The Timeless Existence Of Mathematical Forms Viewed Through Systemic Functional Linguistics

Penrose (2004: 17):

I am aware that there will still be many readers who find difficulty with assigning any kind of actual existence to mathematical structures. Let me make the request of such readers that they merely broaden their notion of what the term ‘existence’ can mean to them. The mathematical forms of Plato’s world clearly do not have the same kind of existence as do ordinary physical objects such as tables and chairs. They do not have spatial locations; nor do they exist in time. Objective mathematical notions must be thought of as timeless entities and are not to be regarded as being conjured into existence at the moment that they are first humanly perceived. 

The particular swirls of the Mandelbrot set … did not attain their existence at the moment that they were first seen on a computer screen or printout. Nor did they come about when the general idea behind the Mandelbrot set was first humanly put forth — not actually first by Mandelbrot, as it happened, but by R. Brooks and J. P. Matelski, in 1981, or perhaps earlier. For certainly neither Brooks nor Matelski, nor initially even Mandelbrot himself, had any real conception of the elaborate detailed designs …. Those designs were already ‘in existence’ since the beginning of time, in the potential timeless sense that they would necessarily be revealed precisely in the form that we perceive them today, no matter at what time or in what location some perceiving being might have chosen to examine them.

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From the perspective of Systemic Functional Linguistic Theory, the existence of 'objective mathematical notions/structures/forms' outside spacetime is their existence as potential meanings of mathematics. Instances of that potential are located in spacetime: the spacetime of the mental or verbal process through which that potential is actualised.

To be clear, logically, 'objective mathematical notions/structures/forms' cannot have existed, as potential, until mathematical systems of meaning existed, and that coming into existence occurred in spacetime.