As a follow-up to an earlier post, where I described how natural laws arise as a result of qualities, this post explores this idea further using an example. Since modern science grew out of the idea that matter is res extensa—i.e., that it has only one property of extension in space—this post also illustrates the …

# 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 …

## 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 …

## Mathematical Novelties in Vedic Philosophy

This is the transcript of the eighth episode of my podcast. In this episode we talk about a number of unique problems that arise in trying to make Vedic philosophy more rigorous in a logical and mathematical sense. I have been presenting some of these ideas while discussing the theories of creation, cosmology, linguistics, the nature …

## The Arithmetic of Concepts

In all religious philosophies, God is the original person, Who creates all else. If we were to count things, then God would represent 1. In Vedic philosophy, additionally, all that is created is also a part of God, Who is then described as the complete truth. In effect, since God is the complete truth, everything …

## The Sāńkhya Theory of Five Elements

This post elaborates on the Sāńkhya theory of the five “gross” elements. The theory is rather complicated, and not well-understood today. One primary source of confusions is a comparison between the Sāńkhya elements and the Greek elements going by the same name. This post will hopefully illustrate how the Sāńkhya elements are deeply enmeshed with …

## The Paradox of Natural Laws and Its Resolution

In an earlier post, I described the problem of computing in nature, namely that scientific laws employ mathematical formulae, but it is not clear how these formulae are being calculated in nature. The reasons for this are historical and date back to Newton’s formulation of the three laws of motion. While Newton had produced mechanics, …

## Reasoning and Semantic Computation

Since the advent of computers, it has been widely believed that the human mind is just like a computer. I have previously described why this is a false analogy due to two problems: (1) the problem of meaning, and (2) the problem of choice. I have also discussed the problem of meaning in computing theory …