Abstract Entities in Realism, Nominalism and Metalinguistic Nominalism
In his work“On What Is”, W.V Quineexamines argumentsrelating to the existence of
abstract entities from both realist and nominalist view points. Quine concludes this investigation
by defining the fundamental ontological commitments which differentiate realists from
nominalists. This paper will outline how realists are committed to the existence of abstract
entities and how nominalists are able to refute their existence. Additionally, this paper will
include a brief explanation of a metalinguistic nominalist approach towards the existence of
abstract entities, specifically through an examination ofSellars’ arguments regarding the
structure of language and how abstract entities cannot exist within it.
A central question in metaphysics is ‘what exists’? A more apt question would be: ‘what
things do we determine as having being/existence’? We can assume that we agree upon the
existence of physical objects (particulars) but what about properties, relations, fictional beings or
possibilities? These are abstract entities. Abstract entities as linguistic elements are the cause of
the fundamental disagreement between Realism and Nominalism.
Quine asserts that what creates this fundamental disagreement between Realism and
Nominalism are the ontological commitments that each viewpoint holds (Quine, 2011, p.9). To
find what each ontology commits to, Quine focuses on their use of quantifiers and bound
variables, as well as the value of said variables. The domain of quantification establishes the
scope over which statements hold true. This domain is denoted with quantifiers like “all”,
“some”, “none” etc. Bound variables are bound by these quantifiers. Let us illustrate this using
logical notation. A realist ontology would hold that: ∀𝑎(𝑃( 𝑎)). Where𝑎is a variable for a given
entity,𝑃( 𝑎) is the predicate that asserts the existence of𝑎, and the universal quantifier ∀ asserts
that the predicate𝑃( 𝑎)ranges overallelements within the domain of quantification. This can be
translated to, “for all𝑎,𝑃( 𝑎) is true.” Thissuggests that the properties described by the predicate
are not limited to particular instances, but are universal and apply across the entire domain. A
nominalist ontology would hold that∃𝑎(𝑃( 𝑎) ).𝑎and𝑃( 𝑎) represent the same things as they do
in the previous equation. The existential quantifier∃asserts that the predicate𝑃( 𝑎) indicates that
there is at least one entity (𝑎) within the domainof quantification that satisfies the predicate
𝑃( 𝑎). This can be translated to, “there existssuch an𝑎such that𝑃( 𝑎) is true.” This assertsthe
existence of onlyspecificentities that relate toa given predicate. What differentiates these two
types of statements are the variables that the domains of quantification are allowed to range over
(p.9).
To analyze this, for a realist,𝑃( 𝑎) is true forall𝑎’s. Therefore, the value of𝑎must be a
universal (property, relation, etc.) for the statement to be true. For a nominalist𝑃( 𝑎) is true for at
least one𝑎in the domain. Here, the domain of quantificationonly encompasses concrete,
particular entities. To conclude, realists are ontologically committed to the existence of abstract
entities because they accept that all entities are bound by predicates that apply universally.
Nominalists are not ontologically committed to the existence of abstract entities because they
accept that variables are bound by predicates in specific, separate instances. Ultimately, realists
claim that non-linguistic, abstract entities exist, whereas nominalists claim that words that seem
like abstract entities are simply linguistic features that allow us to classify particulars into kinds
and categories.
Metalinguistic nominalism and nominalism are both motivated by the same core
ontology: the only objects that exist are particulars and predicates are linguistic features that exist
to categorize such particulars (Loux, 2004, p.62). Metalinguistic nominalism challenges
nominalism’s claim that abstract entities are merely convenient labels and posits that they play a
fundamental role in language and thought. Wilfred Sellars, a prominent metalinguistic
nominalist, in his work “Naming and Saying”, develops his theory through an analysis of the
Tractatus Logico-Philosophicus by Ludwig Wittgenstein. In this work, Wittgenstein attempts to
develop a perfect logical structure of language (as Sellars describes it a perspicuous language.) It
should be noted that, ultimately, Wittgenstein dismisses the theories he sets forth in the Tractatus
as nonsense. However, Sellars interprets the Tractatus through a traditional lens in which
Wittgenstein’s structure of object language is able to be applied to metaphysics.
To provide some context, Wittgenstein states that the fundamental building blocks of the
world are atomic facts and these atomic facts are what make up objects. Objects are entities that
exist in the world (particulars) and names are words that are given to these objects. Objects and
names are then configured in a way such that one can make statements about the state of affairs
in the world (ex.“The apple is green.”) The following will focus on Sellars’ interpretation of
Wittgenstein’s objects and how they relate to the function of abstract entities in language.
To illustrate, let us use the statement, “the apple is on the tree”, as an example. This could
be written as “𝑎𝑅𝑏” or “𝑎stands in a certainrelation to𝑏such that𝑎𝑅𝑏” (Sellars, 2007, p.104).
Sellars posits that this could be written even more clearly. In a perspicuous language, you would
not need a third expression,𝑅, to represent that𝑎and𝑏are related to one another. This would
look like “ab”. The configuration of these variables(names) can signify that they are related to
one another without adding another expression. Similarly, properties of these names could be
signified using a different style or thickness of font. For example, “a” could signify that “a is
green.” In the perspicuous language that Sellars is outlining here, relational words (abstract
entities) are not translatable, they are ineffable (p.109). Abstract entities in this perspicuous
language are the manner in which names are combined, not names themselves. So for
Wittgenstein and, therefore, Sellars, abstract entities (universals) are fundamental, ineffable
features of language, not universal features of the world. This ontology allows one to make
statements using words that seemingly refer to an abstract entity without accepting the existence
of such abstract entities.
Taking all this into account, can we answer the question, “what is?” No, we cannot
concretely answer this question. Abstract entities remain a central question in metaphysics. This
is where Quine’s ontological test comes in. Although one cannot positively say what is, one can
concretely define ontologies that attempt to answer this question.
