The Existence Of The Platonic World Of Mathematical Forms Viewed Through Systemic Functional Linguistics

Penrose (2004: 12):

This was an extraordinary idea for its time, and it has turned out to be a very powerful one. But does the Platonic mathematical world actually exist, in any meaningful sense? Many people, including philosophers, might regard such a ‘world’ as a complete fiction — a product merely of our unrestrained imaginations. Yet the Platonic viewpoint is indeed an immensely valuable one. It tells us to be careful to distinguish the precise mathematical entities from the approximations that we see around us in the world of physical things. Moreover, it provides us with the blueprint according to which modern science has proceeded ever since. Scientists will put forward models of the world — or, rather, of certain aspects of the world — and these models may be tested against previous observation and against the results of carefully designed experiment. The models are deemed to be appropriate if they survive such rigorous examination and if, in addition, they are internally consistent structures. The important point about these models, for our present discussion, is that they are basically purely abstract mathematical models. The very question of the internal consistency of a scientific model, in particular, is one that requires that the model be precisely specified. The required precision demands that the model be a mathematical one, for otherwise one cannot be sure that these questions have well-defined answers. 

If the model itself is to be assigned any kind of ‘existence’, then this existence is located within the Platonic world of mathematical forms.

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To be clear, the notion and value of a 'purely mathematical model' does not logically entail that they exist in a Platonic world. From the perspective of Systemic Functional Linguistic Theory, the existence of mathematical models is within the semiotic order, whereas the existence of 'the world of physical things' is within the material order. Mathematical models exist as metaphenomenal (second-order) meaning, whereas physical things exist as phenomenal (first-order) meaning. Mathematical models are reconstruals of things — or more precisely: of processes, participants and circumstances — in terms of quantification.