Can Mereological Sums Change their Parts
Van Inwagen (Peter)
Source: Van Inwagen (Peter) - Existence: Essays In Ontology, Chapter 2
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Author’s Abstract1

  1. I will defend the following thesis: for every object x (or at least for every object x that has parts) there are objects such that x is a mereological sum of those objects. I will in fact defend the thesis that this statement is true by definition, a consequence of a correct understanding of mereological summation. And (if ‘a mereological sum’ is indeed no more than an abbreviation of ‘an object that is, for certain objects, a mereological sum of those objects’) it follows immediately that every object (that has parts) is a mereological sum. The phrase ‘mereological sum’ does not, therefore, mark out a special kind of object – or, at any rate, it marks out no kind more special than “object that has parts.” (And, of course, if we so use ‘part’ that everything is by definition a part of itself, ‘object’ and ‘object that has parts’ coincide.) An immediate consequence of the correct conception of mereological summation is that ‘mereological sum’ is not a useful stand-alone general term. In this respect, ‘mereological sum’ is like ‘part’. If everything is a part of itself, then the word ‘part’ does not mark out a special kind of object and ‘part’ is not a useful stand-alone general term – for ‘a part’ can be defined only as “an object that is a part of something,” and every object is thus a “part.” The case of arithmetical summation teaches the same lesson: it is possible to lift the word ‘sum’ out of the relational sentence ‘x is the sum of y and z’ and to use the word as a stand-alone general term – for example, ‘The number 17 is a sum’ – but no purpose is served by doing so.
  2. Now if every object (every object that has parts, that has even itself as a part) is a mereological sum, every object that can change its parts2 is a mereological sum that can change its parts. And, since the statement “Some objects can change their parts” involves no conceptual confusion, neither does the statement “Some mereological sums can change their parts.” I grant that if every object is a mereological sum, it may nevertheless be that no mereological sum can change its parts – because no object can change its parts. But what is not true (I shall contend) is this: to speak of amereological sum changing its parts is to misapply the concept “mereological sum3.” And, of course, if every object is a mereological sum, it is not true that although some objects can change their parts, no mereological sum can change its parts.


Originally published in Journal of Philosophy 103 (2006): 614–630.

In-Page Footnotes

Footnote 1: Footnote 2: Footnote 3:
  • Suppose that the very idea of a thing’s changing its parts is conceptually incoherent, that “mereological essentialism” is an analytic or conceptual truth. Would that not entail that “to speak of a mereological sum’s changing its parts is to misapply the concept ‘mereological sum’”? Well, no doubt – but only in a very strict and pedantic sense of misapplying a concept. It would also be true, in this strict and pedantic sense, that to speak of a cat’s losing its tail was to misapply the concept “cat.” The person who said, “That cat has lost its tail” or “That cat is composed of different atoms from the atoms that composed it last week,” would not, in the case imagined, be making a conceptual mistake peculiar to the concept “cat.” That person’s conceptual mistake is better located in his or her application of the concepts “part” and “change.” And so for the person who said, “That object is this week a mereological sum of different atoms from the atoms of which it, that very object, was a mereological sum last week.” We shall consider this question – the question whether it is conceptually coherent to suppose that any object can change its parts – in section iv.

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