Maybe the most interesting question is: how can we explain reality?
If we start by assuming that things are real (ie, nominalism, like empirical science), then we ultimately arrive to a paradox, ie, Russell’s paradox, that is, a double contradiction.
If we instead assume that kinds are real (ie, realism, like cladistics and particle physics), then we ultimate arrive to the same paradox (ie, Russell’s paradox), but this time instead rotating around the paradox trying to find the middle of it (like in the form of “the true tree of life” or “Higgs particle”, respectively).
So, which options does this leave us with? Well, it leaves us with the option of being totally consistent, as mathematics is, avoiding the paradox by simply assuming that it’s real (although it can’t be), and thus connecting nominalism to realism around the corner so-to-speak of Russell’s paradox, like axiomatic set theory does. This option does thus instead assume that Russell’s paradox is real, although a paradox is just a double contradiction and thus can’t be real, thereby avoiding contradiction totally.
So, what does this only solution say about reality? Well, it doesn’t say that Russell’s paradox is real, because it is just an axiomatic assumption, but does by analogy say that reality may be structured similarly and function in the same way as conceptualization is and does.
So, how is a thing like this (ie, reality and conceptualization) structured and how does it function? Well, it is structured as a general orthogonality, what is traditionally called a “trinity”, and functions by lacking a “steady state” (or a “middle” or “perfection”). Such a thing can thus not come to rest once it has originated. It is consistent in terms of its parts (as mathematics thus has shown), but can never come to rest (ie, stop) due to its lack of a “steady state” (or a “middle” or “perfection”).
The only solution does thus explain “things” as we see them – they are consistent in terms of their parts, but can never come to rest. The solution does thus actually explain the things that nominalism assumes are real. Understanding of a general orthogonality (or “trinity”) can further fill in the blank of understanding kinds. Whether this explanation is the explanation we search or not is difficult to say, but the mere thought that we may search a particular explanation is instead frightening. Can we in our search for an explanation of reality actually assume that we can predict what we will find? If so, then we are really stupid.
The explanation of reality that we have found so far is thus that: “things” are consistent in terms of their parts, but they can never come to rest. This explanation of reality may appear trivial, but closer to reality than that will we never come. Instead, we’re restricted to discussing what this explanation means to our lifes, that is, to mere instrumentalism.
(The tempting question is how such general orthogonalities originate, but the answer to this question is, unfortunately, uncountably infinite.)