To finish, Kory, I would avoid the term "essentialist" giving that its modern philosophical use is more precise than our admittedly rather imprecise use of it.
I see what you mean, but we need *some* way of referring to specific (although perhaps imprecise) ideas or beliefs. I might feel comfortable defining "Platonic essentialism" as the belief that there exists a world of essences in which (say) the Ideal Horse exists, and all physical horses are imperfect copies of it, because I don't think this group already has multiple conflicting definitions of the term "Platonic essentialism".
However, this group definitely does have multiple conflicting definitions of the generic term "Platonism", and people usually just assume their own definition when they hear the term. So someone asks someone else if they're a Platonist, and that person ends up answering a totally different question. Hi-larity ensues!
Kory, I am not pretending that your are "jargoning" but I would like to avoid the risk of pointing to the essentialist debate too early
I agree, and in fact, avoiding the essentialist debate is exactly what I'm trying to do. My point is that every time we use the term "Plantonism" simply to refer to "arithmetical realism", we run the risk of starting an essentialist debate (or a constructivist debate) that we didn't intend, because for many other people "Platonism" implies essentialism, or non-constructivism.