Is a Pile of Bricks One Thing or Many? Somebody Worked Out the Rules
By the BrainSnail editorial team. How these articles are written and checked, and how to tell us when one is wrong.
The formal study of parts and wholes sounds like an exercise in the obvious, and it turns out that ordinary assumptions about them produce contradictions almost immediately.
What the subject covers
The field studies the relation of being a part of something and the properties that relation has. A handful of principles look undeniable at first glance. Nothing is a proper part of itself. If one thing is part of a second and the second part of a third, the first is part of the third. Two things with exactly the same parts are the same thing. Formal systems are built from principles like these, and the interest lies in which ones survive contact with actual examples.
Where the trouble starts
Several ordinary cases resist the tidy principles:
- •A statue and the clay it is made of share all their parts
- •Yet the clay survives being squashed and the statue does not
- •So identical parts do not guarantee identity
- •A person's parts are replaced steadily over a lifetime
- •An organisation persists through complete turnover of members
- •Yet nobody counts a scattered heap as one object
The composition question
The central dispute asks when several things compose a further thing, and the answers on offer are all uncomfortable. One position says always, so any collection whatsoever composes an object, including one made of your left shoe and a distant moon, which multiplies objects beyond anything ordinary talk recognises. Another says never, so strictly there are no tables and only particles arranged tablewise. A third says sometimes, under conditions involving contact or joint function, and struggles to state those conditions without arbitrariness. Most people arrive expecting the third and leave uncertain.
The problem of the growing pile
One ancient puzzle sits directly on this territory and has never been satisfactorily resolved. Removing a single grain from a heap of sand surely leaves a heap, and repeating that eventually leaves one grain, which is not a heap, so somewhere a single grain made the difference and nobody can say where. The same structure catches every vague term, including tall, bald and rich. Responses include denying that there is any such thing as a heap, accepting a sharp but unknowable boundary, and allowing statements to be partly true, none of which is comfortable.
Why it is not idle
The subject supplies tools used well outside philosophy, which is the best defence of spending time on it. Formal systems describing parts and wholes underpin geographic information systems, where questions about regions overlapping, containing and bordering each other must be answered consistently and automatically. Medical and biological databases use them to represent anatomical structure so that a query about one part correctly finds everything within it. Legal reasoning about property, and about what happens when things are combined, runs on exactly these relations. In each case the practical system needs the questions answered precisely because ordinary language does not.
The takeaway
Studying parts and wholes formally exposes that ordinary assumptions conflict, since a statue and its clay share every part while differing in what they survive. The central dispute is when several things compose a further one, with always, never and sometimes all carrying heavy costs. The formal systems are used in geographic databases, anatomy and legal reasoning.