Despite the scientific credibility of the claim that all that exists of the world is what we can perceive, we remain unsatisfied. There is an irresistible sense of an independent world made of solid things that truly exist, obey physical laws, and have integral properties that are reflected in our sensations. To deny their existence seems like folly.
Furthermore, to deny we can know anything more about them than our perceptual apparatus permits — that they are forever immune to being known 'in themselves' — seems to ignore the vast progress made by science in recent centuries in probing, understanding and controlling natural phenomena at ever deeper levels. Our abstract descriptions of the world (e.g. e=mc2) are empirically verifiable, which suggests that they way we represent reality in our minds is an accurate depiction of how it really is 'out there', and we continue to find out ever more about the brain, the sub-atomic world, the cosmos, which we can investigate at levels of resolution barely imaginable to those working in, say, the 18th century.
Does all this not mean we are digging behind perceptual appearances into the hidden realm of the 'things-in-themselves', the obscure levels of reality we may not be able to sense with our own apparatus, but which we can divine through powerful calculations or sophisticated measuring devices? Does this not show these things exist in a world of their own, whether we perceive them or not?
What is disputed is not that any of these objects exist, but that they do not exist in the way they are apparent to us without our particular mental processes.
Mind precedes existence.