Thursday, February 23, 2012

Statues and Lumps of Clay

We’re going to soon be getting into a really fascinating discussion in my Metaphysics and Epistemology course having to do with material object metaphysics. One fascinating case raises a host of philosophical issues. The “statue and clay” example has been discussed for centuries. Here’s how Carroll and Markosian spell it out in their book An Introduction to Metaphysics.

“Suppose that on Monday you bring home a lump of clay and place it on your workbench. Then on Tuesday morning you carefully fashion the clay into a beautiful statue of a snowy owl, which remains in your workshop for all your friends to admire... But suppose that on Wednesday you wake up in a bad mood and decide that you don’t like the snowy owl after all. So that morning you squash it back into an amorphous lump of clay”

How many objects are there on your workbench on Monday, Tuesday, and Wednesday? Does the number change over these days? In other words, are the clay and the owl the same thing or are they, alternatively, two distinct objects?

Ted Sider puts one of the problems raised by this case as follows. (This might as well be this week’s paradox. Please suggest a solution to this.)

(1) Before the sculptor's action, a lump of clay exists and after the sculptor's action a statue exists.

(2) The lump of clay continues to exist after the sculptor's actions.

(3) The statue comes into existence when the sculptor makes it.

(4) The lump of clay and the sculpture have different properties after the sculptor's actions: one existed before the sculptor's action, and one did not. (This follows from (1), (2), and (3).)

(5) If x and y have different properties at the same time, then x ≠ y. (This is called Leibniz’s Law - see here for a robust discussion of this principle.)

(6) The statue ≠ the lump of clay. (This follows from (4) and (5).)

(7) The statue and the lump of clay occupy the same location at the same time.

(8) Two distinct objects never occupy the same location at the same time.

(9) The statue = the clay. (This follows from (7) and (8).)

(10) Therefore, The statue = the clay and the statue ≠ the lump of clay. (This follows from (6) and (9).)

Of course, the statue can't be identical to the clay and also not identical to the clay. So what went wrong? Which premise(s) of the argument should we reject?


Chris R said...

I would suggest that instead of defining both "sculpture" and "lump of clay" as objects at the same time, we define one as an attribute of the other at any given time. Which you perceive as the object is a matter of preference or context. For example, an archaeologist may study an object solely interested in it's material properties. In this case, the material may happen to have the attribute of being a statue. On the other hand, a curious artist may be admiring statues in a museum and ask "What material is this statue made of?" In this case, the answer would be an attribute of the statue.

Arpad H said...

Premise one should be rejected. The sculpture is MADE of clay, it IS the clay, just with a different shape.

It's like claiming that you are two different people when you sit and stand. It's pretty clear you're one persona and the clay is one object.

Toby said...

As a first stab, how about: the error is step 3. The statue is not a distinct object which comes into existence when the sculptor makes it. Rather, 'statue' is a word we apply to lumps of clay (stone, wood, whatever) when they have been shaped in particular ways. So the lump of clay is the object, and it persists throughout, but because of a change in its physical properties brought about by the sculptor's actions, it sometimes satisfies the description 'statue' and sometimes does not.

(Yesterday, the books in my office were neatly arranged on my shelves. But last night I was checking some references on a paper, so today my books are scattered messily across my desk and on the floor nearby. Yesterday there was no mess in my office; today there is a mess. For sure, the mess is not identical to the books; it has different properties. But the mess is not a separate object which came into existence between yesterday and today. It's just a description which can be applied to objects in a particular state. Yesterday, the books were not in a state that qualified them to be called a 'mess'; today, they are.)

Jesse Steinberg said...

Thanks for the comments thus far.

Chris, I'm curious which of the premises you're denying. Can you say a bit more about this?

Toby, your example about your books is an interesting one. 'mess' does seem to be about a property of your office or the bookshelf, and not to be about some object in addition to your book collection. But some objects can be composed of other objects (e.g., a solar system or a collection of art). It's not entirely obvious to me that 'statue' works like mess and not like these other terms that involve (arguably) objects. Can you give us some more reasons for thinking 'statue' is more like 'mess' and other terms that denote properties (as opposed to objects)?

Toby said...

Well, I have to admit that the main argument in favour of taking 'statue' to be a description that things sometimes satisfy and other times don't is that it avoids the contradiction described in your post. I do tend to regard the conclusion "X=Y and X\=Y" as a reductio of the premise, already pretty counter-intuitive to me, that we create a whole new object every time we bring about some change in an object's properties such that it satisfies a new description which happens to exist in our language.

Here is some clay. Does it satisfy the description "lump" or "statue"? The answer depends on its physical configuration. It might also (and simultaneously) satisfy many other descriptions: "work of art", "monstrosity", "antique", "creation". Just because these things are linguistically nouns doesn't mean that they necessarily pick out metaphysically fundamental entities. If I use the statue to prop open my door, it would become describable as a "doorstop". Do we want to worry, then, that we have a "doorstop paradox"? That the statue both is and is not identical with the doorstop? that way madness lies.

I would make similar observations about messes, solar systems or collections of art. Our language should not be taken automatically to 'carve nature at the joints'. Especially if it leads to paradox.

Jesse Steinberg said...

Toby--Thanks for commenting. I'm very sympathetic to your reply.

I'm interested in what philosophers call "the special composition question." This is basically a question about what it means for things to COMPOSE something else (e.g., planets purportedly compose a solar system). One way to answer the question is to deny that composition EVER occurs. But this strikes me as equally implausible as saying that we bring about a new object whenever we group objects in such a way that they satisfy a description that happens to exist in our language.

I wonder if you have any thoughts about the right answer to the special composition question.

Laura K said...

This may have been said another way before, but this is the best way I can understand this particular conundrum: the step(s) I have issue with are 3 and 6. The lump of clay does not 'magically' stop existing as soon as the form of the statue takes place. In a case like this there is more of a sliding scale of existence: it takes time for the lump of clay to become the statue. Yes, the statue comes into existence once the sculptor makes it, but it has the potential to return to its former state as a lump of clay. So, as it follows, the statue and the lump of clay are not entirely mutually exclusive from one another in existence. The potential to be either still exists in the object, so to say that the statue is not the lump of clay sounds a bit off. The potential connects the two objects, in my opinion.

Jacob Shepherd said...

I think we should eliminate premise (7). I think it is misleading to say that the statue and the clay occupy the same place at the same time. It seems to me that they may appear to occupy the same place at first glance. But when you bring in the factor of time (especially when you consider it as the forth dimension), then the statue and clay do not exist at the same time. And if time is treated as the forth dimension, then they're not really in the same place either. Everything changes over time, and so the "place" that the clay is in and the "place" the statue is in may look the same, but it is changed and isn't really the "same place" at all. It looks similar to the former place, but it has undergone changes that qualify it for the distinction of separateness from its former appearance.

Toby said...

Jesse: My understanding of the special composition question is something like 'When do multiple objects compose a single distinct object?'.

This isn't my area at all, so I'm probably missing the point, but I don't quite understand what the issue is here. I'd be tempted to ask: what reason do we have for thinking that there's something metaphysically fundamental about the notion of an 'object' in the first place?

It seems to me that there's just stuff and stuff and stuff. We observe it, we interact with it, we sort it into conceptual categories. The category of 'object' is a useful one because it singles out a stuff-lump about which we can say things (it has certain properties, it serves a certain function, whatever).

But that doesn't give rise to any philosophical puzzles. There only appears to be a puzzle if we make the mistake of thinking that 'object' is a category out there in the world. Then we start to worry about questions like 'But when does this object become that object? How many gradual changes can I make to this object before it's not the same object any more? When do multiple objects combine to make up a bigger one?' and so on.

I'm not denying that composition ever occurs, nor that objects really exist. I agree those are implausible positions. It just seems to me that since 'singular object' and 'collective object' and 'composition' are concepts that we own, not metaphysically fundamental facts about the world, the best way to get an answer to the special composition question is to ask a linguist, or a psychologist, or whatever.

Jesse Steinberg said...
This comment has been removed by the author.
Jesse Steinberg said...

I'm glad to see this post is getting such thoughtful comments. Thanks, everyone.

Toby-That's what I thought your position would be. Thanks for clarifying things. I think you did a great job in articulating your thoughts simply, clearly, and powerfully. Your desire to carve nature at its joints is certainly one to maintain and I hope we don't lose sight of this as we discuss these issues in my class.

Laura- You say some interesting things about potentiality but it's not clear which premise you think is false. Is it (8) that you think we should reject?

Jacob- I'm a bit confused by your comment. Suppose we consider the statue on Tuesday afternoon. Isn't it made out of what was once a lump of clay? Is it wrong to say that the clay still exists (even if in the form of a statue)?

Thanks again for commenting!

Kelsey Milliron said...

I think that (4) should be eliminated. The way I grasped this concept a little better was by using a different example. We all have two hands, our hands are at the end of our wrists. If we put our hands together and angle them we can form the shape of a heart. The heart is still at the end of our wrists. Once we decide to separate our hands the heart no longer is visible but we still have our hands at the end of our wrists. The reason I disagree with premise number (4) is because your hands were just setting as normal hands before you placed them together to form the heart. Because of this they both were due to your actions. Likewise, the clay was sitting on the sculptors desk due to his actions. The clay did not just magically appear there. The number does not change over the days. The clay and the sculpture are one thing just as your hands and the heart you formed are one thing. They may seem different but if you think about it they are the same because they are still made up of the same matter. They just have a different look to them but still are only one.

Kelly D said...

Premise (1) should be eliminated. It's odd to think an entire new object comes into existence just by one objects change in form. This would lead me to believe that there really are no objects because everything is made from something that was also made from something and so on. All these things were just altered in their from and composed what people identify as a new thing. In a common-sensical way I surely believe there are things but in a philosophical sense, for me, it seems as though their is not a crisp enough line to define what it is for an object and its parts to exist as one entity. And how one would qualify something as existing or not existing is too blurry to justify.

Anonymous said...

I like Nagel's monument to obfuscation here: The statute would be one possible aspect of the clay much the same as consciousness is, ostensibly, the mental aspect of a working brain.