Nominalism, Existence, and Subsistence

Here are five versions of nominalism by my current count:

Mad-Dog Nominalism: No word has an extra-linguistic referent, not even proper names such as 'Peter' and 'Paul.' 

Extreme Nominalism: The only words that have existing referents are proper names like 'Peter' and Paul'; nothing in reality corresponds to such predicates as 'blond.' And a fortiori nothing corresponds to copulae and logically connective words such as 'and' and 'or.'

Nominalism Proper: Particulars (unrepeatables) alone exist: there are no universals (repeatables). This view allows that something in reality corresponds to predicates such as 'blond' as in 'Peter is blond.' It is just that what this predicate denotes is not a universal but a particular, a trope say, or an Aristotelian accident. What I am calling nominalism proper also allows for abstract particulars where an item is abstract just in case it is non-spatio-temporal and causally inert. Mathematical sets, for example are abstract particulars. The set: {x: x is a prime number and x is less than 1o} is abstract because it has no spatiotemporal location and is causally inert. It is particular because it is unrepeatable which is equivalent to saying that it is not possibly such as to be instantiated. Sets have members — the null set aside — but no instances. (Quiz for the reader: tell me the cardinality of the set just mentioned.)

Reistic Nominalism: Attach the codicil 'There are no abstract items' to nominalism proper and the result is reistic nominalism.  On this view only particulars exist, and all particulars are concrete (non-abstract).  Franz Brentano is his later years was a reist.  See the SEP entry, Reism.

Methodological Nominalism: This is the view that we ought never assume that for each word there is a corresponding entity.

I hope no one is crazy enough to be a mad-dog nominalist, and that everyone is sane enough to be a methodological nominalist. The three middle positions, however, are subject to reasonable controversy. They are not obviously false and they are not obviously true. What I am calling extreme nominalism has little to recommend it, but I think nominalism proper is quite a reasonable position.  As it seems to me, there has to be something extra-linguistic (and extra-mental) corresponding to the predicate in 'Peter is blond,' but it is not obvious that it must be a universal.  

Thomas Beale sent me to a blog post of his that begins as follows:

Nominalism is a philosophical doctrine usually understood to entail a rejection of universals, in favour of the belief that only the concrete exists. Universals are understood as instantiable entities, i.e. something like types. Another flavour of nominalism involves rejection of abstracta, such as mathematical entities, propositions, fictional entities (including possible worlds). 

I personally think that most nominalist arguments are straightforwardly wrong, but not for the usual reasons that universals and/or abstracta are said by realists to exist, but for the opposite reason: types and abstracta are just there, even if they don’t ‘exist’, in the sense of being spatio-temporally concretised. The real problem is that we misuse the word exists at least half the time in philosophy. The way we should talk is to say things like: there are universals . . . .

So that’s why nominalists are wrong. There are universals, but they don’t exist. 

First of all, it is no misuse of 'exist/exists' to use these expressions interchangeably with 'is/are.' It is standard English to use them interchangeably. Examples: I am; I exist. God is; God exists. Island volcanoes exist; there are island volcanoes. Unicorns do not exist; unicorns are not; there exist no unicorns; there are no unicorns.  Scollay Square once existed; Scollay Square once was.  Socrates would never have come to be had his parents never met; Socrates would never have come to exist had his parents never met. And so on.

Nevertheless, we are not the slaves of ordinary language and one is free to distinguish between existence and being as Bertrand Russell did in Principles of Mathematics. 

Now if existence is the mode of being enjoyed by all and only spatiotemporal items, then abstracta and transcendent universals do not exist. (A transcendent universal is one that needn't be instantiated to be. An immanent universal is one that cannot be unless it is instantiated.) If transcendent universals are, but do not exist, then they enjoy the mode of being called subsistence. This seems to be what Mr Beale is telling us. 

Here is an interesting question. Suppose with David Armstrong that universals are immanent –ones-in-many, not ones-over many — and that first-order immanent universals are constituents of thick spatio-temporal particulars. Would not these universals be "spatio-temporally concretised" in Beale's words?  Suppose universal U is a constituent of a, b, and c — concrete existing spatiotemporal particulars — and is wholly present in each without prejudice to its unity as a universal. Would U then not be "spatio-temporally concretised" and therefore existent?

One more question. If there were a good argument for either nominalism proper and/or reistic nominalism, would  that not also be a good argument against universals and abstracta that are but do not exist?  He who fights shy of multiplying entities beyond necessity does not care whether the entities exist or subsist.

Finally, aren't there good objections to the notion that there are modes of being?