The philosophy of mathematics examines the relationship between math and reality, as well as the assumptions and implications of math. It has existed for thousands of years, with ancient Greeks forming a cult around it. There are various schools of thought, ranging from mathematical realism to theories of embodied mind. Some believe math is eternal and immutable, while others suggest it is a uniquely human conception.
A sophisticated field in philosophy that examines the relationship between mathematics and reality, the philosophy of mathematics also looks at the underlying assumptions and implications of mathematics. Sometimes referred to as mathematical philosophy, the term “philosophy of mathematics” is more accurate, as the former term has other meanings, such as the philosophy a particular mathematician takes in his calculations. This is not the same thing as examining the philosophical foundations underpinning mathematics.
The philosophy of mathematics and related fields have existed for thousands of years, at least since ancient Greek times. The followers of Pythagoras – the Pythagoreans – thought deeply about mathematics and even formed a cult of sorts around it. These ancient Greeks thought that mathematics was a beautiful, self-consistent way of looking at the world, and practically magical in its predictive ability. This view was slightly disturbed by the discovery of irrationality, i.e. numbers that extend indefinitely without ever ending, such as pi and the square root of two.
The ancient Greeks had other peculiar qualities in their philosophy of mathematics. For example, they doubted the existence of zero, asking, “How can nothing be something?” They even argued about the existence of 1 or if it was a real number. It was only with the Indo-Arabic numeral system that the modern zero was introduced, including its function as a placeholder at the end of a number. This was a breakthrough in the philosophy of mathematics and its practical application.
There are numerous schools of philosophy of mathematics. Some contemporary examples include mathematical realism, intuitionism, constructivism, fictionalism, and theories of embodied mind. These generally vary on a continuum according to how abstract and eternal we think mathematics is, versus how contingent, psychological, and pragmatic human uses and definitions of it should be. The old Platonists thought mathematical forms were eternal and immutable, and we “discover” new theorems rather than invent them.
Some modern schools of cognitive psychology suggest that our conception of mathematics is a uniquely human conception, derived from our evolved number sense, and that different conceptions could arise, for example, among aliens with a different evolutionary history than ours. Today, thousands of philosophers are making careers in this field.
Protect your devices with Threat Protection by NordVPN
