­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­Philosophy of mathematics:

The philosophical foundations, assumptions, and the implications of mathematics has been the main focus of the study philosophy of mathematics. This branch of philosophy mainly aims to provide an account of the methodologies and the aim of mathematics and it strives hard to understand the place of mathematics in the lives of people. This study has become broad by the structural and logical nature of mathematics.

Though mathematical philosophy can be used to refer several other areas of the study, both the terms mathematical philosophy and the philosophy of mathematics are used as synonyms. The book Principles of Mathematics and Introduction to Mathematical Philosophy by Bertrand Russell has made some people to comprehend the term “mathematical philosophy” The origin of mathematics is subject to argument. It is still a matter of debate that whether the origin of mathematics was just a random happening or it has been necessitated by other subjects like physics or any other subjects.

There are a variety of thinkers who have contributed their understanding about the nature of mathematics. Some philosophers aimed to give an account of this form of inquiry and the products of mathematics while others stressed on emphasizing a role for themselves going beyond the normal interpretation of mathematics and taking a critical analysis to the subject.

The western philosophy and the eastern philosophy have seen many traditions of mathematical philosophy. The western philosophies takes one back to Plato who emphasized on the ontological status of mathematical objects. It also connects to Aristotle who entangled logic and the issue in relation with infinity.

The study of geometry has been the main focus of Greek philosophy. The people of Greek at one time had the opinion that the number “1” was a unit of arbitrary length and not a number. According to the Greek the number is defined as multitude. For example, the number 3 has got a multitude of units, and 2 were not considered as a number but a basic notion of pair. All these have originated from the geometrical straight-edge-and-compass viewpoint of the Greeks. The numbers on a number line is just measured like the lines drawn in a geometric problem.

In the Philosophy of mathematics, there has been Platonism, logicism, empiricism, formalism and so on. Of this, the formalism has got the mathematical statements which had faced several consequences of the manipulation rules. On the other hand, Logicism emphasis on the thesis telling that mathematics is reducible to logic.

Questions:

• What is the main focus of the philosophy of mathematics?
• What is the main focus of Greek philosophy of mathematics?