Was Language Invented or Discovered? The Case of Mathematics
In the realm of human knowledge, the question of whether language, including mathematics, was invented or discovered is a longstanding debate. While some argue that language is a construct invented by humans, this article explores the boundaries of this argument, especially in the context of mathematics, a linguistic form that often seems to describe abstract concepts with a clarity that implies discovery.
Language as an Invention: The Humanness of Mathematics
The position that language, including mathematics, is an invention by humans is widely held and supported by cognitive science. Mathematics is, at its core, a language that we have created to describe and analyze abstract concepts. Just as we invented words to communicate ideas, we invented symbols and formulas to represent and manipulate numbers and algebraic expressions. For example, the concept of '15 - √' or '2 2 4' is defined by the rules we have collectively agreed upon. Even something as fundamental as '1 1 2' is a human-invented principle, applied and accepted based on our need for logical and systematic thinking.
Mathematics and Abstract Concepts
One might argue that mathematics is more about discovering pre-existing abstract truths rather than inventing them. This perspective is often associated with views that mathematics is a fundamental part of the universe and therefore exists independently of human thought. However, such a view faces significant challenges. The proof of mathematical truth, like the truth of '1 1 2', has not been conclusively demonstrated in a way that proves its absolute truth beyond human invention. Proponents of the mathematical discovery theory often point to the nice behavior of mathematical systems as evidence that these are not just invented but discovered.
The Role of Human Nature in Mathematics
Yet, even if mathematical principles are discovered, the way we use and describe them is undoubtedly a human creation. For example, when we put two apples next to two more apples, calling each pair 'two' and the total 'four', we are using language to describe a physical reality. This exercise in counting is a basic form of mathematics and a manifestation of our innate human ability to understand and manipulate abstract concepts.
Abstract Concepts and the Human Mind
The question of whether a fantasy story like "Little Red Riding Hood" was invented or discovered is reflective of the broader issue of abstract creation. Just as stories are human inventions with rules and structures, so too are the symbols and rules of mathematics. We invent these symbols and rules to represent abstract concepts and manipulate them according to our logical and intuitive understanding of the world.
Mathematics often serves as a tool for applying logic and reason to solve problems. When we put a price on each apple and multiply it up with a discount, we are using higher mathematics, a form of invented language that allows us to perform complex calculations. This form of application shows that mathematics is a tool invented by humans to represent and analyze the world around us.
In conclusion, while the principles of mathematics might have a basis in universal truths, the language and rules we use to describe these principles are indeed invented. Mathematics is a human creation that allows us to explore and understand complex abstract concepts with precision and clarity.
Note: This article draws on insights from cognitive science, philosophy, and mathematics to explore the nature of language and mathematical discovery. For more detailed discussions, readers are encouraged to refer to works by mathematicians and philosophers.