By Natural Philosopher Mike Prestwood

Does infinity exist?

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Philosophy of Math < Philosophy of Science < Philosophy

Can you do, see, or produce infinity?

Infinity exists as a philosophical concept, not physically. This perspective dates back to Aristotle, who explored infinity as an idea that can never be physically realized. He distinguished between potential infinity—an endless process—and actual infinity, a completed infinite state. Infinity serves as a useful abstract concept that helps describe the physical world conceptually. For instance, consider calculus, which evolved from the infinitesimal concept developed by Galileo and others, laying the groundwork for Newton and Leibniz. They essentially use the concept of an infinite number of straight lines to define a curve.

When discussing infinity, it’s important to remember it cannot take a physical form. If someone says that a river stretches to infinity, understand this as a poetic expression, a literary device. 

Various groups are exploring the notion that infinity might actually exist. For example, religiously oriented people often assert their belief in an infinite universe. Similarly, physicists like Stephen Hawking have developed mathematical formulas that predict physical infinities, such as infinitely dense or infinitely hot objects. Just remember, these ideas are built on speculative frameworks. As these frameworks are tested and potentially validated, we’ll update our Grand Rational Framework of common knowledge. Until then, infinity remains only an abstract idea. To learn more about the Idea of Ideas, a new look at epistemology, take the deep dive: The Idea of Ideas.

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June 16, 2024 Edition
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