What is a Number? Is it an idea or a thing? This question has been debated since Greek times, and it still remains unanswered in philosophy and science. This post examines the nature of the problem, and what its likely resolution will look like. It illustrates how the problem of numbers leads to the problem of choice, which then results in...
Since the time of Greek philosophers—Plato, Aristotle, and Socrates—it has been believed that the present universe is comprised of two things: form and substance. Forms are the ideas that exist even when substances don’t; the world of things combines form and substance, kind of like the form of a statue exists in the mind of a sculptor and is applied to a...
A computer is a canonical example of a machine. Every machine can be described by a mathematical theory, and every mathematical theory can be automated on a computer. Therefore if you could describe something mathematically, you could also automate it in a computer. People often suppose that this means if we had a mathematical description of nature, that description could also...
