Apples and mathematical sets both exist. Both are real. Both have substance, both mean something, both have effects on other things. Both are something delimited and which is not something else.
I see from you only the typical bullshit materialist arguments; rather than acknowledge that mathematical sets exist, because it’s crazy to say they don’t since we can actually talk about them and use them and know what they are, just try to turn the tables and make the other person explain their fundamental ontological categories. It’s deceptive.
Your standard is “dur I can like see it and pick it up so that’s what ‘exists’ means”, that’s fucking retarded, pardon my French. Things exist if they exist, its truistic. Whatever happens to be the case is the case. Ideas exist, as ideas. Apples exist as apples, numbers exist as numbers. Would be nice to develop a comprehensive ontoepistemological system of categorization to relate the how/why of all those sort of things to each other, but philosophy is too stupid for that. It’s still trying to think backwards, from “do maths exist?” as if that were a legitimate premise. You can’t think backwards from false questions, you have to think forward from true questions and build from there. Anything else is cart before the horse metaphysical bullshit and has nothing to do with philosophy.
Proper philosophy proceeds from a real and certain question and creates step by step explanations that build on and up from there. What is a mathematical set? A group of numbers, or a group of things other than numbers. What are numbers? Quantities. What is quantity? The fact that there can be one or more of something. What is “the fact that there can be one or more of something”? A basic logical fact, deriving from the fact that everything isn’t all one thing; deriving from the fact that differentiation exists and relation is possible. The basic facts of differentiation and relation lead to the further fact of quantity. But how to understand quantity in terms of sameness or difference between things quantified?
This is because we can always scale up our consideration and understanding to a point where similarities are understood to exist between even very disparate things. We derive this understanding of sameness from the fact that such sameness is the case in fact. An apple and an orange look, taste, feel, smell and sound different, but we nonetheless understand there is a sameness between them and thus we understand what it means to quantify an apple and an orange as “two of something”. This is so basic I shouldn’t even need to lay it out, but apparently I do. So that same operation is taken to further levels and you are able to generate sameness between even more disparate things, like apples and mathematical sets.
Why am I the only one doing any of this fucking work? You pretend to be a philosopher and I don’t see any evidence that you are. Empty materialism and evasive simplistic questions meant to shift the onus on the other person and put them on the defensive by framing issues in obfuscating ways is not… philosophy. Asking “do they exist in the same way” is not at all touching on the basic point I made, that they both exist.
You are choosing to ignore this, and shifting the goalposts to “how” or “in what way” do they exist. We aren’t even there yet, that would take a fuck lot more work of the kind I just exampled briefly above, but I’m not going to sit here and do it for you. I don’t think for other people, fuck that.
Both apples and mathematical sets exist, that is a fact. You can acknowledge this as either true or false if you have any interest in being honest. And then only after we get to an agreement on that issue can we begin to do some phenomenological, ontological and epistemological investigations to try and get to some of the how/why/what does it mean.