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What is the Philosophy of Mathematics?

The Philosophy of Mathematics examines the nature and implications of mathematical concepts, asking profound questions about the existence of numbers, the truth of mathematical propositions, and the mind's role in math. It bridges abstract thought with reality, challenging our understanding of the universe. How does this philosophical inquiry shape our comprehension of the world around us? Join the conversation and share your thoughts.
Michael Anissimov
Michael Anissimov
Michael Anissimov
Michael Anissimov

A sophisticated field in philosophy that examines the relationship between math and reality, the philosophy of mathematics also looks at the underlying assumptions and implications of math. Sometimes referred to as mathematical philosophy, the term "philosophy of mathematics" is more precise, as the prior term has other meanings, such as the philosophy a particular mathematician takes in his calculations. This is not the same thing as examining the underlying philosophical foundations of math.

Philosophy of mathematics and related fields have been around for thousands of years, since Ancient Greek times at least. The followers of Pythagoras — Pythagoreans — thought deeply about mathematics and even formed a sort of cult around it. These ancient Greeks thought that math was a beautiful, self-consistent system of looking at the world, and practically magical in its predictive capacity. This view was slightly disturbed by the discovery of irrationality — that is, numerals that extend indefinitely without ever terminating, such as pi and the square root of two.

A sophisticated field in philosophy that examines the relationship between math and reality.
A sophisticated field in philosophy that examines the relationship between math and reality.

The Ancient Greeks had other peculiar qualities in their philosophy of mathematics. For instance, they doubted the existence of zero, asking, "How can nothing be something?" They even debated over the existence of 1, or whether it was a real number. It was not until the Hindu-Arabic numeral system that the modern zero was introduced, including its function as a placeholder at the end of a numeral. This was a step forward in philosophy of mathematics as well as its practical application.

Early math theorists questioned some of the principals -- such as the existence of zero and one -- that are now considered elementary.
Early math theorists questioned some of the principals -- such as the existence of zero and one -- that are now considered elementary.

There are numerous schools of philosophy of mathematics. Some contemporary examples include mathematical realism, intuitionism, constructivism, fictionalism, and embodied mind theories. These generally vary on a continuum depending on how abstract and eternal one thinks math is, versus how human contingent, psychological, and pragmatic its uses and definitions should be. The old Platonists thought that mathematical forms were eternal and unchanging, and we "discover" new theorems rather than inventing them.

Some modern schools in cognitive psychology suggest that our conception of math is a uniquely human conception, derived from our evolved sense of numbers, and that different conceptions could arise, for example, among aliens with a different evolutionary history than our own. Today, thousands of philosophers make their careers in this field.

Michael Anissimov
Michael Anissimov

Michael is a longtime LanguageHumanities contributor who specializes in topics relating to paleontology, physics, biology, astronomy, chemistry, and futurism. In addition to being an avid blogger, Michael is particularly passionate about stem cell research, regenerative medicine, and life extension therapies. He has also worked for the Methuselah Foundation, the Singularity Institute for Artificial Intelligence, and the Lifeboat Foundation.

Michael Anissimov
Michael Anissimov

Michael is a longtime LanguageHumanities contributor who specializes in topics relating to paleontology, physics, biology, astronomy, chemistry, and futurism. In addition to being an avid blogger, Michael is particularly passionate about stem cell research, regenerative medicine, and life extension therapies. He has also worked for the Methuselah Foundation, the Singularity Institute for Artificial Intelligence, and the Lifeboat Foundation.

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    • A sophisticated field in philosophy that examines the relationship between math and reality.
      By: captblack76
      A sophisticated field in philosophy that examines the relationship between math and reality.
    • Early math theorists questioned some of the principals -- such as the existence of zero and one -- that are now considered elementary.
      By: danilkorolev
      Early math theorists questioned some of the principals -- such as the existence of zero and one -- that are now considered elementary.