The Infinite Viewed Through Systemic Functional Linguistics

Penrose (2004: 357):

It appears to be a universal feature of the mathematics normally believed to underlie the workings of our physical universe that it has a fundamental dependence on the infinite. In the times of the ancient Greeks, even before they found themselves to be forced into considerations of the real-number system, they had already become accustomed, in effect, to the use of rational numbers. Not only is the system of rationals infinite in that it has the potential to allow quantities to be indefinitely large (a property shared with the natural numbers themselves), but it also allows for an unending degree of refinement on an indefinitely small scale. There are some who are troubled with both of these aspects of the infinite. They might prefer a universe that is, on the one hand, finite in extent and, on the other, only finitely divisible, so that a fundamental discreteness might begin to emerge at the tiniest levels.

Although such a standpoint must be regarded as distinctly unconventional, it is not inherently inconsistent. Indeed, there has been a school of thought that the apparently basic physical role for the real-number system ℝ is some kind of approximation to a ‘true’ physical number system which has only a finite number of elements.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, limitlessness in the physical universe and limitlessness in mathematical systems pertain to distinct orders of experience: first-order meaning (phenomena) and second-order meaning (metaphenomena), respectively. Mathematics is meaning construed of the meaning of the physical universe, but, as different systems, limitlessness in mathematics does not logically entail limitlessness in the physical universe.