is either a maximally natural sense of“some”or it is not. If it is a maximally natural
sense, then properties exist to the maximal degree. If it is not, then properties exist to
at least the extent that this sense of“some”is natural. Either way, properties exist
to some degree or other.^11
Could it be that the quantifier employed in the sentence“something is a property”
ismaximally unnatural? Let’s provisionally identify being maximally unnatural with
being natural to degree zero, and let’s provisionally assume that there might be some
properties or relations that are natural to degree zero. An entity that fallsonlywithin
the range of amaximallyunnatural quantifier is an entity that exists to zero degrees.
Perhaps the claim that properties exist to degree zero is a version of extreme
nominalism worth considering.
Unfortunately for the extreme nominalist, even if the quantifier in question is
highlyunnatural, it is notmaximallyunnatural. With respect to the naturalness scale,
there are possible semantically primitive quantifiers that score far worse. Consider,
for example, a semantically primitive quantifier that ranges over everything ranged
over by the ordinary English quantifier except for pinkyfingers, things with exactly
seven proper parts, and the property of being a bachelor. The ordinary English
quantifier, which ranges over properties, is doing better on the naturalness scale
than that one! So there is at least one quantifier that ranges over properties that is not
maximally unnatural, i.e., that is natural to a degree greater than 0. Since there is at
least one possible quantifier ranging over properties whose naturalness is greater
than 0, properties exist to a greater than 0 degree.
Extreme nominalism cannot be sustained. If the analysis of naturalness in terms of
degrees of being ineliminably presupposes that extreme nominalism is false, then so
be it. Good analyses are allowed to assume that false theories are false.
Moderate nominalism, on the other hand, is not obviously unsustainable. How-
ever, the analysis offered here doesnotpresuppose the falsity of moderate nominal-
ism. Recall the analysis of naturalness in terms of degrees of being: property P ismore
natural thanproperty Q = df. P is more real than Q; property P is natural to degree
n= df. the degree to which P exists isn. Neither part of the analysis ineliminably
presupposes that any property exists to a maximal degree. A perfectly natural
property is a property such that no otherpropertyis more real than it. Maybe there
are other entities than properties that are more real than even the perfectly natural
properties.
LetPlatonismbe the view that some properties are more real than any individual;
letnon-reductive realismbe the view that some individuals and some properties are
such that nothing else is more real than they are. Letotherismbe the view that there
are some entities that are more real than any property or individual. Platonism, non-
reductive realism, and otherism are the main competitors to moderate nominalism.
(^11) To be clear, I am not committing myself to the claim that“some”does have these two senses, but
rather merely noting that even if it does, this does not help the extreme nominalist.