The Platonic World As The Most Primitive Viewed Through Systemic Functional Linguistics

Penrose (2004: 1029):

But are mathematical notions things that really inhabit a ‘world’ of their own? If so, we seem to have found our ultimate reality to have its home within that entirely abstract world. Some people have difficulties with accepting Plato’s mathematical world as being in any sense ‘real’, and would gain no comfort from a view that physical reality itself is constructed merely from abstract notions. 

My own position on this matter is that we should certainly take Plato’s world as providing a kind of ‘reality’ to mathematical notions (and I tried to argue forcefully for this case in §1.3), but I might baulk at actually attempting to identify physical reality within the abstract reality of Plato’s world. I think that Fig. 34.1 best expresses my position on this question, where each of three worlds — Platonic-mathematical, physical, and mental — has its own kind of reality, and where each is (deeply and mysteriously) founded in the one that precedes it (the worlds being taken cyclicly). 

I like to think that, in a sense, the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very self into existence through logic alone. Be that as it may, there is the further mystery, or paradox, of the cyclic aspect of these worlds, where each seems to be able to encompass the succeeding one in its entirety, while itself seeming to depend only upon a small part of its predecessor.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'reality' is meaning construed of experience, so the meanings of mathematics are mathematical 'reality', which does not logically entail an 'ultimate reality'.

In this view, physical reality is not constructed from abstract notions, but the the reverse: the abstract notions of mathematics are intellectually constructed from physical reality. That is, first-order physical reality, construed of experience, is reconstrued, by conscious (mental) processing, as the second-order reality of mathematics.

In this view, then, the relation between the three realities is not cyclic, and mathematical reality is the least 'primitive', since it depends first on conscious processes, then on these construing experience as physical reality, and then on these reconstruing physical reality as mathematical reality.