It has been demonstrated that humans have no easy way to universally distinguish artifacts of perception from empirically real phenomena. So I really take issue with this use of "exist". It's never that simple.
And that's before getting into categorization issues. Does Pluto "exist" as a planet? It'd be pretty non-sensical to say it stopped existing when scientific authorities changed its designation. But then was Pluto really a planet before that happened? Or was its planetary status a figment of collective imagination?
Are you suggesting that the concept of symmetry may conceivably be an artifact of perception? Though I accept the statement of your first sentence, I find this application of it extremely hard to accept.
I agree categorization is a (almost?) purely human concept. I'm not sure how that relates to my question.
Yes. This extends not just to things like symmetry but also to what we think the concepts of "space" and "time" to be. The Critique of Pure Reason is the classic work on this.[1] There Kant defines the phenomenon and the noumenon, sort of as aspects of everything that isn't us. The phenomenon is what we perceive, the noumenon is the "thing-in-itself" which lies beyond our perception. Though there's an open question if it's beyond our conception, Kant left that unanswered, which is where the ensuing debate over the nature of math comes in.
Why does this relate to your question? Because we cannot prove _anything_ not to be an artifact of our perception, nothing that we conceptualize is necessarily inherent in reality. In a strict sense, reality is unknowable to us. In a practical sense, none of this matters because math seems to work well. Still, if we wish to be undogmatic, then we should approach questions of existence or non-existence with humility and not base ontology entirely on perceptual illusions.
And that's before getting into categorization issues. Does Pluto "exist" as a planet? It'd be pretty non-sensical to say it stopped existing when scientific authorities changed its designation. But then was Pluto really a planet before that happened? Or was its planetary status a figment of collective imagination?