596 words - 3 pages

The philosophy of Mathematics is defined as the branch of Mathematics concerned with the assumptions, foundations, implications of mathematics to be able to provide the details about its nature and its place in people’s live. The matters in which Philosophy of Mathematics so concerned varies depending on how mathematics so useful towards the advancement of people in every society. Here, we will look at how mathematical assumptions, foundations, and its place in the society of men changes over a period of time. In the first decades of the twentieth century, logicism, formalism and intuitionism emerged as philosophies of mathematics.

Logicism holds that Mathematics is logic. This means that logic is the foundation of mathematics and all mathematical statements are logical truths. Although the idea of logicism can be associated to Leibniz, it is Gottlob Frege who is considered the founder of Logicism since it was in his time when the principles of logic were revealed. He built a logistic program and devoted much of his time trying to show that mathematics can be reduced to logic. Unfortunately, his endeavor wasn’t successful and his program was abandoned. Nevertheless, his program was continued by Russell and Whitehead. The problem with this view is that it could not resolve the paradoxes that arose in set theory but despite its validity is being undermined; it is considered the key in the development of analytical philosophy.

Formalism, in contrast to Logicism, adheres that mathematics is developed through manipulation axioms. It agrees on the principles of Mathematical proof. It further holds that numbers and other mathematical objects because man created and described it through axioms. Formalists believe that for a mathematics progress from one step to the next, it needs established rules on deduction. Unlike logicism which aims to prove the...

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