosophy through mathematics

Modern philosophy in Europe

Professor Sjursen

Assigned: 3/15/2011

Due: 5/18/2011

Philosophy through Mathematics

For centuries mathematics has been the bases to almost everything we do. Whether we are dealing with complex physics or modern medicine, without mathematics almost nothing we have now would be possible. Mathematics is a broad topic that can be broken down into many different categories. Most people limit their mathematics to just basic arithmetic and some geometry but the world of mathematics can be expanded to be so much more. The world of mathematics includes more than just simple arithmetic and geometry. As you progress in the world of mathematics you encounter algebra, calculus, complex mathematics, and then eventually the analysis of mathematics which include both real and complex world and even number theory. These various math forms can be used in all sorts of scientific discoveries in physics, chemistry, engineering and many other fields of science and technology; however, what many people overlook is the importance of mathematics in the world of philosophy.

Before we can begin on our discussion on the impact mathematics has had in the world of philosophy we must understand a few things first. The first thing we need to look at is the philosophers we are going to use to see the important of math in philosophy. The first philosopher we will use is Descartes, who is a rationalist and uses mathematics to prove his own existence. The second philosopher we will be using is Leibniz, who is also a rationalist and using mathematics as a basis of all his philosophical theories. The last person we will be using was not a philosopher, but a pure mathematician. His name is Euler, and though he did not use his mathematic discoveries for philosophy his discoveries brought about so many different philosophical possibilities. We will use Euler, but not to the extent in which we use the other two, because the broadness of the topic would make this an endless paper. Euler will represent all mathematicians who have opened the doors for philosophers to succeed and make tremendous contributions. The next thing that needs to be understood is what is meant by mathematics. Mathematics can be geometry, arithmetic, algebra, and calculus but these are just analytical parts of math. Which also have a pretty large impact on philosophy as we will see with Euler and Leibniz but what we will initially be looking at is how these different parts are applied and through these applications great philosophers came up with extraordinary theories and ideas that shaped the world we live in now. So this is the first big idea that we must understand, that it is not the analytical part of math that is used, but how math can be applied to generate great ideas. Through these applications we will see the impact of mathematics in philosophy. Once we see this in our analysis of Descartes we will then see how important analytical math can be with Euler and Leibniz.

The impact that the world of mathematics has had on the world on philosophy is very clear and the evidence is everywhere. It is so evident that there is an entire section of philosophy dedicated to math. People today dedicate their lives studying the philosophy of mathematics which is the study of the foundation, assumptions and implications of philosophy. Which is a very in depth study. This clearly and distinctly shows the impact mathematics has had in philosophy. However, in this paper we will be looking at the people who have first discovered the importance of mathematics in philosophy, and seeing how their philosophical views have shown the importance or impact of mathematics in philosophy.

Throughout this paper we will be talking about impact or importance and although the meaning may seem apparent I feel the need to explain what I mean when impact or importance is referred to. Impact is defined as an influence. For our purposes when we say...

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