• Mathematics

    The Reality of Rational and Irrational Numbers

    In the previous post we talked about the problem of mathematical realism of negative and complex numbers; the issue was that you can construct these numbers logically and conceptually, but you will never find them in the real world. The problem of irrational numbers is the opposite: you can easily find irrational numbers such as √2, π, and e in the real world, but they appear to have infinite irreducible complexity. Similarly, many rational numbers such as 1/3 have infinite digits in them. Unlike negative numbers which are fully understood but never seen, rational and irrational numbers are seen but never fully understood. In what sense are these numbers then…

  • Mathematics

    Do Negative and Imaginary Numbers Exist?

    Numbers for the greater part of history have been viewed alternately as concepts and as quantities. Now, this raises problems about many types of numbers, which include negative numbers and imaginary numbers, because these cannot be viewed as quantities although there are compelling theories that can treat them logically as concepts. In what way are these concepts real when they cannot be represented in the real world, now presents a problem of mathematical realism, which remains unresolved today. This post discusses the issues of realism in mathematics outlining how there are two ways of counting, only one of which involves negative numbers, while the other doesn’t. Why both schemes are…

  • Mathematics,  Overview,  Philosophy

    Numbers, Truth, Morality and God

    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 the problem of morality, which then results in questions of happiness. The resolution of these problems requires the idea of universality—namely universal ideas, universal moral principles and universal ideas about happiness.