It helps to differentiate between “real” and “existant”. Mathematics is as real as the laws of logic—neither, however, exists.
What is “real” is that which proscriptively constraints that which exists. That which exists is that which interacts directly with other phenomena which also exist (that also interact).
When we say “2+3=5” what we are doing is engaging in the definition of real patterns of that which exists. So while, yes, the patterns themselves are external to us; the terms we assign them are subjective. In mathematics we ‘understand’ what happens when you add 2 and 3 together. But these are just symbols; just representations by which we predict outcomes based upon our understanding of those constraining patterns. In other words; we define 0 as none of a thing, and 1 as a single thing. We therefore define 2 as 1+1, 3 as 1+1+1, etc., etc.. (The dots).
However, if we were to encounter a person who defined 6 as 1+1+1+1+1, and we were to continue definining 1+1+1+1+1 as five, then neither would agree with one another, and both would be correct. This is, given the understanding involved of the difference between “real” and “existent”, neither exceptional nor inscrutable. It’s a trick of definition—much as is the Law of Identity and the Law of the Excluded Middle. (That which I define as “only-A” cannot ever simultaneously be “not-A”.)
I have often stated that, as a physicalist, the mere fact that something does not independently exist—that is, it has no physically discrete existence—does not mean it isn’t real. The number three is real—but does not exist. It cannot be touched, sensed, or measured; yet if there are three rocks there really are three rocks. I define “real” as “a pattern that proscriptively constrains that which exists”. A human mind is real; but there is no single part of your physical body you can point to and say, “this is your mind”. You are the pattern that your physical components conform to.
It seems very often that objections to reductionism are founded in a problem of scale: the inability to recognize that things which are real from one perspective remain real at that perspective even if we consider a different scale.
It would seem, to me, that “eliminativism” is essentially a redux of this quandary but in terms of patterns of thought rather than discrete material. It’s still a case of missing the forest for the trees.