Can I try a few steps?
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So you would agree that there is a sense in which an equation is more than merely the idea in a particular person's head? Note that I'm not suggeting weird parallel dimensions, or similar in which perfect equations float, merely that there is more to it than is contained in the head of a particular speaker. With me so far?
Everything in math is true because it is internally consistent with a set of rules we all agree to follow.
Math is necessarily the product of sentient minds because sentient minds have to come up with the rules and agree to follow the rules before you can arrive at any truth that derives from following those rules. Math is thus necessarily the product of sentient minds, and thus it is absurd to use math to prove that ideas can exist independent of sentient minds,
Nah, not so much.
Let's say a guy measures a loop of string, stretched tight into a line, and it turns out to be 30cm. Based on that, he estimates that if he cuts the loop, the resulting length of string will be 60cm.
Then they fall into a volcano. Their mind, every trace of it, is entirely destroyed.
100 years later, someone comes along, and measures the loop again. Are they still gonig to estimate the length after the loop is cut as 60cm?
Clearly yes.
The point of this is that maths is an abstraction, and using that abstraction, the universe is consistently treated. In abstract, the length of the cut loop is twice the length of the uncut loop, and there is no continuity of mind or sentience or conscious thought needed to maintain thin sat state. It's not a feature of an observing mind, because we can eliminate all such observing minds. It's not, in any sense, stored in someone's head.
30+30 is 60. It's 60 not because there is an eternal 30 floating around in space, and not because there is someone, somewhere, thinknig about 30+30=60 in order to keep the flame of it's existance alive. It's 60 because that is how mathematics handles these abstract concepts.
So from Maths to Platonic forms. Platonism is a abstract system concerned with the classification of concepts. The Platonic ideal of a horse is not floating off in space somewhere, nor is it a running thought process in someone's head. It's an abstract concept. Like mathematical concepts, it can have attributes, it can have qualities, and so on.
This idea is very troubling to certain philosophical schools of thought, which rely on relationship to the phyhsical world as the cornerstone for how they definine things. The idea of a non-physical concept with attributes is problematical to them, since only phyiscal objects should have attributes. And thus, we get people attempting to ridicule particular philsophical ideas, such as Platonis forms, so that they can remove these problems from discourse without all the bother of having to deal with them.
Now clearly, if you characterise concepts with attributes as 'things' within a 'realm of ideas' then someone could, intentionally or otherwise, misunderstand you and start going on about mystical sub-dimensions, but that would be a mis-characterisation of the original ideal.