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?

Comments

[Thomas Beale]

Dear Bill,
thanks for considering the question, much wisdom here - I had not seen this taxonomy of nominalism before. We can refer to abstract entities (let's say, a particular math formula) that are not necessarily concretised in the immanent sense, without difficulty. You say that such entities 'subsist' (this seems like a good distinction). So such universals are transcendant rather than immanent, but are still perfectly good universals, are they not? After all, we don't wait around until some particular partial differential equation is concretised in reality before we can talk about it.

A (probably secondary) question philosophically is the one I originally had in mind, which was: does the existence of genotypes, designs etc (acting as they do as ontic expressions of 'type' for phenotype instances) modify any standard nominalist view of the world, and/or our understanding of classes within formal ontologies? The latter question is about distinguishing a class in an ontology for entities that have a genotype (and thus for which we might claim that a 'universal' template is directly realised in the world) versus entities that are merely classified by a collection of properties we put together in our minds. Perhaps this is no more than the difference between natural kinds and fiat classifications.

[BV]

Thomas,

Consider the proposition expressed by the sentence '7 + 5 = 12.' This proposition is an abstract object in that it is not in space, not in time, and is not causally active or passive. What do you mean by "concretised in the immanent sense"? The proposition is an abstract particular (an unrepeatable). It has various different expressions, e.g., in Roman numerals, base-2 notation, base-10, etc. But these expressions are not instances of the proposition.

Since the proposition is a particular, why do you refer to it as a universal? Universals are instantiable, particulars are not. Socrates has no instances. The property of being wise has instances, one of them being Socrates. The proposition *Socrates is wise,* is like Socrates in that it cannot be instantiated; it is like the property of being wise in that it is abstract.

By the way, I did not say that abstracta subsist; I imputed that view to you because of your distinction between being and existence.

[Michael Brazier]

What of words like "dog" and "cat"? They do not name particulars, either concrete or abstract. Moreover, the things they name are instantiated - "Fido is a dog" means that Fido is an instance of the class of dogs. If "dog" isn't a universal, what is it?

[Hector Cruickshanks]

Bill,

Would you characterise Derrida as a 'mad-dog nominalist' or do you think his conception of meaning as both endlessly deferred and lacking any ultimate authorising grounding outside the system of linguistic signs goes beyond even that? (What this 'beyond that' is or could be, I don't know - incoherent gibberish most likely).

'I hope no one is crazy enough to be a mad-dog nominalist'. As an English lit grad I can testify that that view is now practically dogma for many folks in literary studies.

[BV]

Hi Hector,

What could be worse than a mad dog?

John Searle said of Derrida that he gave bullshit a bad name.

You may enjoy this post from my first blog: http://maverickphilosopher.blogspot.com/2004/10/from-mail-what-derrida-really-meant.html

[Hector Cruickshanks]

'What could be worse than a mad dog?'

A mad frog!

Thanks, I enjoyed the post! Derrida seems to have proved for many the astonishing thesis that if you write obscurely your meaning is obscure and therefore language isn't always clear. For some reason he and his followers think that means that language is always opaque and non-referential and all writing is therefore obscure and self-contradictory. Bizarre.