Dear George,
I hope you don't mind, but I don't agree with Platonism for the following 3 reasons: 1) Platonism seems to imply that the power to bestow rules exists outside the universe, with the Platonic realm being like a puppeteer, and the universe being like a poor puppet. 2) Platonism seems to hypothesise that all rules must abstractly exist, rather than hypothesising that what exists is the raw material to make rules (where the raw material is an inherent ability to create rules/categories; rules being equivalent to categories because a category is like an equation re-arranged so that the category is on one side of the equal sign). 3) Platonism is seemingly uneconomical about numbers as well: it seems to hypothesise that all numbers must abstractly exist, rather than hypothesising that what exists is the raw material to make numbers. Surely numbers, even numbers like pi, must ultimately derive from the fact that with some rules/relationships, you can cancel the numerator and denominator categories, and end up with a number: a thing without a category. I'm contending that numbers are essentially due to relationships, rather than being like little rocks. (I also contend that the set theory view of numbers is too unlike the equation-like structure of law-of-nature rules, for numbers-as-sets to exist at the level of fundamental-level reality.)
In any case, I think the hypothesis that what exists is the raw materials with which to make new rules/categories and numbers, is no more fantastical than the hypothesis that what exists is an (uneconomical!) Platonic realm of every possible rule and number.
I hope you don't mind if I say that Platonic realms seem to be all about deterministic mechanisms and a universe that has no control over the functions bestowed upon it by the realm; complex systems are all about deterministic mechanisms and the illusion that new function could evolve purely from the mechanism; but actual reality is both mechanism and continually creative of the truly new:
Les Poules à Colin perform live on the radio this very morning: http://mpegmedia.abc.net.au/rn/podcast/2017/02/bst_20170224_0848.mp3 (song starts at 2:56 of 7:43), http://www.abc.net.au/radionational/programs/breakfast/les-poules-%C3%A0-colin-perform-live-in-the-studio/8299720 .
Also on the radio this morning: Bees are smarter than we give them credit for - "They may have tiny brains, but it turns out that bumblebees can not only learn to use tools by observing others, they can improvise and make the task even easier", http://www.abc.net.au/news/2017-02-24/smart-bees-learn-how-to-use-tools-by-watching-others/8297576 .