The Foundation

The universe comprises various forms and types of quantities that humans seek to measure.

The question arises: "Why do we want to measure something?"

It is an individual's choice whether to measure or not, and this decision does not impact on the existence of these quantities. These quantities existed before the decision was made, exist now, and will continue to exist thereafter.

In contemporary society, we have assigned numbers, an independent existence, which is misleading and causes ambiguities in mathematics. The current mathematical foundation lacks solidity because the symbols used to represent quantities act as quantities themselves. This is analogous to representing an apple with a mango, then the mango with a ball, and subsequently the ball with a grape, leading to infinite regression. This approach makes it challenging to precisely explain the concepts and ideas that numbers represent. Hence, numbers cannot be defined in the modern context.

What is the irony here? We don’t know what numbers are, but we are using them and define further concepts which use these numbers to exist. This is one of the reasons why we need axiomatic or formal mathematical structures.

Numbers gain significance only after the act of measurement. Measurement gives rise to the existence of numbers, as they represent measurement itself (How? Why?).

This leads us to inquire: What exactly is measurement, and what exactly are numbers?