RUTH BARCAN MARCUS AND MODALITY (6): Can Two Things Be In Exactly the Same Time and Place At Once?

The problem is this: can two different objects occupy exactly the same place at exactly the same time? And if they can, how do we tell them apart? And if they cannot, why not? This question is called the problem of spatio temporal coincidence.

To understand the question, imagine you have a piece of clay on your desk. You squish it into the shape of a small statue. Now you can say two things. You can say “There is a lump of clay here,” and you can also say “There is a statue here.” But the lump of clay and the statue seem to be in exactly the same place, at exactly the same moment. So are they one thing or two things? If they are one thing, why do we have two different descriptions? If they are two things, how can two things be in the same place at once? People have been arguing about this for a very long time. Marcus wants to bring modal logic to bear on the problem. She uses the ideas of identity and essential properties that she has been developing.She begins with the basic idea that an object is something that keeps its identity over time, even if it changes in some ways. For example, you are the same person today as yesterday, even if your hair looks different or you are wearing a different jumper. Those changes are accidental. They do not destroy your identity. In the same way, a lump of clay can be reshaped without becoming a new object. What counts as the same object depends on which properties are essential to it and which properties can change. 

Now consider the statue made from the clay. The statue has a form, a shape, and perhaps even a function or purpose. These seem more essential to the statue than to the clay. If you flatten the sculpture again, the statue is gone, but the clay still exists. So we have one object, the clay, that continues through many shapes. And we have another thing, the statue, that exists only as long as the clay has a certain shape. Marcus says this shows that the clay and the statue do not have the same essential properties. The clay can survive being squashed. The statue cannot. They also have different criteria for when they begin and end. The clay existed before the statue was shaped. The statue begins only when the shape is made. She uses this to show why identity cannot be determined simply by looking at what is in front of us at a single moment. At the moment the statue exists, the clay and the statue share all their visible properties. They have the same shape, weight, size, and location. If you only look at that moment, you might think they are identical. But identity involves looking at possible changes. If squashing destroys the statue but leaves the clay, that is enough to show they are not the same object. Marcus says this is an essentialist point. Essential properties help us distinguish objects even when they coincide in space and time. 

Next she considers the idea that many logicians and philosophers have used to solve the problem. Some say that no two distinct objects can occupy the same place at the same time. They insist on a rule: if two things coincide in all their observable properties, then they must be identical. Marcus says this is too simple and does not match our usual way of talking. We often distinguish between things that happen to be located together even though they are not the same thing. The clay and the statue are a good example. Another example might be a coin and the metal from which the coin is made. One can melt the metal and destroy the coin while the underlying material remains. This shows that the coin and the metal have different essential properties. They are not the same object, even though they share the same space. She then explores another route sometimes taken by philosophers. They say that objects have temporal parts, like frames in a film, and that the only real objects are spread out in time like long worms. On this view, the clay worm overlaps the statue worm for a while, so there is no real mystery. Marcus is not happy with this idea either. She thinks it turns identity into a complicated matter of slicing objects into time segments. It also does not explain how we distinguish objects in ordinary speech. We do not talk about worms in time when we talk about our belongings or the things around us. We talk about objects that last through change and have essential and accidental properties. Marcus uses modal logic to clarify the problem. She says that if we treat identity as necessary, we can draw clear distinctions between objects that only coincide for a moment and objects that are truly the same. If x = y, then necessarily x = y. But the clay and the statue do not satisfy this. In some possible situations the clay continues while the statue does not. So the identity “clay = statue” is not necessary. Therefore it is not identity at all. This allows the logic to say that two objects can coincide without being the same. She introduces another idea. When we talk about the clay and the statue, we seem to be using two different ways of classifying the same material. One classification uses shape and artistic function. The other uses material composition. These classifications give rise to different persistence conditions over time. A statue ceases to exist when its shape is lost. A lump of clay ceases to exist only when its matter is destroyed or scattered. Marcus argues that this shows why spatio temporal coincidence is not a paradox but rather a clue to how we classify objects. We are not mistakenly multiplying objects. We are recognising real differences in their essential structure.

She also touches on the idea of reference. When we use names, such as “this statue” or “this lump of clay,” we are not simply sticking labels on locations. We are referring to objects with particular histories and possible futures. Reference depends on more than simple observation. Marcus says that a logical system must respect this. It must allow us to refer to an object in a way that keeps track of its identity across different possible situations. This is why she prefers an actualist modal logic with strict identity rules. It makes sense of how we talk. A subtle part of the chapter concerns the danger of multiplying entities simply because we have different descriptions. If we say “the statue exists” and “the clay exists,” we must make sure we are not turning different descriptions of the same thing into two objects by mistake. Marcus says the way to avoid this is to check their essential properties. If two descriptions pick out something that has the same essential properties, then they are descriptions of one object. If they pick out things with different essential properties, then there are indeed two objects, even if they coincide for a time. Her modal logic helps us decide which is which.

She says this problem shows the importance of essentialism. Without essential properties, we could not tell objects apart when they coincide. We could not say why the clay survives crushing while the statue does not. We could not make sense of identity across time and change. Modal logic would become thin and unhelpful. Essential properties give modal logic its grip on the real world.

She says all this shows that identity is not judged by looking only at one moment. We need to look at how objects could change, what is essential to them, and how we pick them out. When we do that carefully, the clay and the statue are different objects that can happen to share space for a while. Modal logic, with necessity, possibility, and essential properties, allows us to describe this.