Platonic Existence As The Objectivity Of Mathematical Truth — Viewed Through Systemic Functional Linguistics

Penrose (2004: 13):

It may be helpful if I put the case for the actual existence of the Platonic world in a different form. What I mean by this ‘existence’ is really just the objectivity of mathematical truth. Platonic existence, as I see it, refers to the existence of an objective external standard that is not dependent upon our individual opinions nor upon our particular culture. Such ‘existence’ could also refer to things other than mathematics, such as to morality or aesthetics, but I am here concerned just with mathematical objectivity, which seems to be a much clearer issue.

Blogger Comments:

To be clear:

In its most basic fundamentals, platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness

Clearly, the mere objectivity of mathematics does not logically entail the existence of a world that is distinct from both 'the sensible external world' and 'the internal world of consciousness'.

From the perspective of Systemic Functional Linguistic Theory, 'the sensible external world' is the construal of experience as material and relational processes, and 'the internal world of consciousness' is the construal of experience as mental and verbal processes. As a semiotic system, mathematics is the content of consciousness that is projected by mental and verbal processes. Mathematical objectivity simply refers to the internal consistency of a semiotic system that is concerned with relations between quantities.