Carlo Rovelli against Mathematical Platonism I disagree with him entirely-
The problem, though, is that this world is essentially full of junk. The vast majority of it is simply useless, and of no interest to anyone whatsoever. — Streetlight
There is no junk, there is only mathematical truth. An example is chess: Chess is a concept built on a few simple ideas and rules. Once these ideas exist chess exists, potentially, in its entirety. But this entirety contains good chess and 'bad' chess. All possible games of chess from genius to silliness. They exist because chess as a concept exists. If math exists all math exists
potentially. Is there a difference between an actual Platonic realm (containing good math) and a potential Platonic realm (containing 'junk')?
the idea of natural numbers (1, 2, 3...). Rovelli basically asks: why does anyone think natural numbers are natural at all? We certainly find it useful to count solidly individuated items, but he notes that what what actually counts as 'an object' is a very slippery affair: "How many clouds are there in the sky? How many mountains in the Alps? How many coves along the coast of England?". — Streetlight
Very woolly thinking here. Numbers exist as an abstraction, there is no need to have 2 or 3 actual things to have numbers:
/ = 1
// = 2
/// = 3 etc.
If all mathematics exists then it is natural for our experience to awaken (induction) particular aspects of mathematics. eg. If there are sheep their multiplicity might awaken numbers in our intuition. If we lived without a need for numbers their existence might not have been awakened by our experience. But numbers would exist anyhow.
As for the Platonic realm - does it mean that the number 3 exists in some concrete reality
or does it mean that in the depths of mathematical reality there is a potential for '3' to exist - depending on what events bring it into existence? That is, is there a mathematical potential, above our specific forms of math, that makes these forms of math possible? If we say mathematics 'exists' we have to be very clear on what we mean by 'exist'.
The concept of chess can exist without a single game of chess being played in 'real' terms. In this situation, does chess exist if it exists as a concept but no games are ever played? What is the difference between a game of chess that is played and one that is merely possible, because the concept of chess exists? I think the Platonic realm does exist in the sense that it makes all kinds of math possible but not necessarily realized. I don't think he is getting very far by making a distinction between math that we have become aware of and math that might have been if the world had been different.
Maybe the Platonic realm is God's Mind, which contains all
possible forms of math in the way the rules of chess makes all chess games possible.