Physical Vs Geometrical Objects Viewed Through Systemic Functional Linguistics

 Penrose (2004: 58):

A physical object such as a square drawn in the sand or a cube hewn from marble might have been regarded by the ancient Greeks as a reasonable or sometimes an excellent approximation to the Platonic geometrical ideal. Yet any such object would nevertheless provide a mere approximation. 

Lying behind such approximations to the Platonic forms — so it would have appeared — would be space itself: an entity of such abstract or notional existence that it could well have been regarded as a direct realisation of a Platonic reality. 

The measure of distance in this ideal geometry would be something to ascertain; accordingly, it would be appropriate to try to extract this ideal notion of real number from a geometry of a Euclidean space that was assumed to be given.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a square drawn in the sand or a cube hewn from marble in physical space is phenomenal, whereas a geometrical square or cube in Euclidean space ('Platonic ideal') is metaphenomenal. Phenomena are first-order meanings construed of experience, whereas metaphenomena, such as the notion of real number, are second-order meanings construed of first-order meanings.

Importantly, the metaphenomenal (Platonic geometrical ideal) also differs from the phenomenal in being a construal only of the numerical relations of the physical object: the relative lengths of its sides, the relative angles of intersecting sides or planes, etc.