1. Parts

The partition of a thing and the parts of that thing entail one another.

This book begins with everything, and then introduces a partition (or division). This partition entails the creation of at least two other things, each of which is a part. Parts constitute everything, are potentially collections of smaller things, and are of course things in and of themselves. The part structure of things can be represented as an upside-down tree: a single trunk at the top represents everything, or at least everything in the domain of discourse. This tree can be described using the terminology of a family tree: the parent thing gives rise to (and is depicted above) the child things, which are siblings of one another.[12]

Often, something is described in terms of its constituents, the somethings of which it is composed. For example, sets are often defined as collections of elements; cars are often described in terms of their engines, wheels, and so forth. In this book, this bias is countered by emphasizing that things are parts of a larger whole, thereby emphasizing the relationship of a part and its complement. These two descriptions are not incompatible, but they are certainly different; they emphasize different points of view. How a thing is initially defined often emphasizes what is most important about that thing, or at least what about it is most salient. It is also indicative of which concepts arose first in the conceptual universe. The first concepts are often used as the edifice of subsequent concepts, and are essential to the archeology of our conceptual landscape.

The holistic tendency to explain things in terms of their relation to everything contrasts with the reductionistic tendency to explain things in terms of their relation to their smaller constituents. The holistic point of view emphasizes that something is always a part of something larger, with only one exception: everything, which is the singular starting point for all part hierarchies. This everything cannot be explained by holistic theories, just as atoms cannot be explained by reductionistic theories. Despite this holistic emphasis adopted here, it is probably not possible to divide an undifferentiated whole into two parts if there is not some difference within its constitutive “stuff” . Therefore, the creation of something is collectivizing as well as dichotomizing.

As the epigraph of this section states, “The partition of a thing and the parts of that thing entail one another” . This implies both that a partition implies parts and that a part implies a partition. The later fact tends to be overlooked by a reductionistic description of the part: for example, we may describe some part of a thing, but neglect the effect of that description on the counterpart of the described thing. In other words, the fact that two things are created by dividing the larger whole sometimes goes unnoticed, despite the fact that it has a number of logical consequences. One way to ameliorate this issue might be to ask “which boundaries really exist?” instead of “which things really exist?” . Although it is a bit of a chicken-and-egg situation, perhaps it is useful to conceive of the division between parts coming before the identification of the parts themselves: the boundary between objects creates the objects.

The following picture illustrates, by means of a dotted line, the things which are implied whenever we talk about “something” (i.e. that something is almost always a part of something larger). This larger thing serves as a context in which something should be understood: the role played by this larger whole is analogous to the domain of discourse [ Boole ]. As it is larger than the thing under consideration, another thing (the copart of the original part) is also implied.

The creation of a partition also implies the creation of a dimension, which is simply an axis along which divisions are possible. In the simple case of a dichotomy, the dimension allows the parent thing to be divided into two children. For example, if an apple can be divided into a stem and a fruit, then this dichotomy implies a dimension along which these parts are divided (although in this case, the dimension is neither linear, nor associated with a well-known name).[13]

Clearly, some divisions have a greater pragmatic value than others; if we are hungry, it makes more sense to identify apples as opposed to red things. However, apart from this pragmatic valuation, are there any qualities of the objects to which we refer that make them more highly qualified as objects, as opposed to other possible objects? In other words, is there any reason to (necessarily) decompose the universe in one way as opposed to another? Although the answer to this question necessarily remains speculative, it seems that everything has the capacity to be divided in numerous different ways (at least conceptually). The basis of this partitioning is a central topic of this book.

To summarize, here is a brief list of the characteristics of somethings (parts) that will be investigated in further detail:

[12] It is a rather modern family, in which no child has more than one parent.

[13] Dimensions tend to characterize certain perspectives. Objects may be obtained by partitioning and recombining a whole in numerous different ways, so the selection of a particular partitioning strategy is generally motivated by a particular desire or perspective. Analogously, the parts into which a thing is decomposed are those parts that are relevant to the analysis which is being carried out. If you are hungry, you will look for food objects; if your only tool is a hammer, you will partition reality in virtue of its resemblance to nails.

[14] Whether one labels parts or not is a pragmatic decision. For a proper partition of an entity, at least two parts are created (both the part and the complement of that part are nonempty), and either or both parts may be named. If only one part is named, then the complement is denoted as the negation of the named part.

[15] In other words, even if the separation of a thing into parts creates only connected entities, the collection of certain of these separated parts into a larger thing may create a thing which is not (topologically) connected.