You used an example like Newton's law.

It may be viewed as a formula expressing a *causal connection* between "natural" facts : *force* (acting on bodies) and *acceleration* (change of velocity, that is - according to Newton - change of "status").

But, with the development of physical theory, it can be viewed as a *theorem* proved from "axioms" or more general principles of physical theory.

In the first case, it is difficul how to relate to Plato's conceptions. It can be viewed (as Hume do) as an "empirical generalization" that cab be inductively supported but that - in principle - can be confuted with the progress of knowledge and with the aid of new experiments.

In the second case, it can be treated like a mathematical theorem : from arithmetics, like Pythagorean theorem or one of the theorem of Euclidean geometry.

A new comment : arithmetics for Pythagora and ancient Greeks were very very different from ours. Numbers were only natural numbers, what we use for counting, and the discovery of *irrationals* (square root of 2 = lenght of the diagonal of the square with side 1) forced them to develop axiomatic geometry including a general theory of *ratios* of magnitudes, where magnitudes were not (for Greeks) numbers.

So, the issue is about the relation of a theorem of mathematics (in axiomatic form) to natural facts : e.g. the parallel axiom is "applicable" to our physical space ?

This is the point where Plato fits : the realtion between "ideal" concepts and truths to the "natural" (empirical) facts and experiences.

The *form* of the circle is an ideal (but a real existing one) to which physical circles must be "compared" : they incarnate it, they are copy of it, they ...

The usual metaphor is with a chair : all physical chairs are different, but they share a common form (but which : four legs ? the function of being used to sit on them ? what is the abstract "chairness" ?); or with moral and esthetical concepts: the Good or the Beatiful.

Going back to geometry, the physical straight lines (a stick) are copies of the ideal platonic line: but a stick is not without thickness, it is not perectly straight, ...

We can adopt a "moderate" platonic attitude, like the one you can find in Galileo: yes, the language of nature is mathematical, and if we found an iron ball that is not "perfectly" spherical, the problem is not that it "incarnate" the sphericity in an imperfect way: a sphere is a sphere. If it is not perfect, it is only due to the fact that its shape has a geometrical shape that is different: a shape more complicated, that needs a more complex "equation" to be described.

A sphere in the natural world is a sphere as a perfect one ... if there is one. Otherwise is not a sphere at all, but only a more complex geometrical shpe.

So we use approximations, and our calculations works well.

So, what is the conclusion ?

Palto is still worth to be read for a lot of reason; Plato's conception of a realm of "pure", "abstract" existing thing (but immaterial) is still appealing in some field, like philosophy of mathematics, but to say that a physical law is a platonic form, without other clarifications, it semmes to me of little usage for a correct understanding of a deep and complex issue like the nature of scientific laws and the applicability of mathematics to the natural world.