> tl;dr the natural world is not fungible, but behaving as if it is, is a convenient abstraction for mathematics and commerce, not a property of the natural objects.

If it wasn't a property of natural objects (in some way), then how could our predictions work so well in the real world?

What prediction is that? Are you arguing that two rocks or apples or people are actually "can't tell them part" identical?

It works for electrons. But when was the last time that you interacted knowingly with a single electron?

> What prediction is that?

For example, all the predictions that make us capable of building skyscrapers that don't fall down for centuries. Does it matter that two bricks are not "the same piece of matter" if our predictions work the same for both of them? In terms of their behavior under particular circumstances, they are the same.

" In terms of their behavior under particular circumstances" is very specific. "The maths is useful under particular circumstances" is not the same thing as "numbers are real"

Bricks are in the category of "made objects" not natural objects, which generally means that they are _designed_ to come off a production line as similar as humanly possible to the other products. "My iPhone is physically interchangeable to yours" is a statement about the huge efforts of industrial manufacturing to standardise matter, not about the natural world.

Bricks too have quality thresholds that they have to meet or exceed. That alone should tell you that treating them like integers is a convenient abstraction, nothing more. The sibling comment has it right: counting bricks is a great model, but confusing your model for reality is still an old error.

> Does it matter that two bricks are not "the same piece of matter" if our predictions work the same for both of them

No, because of a dense, interconnected web of other social truths (the rest of the arithmetic model), the relative error of this one truth/model is negligible.

However, confusing your model for reality is a fallacy perhaps older than time.

I don't understand how is "the arithmetic model" a social truth, when it clearly corresponds to physical phenomena. You can make a skyscraper that doesn't fall, and it exists regardless of whether other people see it or not. You see it - it's there. What is "social" about that?

> However, confusing your model for reality is a fallacy perhaps older than time.

I think that the human perception the world is a robust enough model to be equated with reality without issues. If you go down the path of denying perception, you might as well go full solipsism, in which case it doesn't even make sense to discuss reality at all.

We have a model of physics which is pretty accurate. The engineers who designed the skyscraper did not even use this model, they used a much simpler one, with known errors. Why? It is simply good enough™. But you can't claim it is even "true" when we know more accurate methods.

My claim is not that the model itself is true - I'm claiming that the underlying mechanisms that rule the world are true and are not subject to change by social consensus.

The model is "good enough" for the purpose of creating a building, but that doesn't make the act of "creating a building" any less real, nor the underlying rules that govern matter any less true. Our descriptions are not real - the rules themselves (which we may not know exactly) are real.

Therefore, mathematics - the set of rules that corresponds to how reality works - itself exists in reality regardless of social consensus. Society can't change them by making a different consensus.

Nothing about mathematics describes how the world works.

As far as rejecting perceptions i think going straight to solipsism is a big jump. We may live in a reality that we have no access to. Donald Hoffman's theories in this area are fun.