Complex
A complex thing or whole is a thing that has parts.
By ‘thing’ I mean the same thing as ‘Being’. I treat
the term ‘part’ or ‘is a part of’ as a primitive term.
I grasp its meaning by virtue of direct awareness of things being parts of
things (e.g., the left half of your visual field being part of your complete
visual field). When I say that something has
parts, I mean this:
(1) ‘x is a whole’ =def
‘There is a y, such that (y is a part of x)’.
Here is a slightly more complex definition:
(2)
‘x is a whole’ =def ‘for some ys, such that x
is not one of the ys, x is a mereological sum of those ys’,
where
(3) ‘x is a mereological
sum of the ys’ =def ‘for all z (if z is one of
the ys, then z is a part of x or z = x) and for
all z (if z is a part of x, then there is a
w, (w is one of the ys and there is a u ((u
is part of z or u = z) and u is part of w))’.
I include the phrase ‘x is not one of the ys’
because I do not think that “improper parts” are parts, as I understand the term ‘part’. I mean by ‘part’ the same
thing the woman on the street means by ‘part’ when she says that she ate part
of her sandwich; or when Tom says he wrote part of the story; or when Erica
says that part of her room is clean; or when Alex says he heard part of the
song; and so on. I assume that in each of these examples the term, ‘part’,
means the same thing, or that there is a general meaning in common between
them. So by ‘part’, I have in mind the most general meaning that it might have
when ordinarily used by ordinary English-speaking folk. It seems obvious to me
that as the average person would not ordinarily call a thing part of itself.
Since improper parts are parts of themselves, I don’t think improper part fits
the ordinary conception of part. I would define ‘x is an improper part of y’ to
mean ‘x is a part of y or x is identical to y’.
I believe that (1) answers what Peter van Inwagen
calls the ‘general composition question’. (1) says what it is to be a whole in
terms of primitive terms whose reference I believe we can grasp directly. This
leaves open various special composition questions. For example, we still want
to know the general mereological principles by virtue of which we can say when
any given xs form a whole. I think there are different kinds of wholes and that
the principles differ depending upon the kind of whole in question. Thus, I do
not believe that the axioms of classic, extensional mereology, for example,
come even close to giving correct principles of wholes in general. They might come somewhere close, however, to giving
correct principles of unordered wholes,
which I call ‘sets’.