## Wednesday, October 2, 2019

### Shape and parts

Alice is a two-dimensional object. Suppose Alice’s simple parts fill a round region of space. Then Alice is round, right?

Perhaps not! Imagine that Alice started out as an extended simple in the shape of a solid square and inside the space occupied by her there was an extended simple, Barbara, in the shape of a circle. (This requires there to be two things in the same place: that’s not a serious difficulty.) But now suppose that Alice metaphysically ingested Barbara, i.e., a parthood relation came into existence between Barbara and Alice, but without any other changes in Alice or Barbara.

Now Alice has one simple part, Barbara (or a descendant of Barbara, if objects “lose their identity” upon becoming parts—but for simplicity, I will just call that part Barbara), who is circular. So, Alice’s simple parts fill a circular region of space. But Alice is square: the total region occupied by her is a square. So, it is possible to have one’s simple parts fill a circular region of space without being circular.

It is tempting to say that Alice has two simple parts: a smaller circular one and a larger square one that encompasses the circular one. But that is mistaken. For where would the “larger square part” come from? Alice had no proper parts, being an extended simple, before ingesting Barbara, and the only part she acquired was Barbara.

Maybe the way to describe the story is this: Alice is square directly, in her own right. But she is circular in respect of her proper parts. Maybe Alice is the closest we can have to a square circle?
Here is another apparent possibility. Imagine that Alice started as an immaterial object with no shape. But she acquired a circular part, and came to be circular in respect of her proper parts. So, now, Alice is circular in respect of her proper parts, but has no shape directly, in her own right.

Once these distinctions have been made, we can ask this interesting question:
• Do we human beings have shape directly or merely in respect of our proper parts?
If the answer is “merely in respect of our proper parts”, that would suggest a view on which we are both immaterial and material, a kind of Hegelian synthesis of materialism and simple dualism.

#### 1 comment:

Philip Rand said...

Alice is a three-dimensitonal object and she is sticking her finger into a two-dimensional space; her three-dimensional finger looks like a circle in two-dimensional space.