Introduction

Peter van Inwagen first formulated the Doctrine of Arbitrary Undetached Parts (DAUP). Here is his presentation of that thesis:

For every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t.

DAUP says that if some arbitrary region of space sub-R is a part of the region occupied by an object, then there is another object that exactly occupies sub-R. To make this more clear, consider an example: call the region occupied by my left hand 'Left'. Left is a part of the region I occupy. So, according to DAUP, there is an object that exactly fills Left.

DAUP is an odd thesis in that its name tells us the thesis is a doctrine about parts, but no synonym of 'part' appears in the thesis. Why think it is a thesis about parts at all?

[This part added]

Three reasons:

  1. First reason.
  2. Second reason.
  3. Third reason.

[End addition]

Consider this definition of part:

Part as Overlap (PAO)
"[O]ne thing is part of another if and only if whatever overlaps the former also overlaps the latter." (Goodman 1951, 44)1

References

Goodman, Nelson. 1951. The Structure of Appearance. Cambridge, MA: Harvard University Press.

Simons, Peter. 1987. Parts: A Study in Ontology. Oxford: Oxford University Press.

  1. Goodman uses the notion of overlap to define all the other mereological notions. This means that, for example, identity gets defined as "a and b are identical if and only if they overlap exactly the same individuals," and sum as "that individual which overlaps just those individuals which overlap at least one of the two .

    But as many have pointed out, there are a handful of mereological notions one could take as primitive, defining the others in terms of that one; for example, part, proper part, and disjoint could work equally well. See Simons (1987) for more on this. ↩