Regarding Nominalism, are you happy to say that ‘abstract entities’ such as ‘numbers’ exist but that they are not objects? — I like sushi
On my view, all abstracts, all abstraction is only a (particular, physical) mental event. It's a way that we think about things, about relations, etc. So this includes numbers.
From my understanding of nominalism many would hold that a ‘chair,’ ‘banana’ or other such ‘concrete entity’ doesn’t exist, but that ‘numbers’ - as ‘abstract entities’ - do exist (just not as ‘objects’). — I like sushi
It's primarily a position on universals. The idea is that there's not a "chair" universal (or a "round" universal, or a "red" universal, or anything like that), which isn't identical to any particular chair (or roundness or redness), that's then somehow instantiated in various particular chairs (or round or red things). Most nominalists don't buy realism (extramentalism or objectivity) for abstracts in general--whatever you want to call them, abstract objects, abstract entities, etc.
The confusion and misapplication of terms seems to me to be the main purpose of the nominalistic approach to discussion. — I like sushi
The gist of it isn't that it's an "approach to discussion." It's ontology. It's a stance about what sorts of things there are in the world.
Re "object" and "entity" I'm not using them in some technical manner. I use them as synonyms for a <whatever you want to call it> that exists, or subsists, or occurs, or is instantiated, or whatever you want to call
that, in any manner whatsoever.
Re "real," it's traditionally used in these discussions to refer to something existing (or subsisting, or again any word you want to use like that) "outside of" mentality. So if you think that x is real, or if you're a realist on x, that implies that you believe that x occurs apart from the mental.
"Concrete" is used for particulars--single things that are some specific way ("thing" is not being used technically there). "Concrete" usually has the additional connotations of being physical, in spacetime, etc.
"Abstract" is in contradistinction to "concrete." Abstracts are usually thought to have no physical referent, no referent in spacetime, and/or they are not particular things (again, "thing" there is just a nontechnical "<whatever it is>"); they rather arch over many particulars--for example, as universals. On my view, and on the view of "conceptualist" nominalists in general, abstracts, or the act (or event) of abstraction, is a mental phenomenon (and actually concrete, particular as such) whereby we formulate a concept that arches over many particulars by focusing on some more or less similar feature in a number of particulars (which can include particular relations) while ignoring other details and more fine-grained differences.