Theo Todman's Web Page - Paper Abstracts

Author’s Introduction₁

1. Many philosophers accept what I shall call the Doctrine of Arbitrary Undetached Parts (DAUP). Adherents of this doctrine believe in such objects as the northern half of the Eiffel Tower, the middle two-thirds of the cigar Uncle Henry is smoking, and the thousands (at least) of overlapping perfect duplicates² of Michelangelo’s David that were hidden inside the block of marble from which (as they see it) Michelangelo liberated the David. Moreover, they do not believe in only some "undetached parts"; they believe, so to speak, in all of them. The following statement of DAUP, though it is imperfect in some respects, at least captures the generality of the doctrine I mean to denote by that name:
   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.
   (It should be obvious that DAUP, so defined, entails the existence of the northern half of the Eiffel Tower₃ and the other items in the above list.) This definition or statement or whatever it is of DAUP has, as I have said, certain imperfections as a statement of the doctrine I wish to describe certain philosophers as holding. One was mentioned in (the previous) footnote. Another is this: there are philosophers who hold what is recognizable as a version of DAUP who would not be willing to admit regions of space into their ontologies. Here is a third: this statement entails that material objects have boundaries so sharp that they occupy regions that are sets of points; and no adherent of DAUP that I know of would accept such a thesis about material objects. But these defects are irrelevant to the points that will be raised in the sequel and I shall not attempt to formulate a statement of DAUP that remedies them. For our purposes, therefore, DAUP may be identified with my imperfect statement of it.
2. What I want to say about DAUP involves only two components of that doctrine;
   1. The arbitrariness of the parts - a part of an object is of course an object that occupies a sub-region of the region occupied by that object - whose existence it asserts (". . . any occupiable sub-region of R whatever . . .") and
   2. The concreteness and materiality of these parts.
   The second of these features calls for a brief comment. A philosopher might hold that, e.g., the northern half of the Eiffel Tower exists, but identify this item in his ontology with some abstract object, such as the pair whose first term is the Eiffel Tower and whose second term is the northern half of the region of space occupied by the Eiffel Tower. (If this idea were to be applied to moving, flexible objects or to objects that grow or shrink, it would have to be radically elaborated; I mean only to provide a vague, general picture of how one might identify parts with abstract objects.) This paper is not addressed to that philosopher's doctrine. It is addressed to DAUP, which holds that, e.g., the northern half of the Eiffel Tower is a concrete material particular in the same sense as that in which the Eiffel Tower itself is a concrete material particular.
3. The Doctrine of Arbitrary Undetached Parts is false. It is also mischievous: it has caused a great deal of confusion in our thinking about material objects. But I shall not attempt to show that it is mischievous. I shall be content to show that it is false.