least as much being as the others. An unusual view to be sure—presumably not
Aristotle’s—but defensible.
Aristotle’s claim that some entities (relatives) are lesser beings than all others
does not imply premise 2. It is in fact logically independent of premise 2. To see that
the claim that relatives are the least of allthingsislogicallyindependentofthe
claim that beings are always comparable as beings, consider the following model.
Suppose that there is one thing that is less of a being than all others. It is consistent
with this claim that no other beings are comparable with respect to how much
being they have. On this model, the least being is the bottom point of a structure
that branches like a tree. A similar model in which there are many equally low
things occupying the bottom point (e.g., all the relatives) suffices for the same
conclusion. Conversely, suppose that everything has exactly the same amount of
beingaseverythingelse.Thenbeingsarealwayscomparableasbeingsbutnothing
has the least being of all beings. That relativesaretheleastofallthingsislogically
independent of the claim that beings are always comparable as beings. Aristotle can
consistently reject premise 2.
Suppose we deny that beings are always comparable as beings. Then we can say
something like the following. Objects and properties enjoy different ways of being.
Both you and your shadow are objects, but you are more real than your shadow.
Having -1 chargeis more real thanbeing grue. But since you enjoy a different kind of
reality thanhaving -1 charge, it is not the case that either one of you has at least as
much reality as the other.
What is the proper linguistic guise forx has at least as much being as y, if we wish
(as I do) to preserve a connection between being and quantification? The idea of a
polyadic quantifier, which informally we can take to be a single expression capable of
binding multiple free variables within an open sentence so as to yield a sentence with
no free variables, has been well studied.^26 On the view under consideration, the
fundamental existential expression would be a kind of polyadic quantifier. Although
this is not the place to develop a formal semantics for such an expression, it might be
useful to briefly see how such a device could function. Let’s have“$”be the polyadic
quantifier that has as its semantic valuex has at least as much being as y. Informally, a
sentence such as“$x,y(Fx,Gy)”could be used to say that some F has at least as much
being as some G, while a sentence like“$x,y(x=a,y=b)”could be used to say that
ahas at least as much being asb. And either ofxorymight be individuals, or
properties, or objects of any ontological type.
We have now discussed two arguments for the priority of naturalness over degrees
of being: the meta-Euthyphro argument, and the argument from modes of being.
Both arguments failed. I know of no other arguments for taking naturalness to be
more basic than the notion of a degree of being.
(^26) See, for example, Peters and Westerståhl (2006).