The philosophy of mathematics refers to a branch of philosophy which focuses on the assumptions, applications and foundations of mathematics. As well as this, the discipline concentrates on nature and methodologies used by mathematics, aiming to understand the role that this topic has in individuals’ lives. Due to the nature of mathematics, this discipline is very broad and unique.
This subject tries to answers different questions including;
What is the role of humans in developing mathematics?
What is the ontological status of mathematical entities?
What are the objectives of mathematics?
What is mathematical beauty?
What are the objectives of mathematical inquiry?
Over the years, there have been many philosophers that have focused on the nature of mathematics. Among the most well-known philosophers who focused on this area, there are Pythagoras, Plato and Aristotle.
In the 20th century, philosophers have started to analyse different aspects of this topic and that have been divided into various schools. At this time, the main schools were formalism, intuitionism and logicism. Formalism considered mathematics and logic as statements describing results caused by specific rules. Intuitionism viewed mathematics as a result of a human constructive mental activity rather than the discovery of principles pretended to exist in an objective reality. Finally, logicism considered mathematics as an extension of the logic, believing that mathematics was reducible into logic.
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