Numerical Identity and Identity over Time

Clones and Perfect Duplicates

Suppose we grew a clone of you. Would the clone be the same person as you? Or would it be a different person?

Well, let's say we raise the clone in a locked room, with no English newspapers or radio or internet access or anything like that. It's attended by nurses who never speak English in its presence. It grows up to be 18 years old. Do you think it would be able to speak English?

No? Why not? It's a copy of you, and you can speak English.

The answer is that clones are just genetically the same as their originals. They can grow up to have very different properties, because what properties you have isn't just a function of your genes. Your environment also plays a role.

Do you know any genetic twins? They can have very different tastes and opinions. If they have different careers, and went to different schools, then we can expect them to know different things. On a given Monday afternoon, one twin might be thinking about a math problem, and the other one thinking about dinner. If we made a clone of you, the relationship between you and your clone would be just like the relation between genetic twins. (Except that in the clone case, the "twin" was born much later.)

As we talk about personal identity, we'll sometimes be talking about perfect duplicates. These are supposed to be much more like each other than a clone would be like its original. They don't just have the same genes. They are supposed to be molecule-for-molecule identical. So if the one duplicate is digesting a ham sandwich, then so too is the other. If the one duplicate has a chipped tooth, or a broken arm, or a migraine headache, then so too does the other duplicate. At a given moment, their brains would be perfect Xerox copies of each other.

Suppose we made a perfect duplicate of this sort of you. (Don't ask me how we did it! Just suppose we did.) Would it be the same person as you?

Different Ways of Talking about "Being the Same"

We should distinguish:
  1. being one and the same thing as X--philosophers call this strict or numerical identity
  1. what philosophers call qualitative identity--identity in the sense of being perfectly similar, or exactly alike

Clark Kent is numerically identical to Superman. Two pieces of chalk, or two Xerox copies of the same original, are not numerically identical. They are only qualitatively identical.

Now, recall Leibniz's Law. It said:

If A is identical to B, then: every property that A has, B also has to have, and vice versa.
How should we understand this? Is it talking about numerical identity or qualitative identity?

Well, it's not talking about qualitative identity. For we generally count things as qualitatively identical even if they don't share all of their properties. For instance, two pieces of chalk fresh out of the box may be qualitatively identical, but the one piece of chalk will be held in my left hand, and the other won't be. That is a respect in which they don't have the same properties.

To make sense of this, we need to introduce a further distinction, between:

  1. how a thing is in itself, or intrinsically
  1. how the thing is in relation to other things (how it is relationally or extrinsically)
Being 5 foot 9 inches tall is an intrinsic feature of me. Being taller than Joe is not an intrinsic feature of me. It doesn't just depend on how I am in myself. It also depends on how tall Joe is. Similarly, being 10 feet away from Joe is not an intrinsic feature of me, either.

Now, when philosophers talk about "qualitative identity," that doesn't have to include being identical in all extrinsic or relational respects. The two objects will usually differ in some of their relations to other things, like whether they are held in my hand, or how far away they are from the window. To be qualitatively identical, things only have to share their intrinsic features.

The contrast between intrinsic and extrinsic properties is a very important distinction in philosophy. We'll be coming back to it several times this term.

Anyway, so we see that A and B can be qualitatively identical--they can share all their intrinsic properties--even if they differ in respect of some of their extrinsic or relational properties. If A and B are one and the same thing, though--if they are numerically identical--then it's hard to see how they could differ in respect of any of their properties. (Here we set aside properties having to do with what people believe or doubt or hope about A and B.)

So we should understand Leibniz's Law as saying:

If A is one and the same thing as B (that is, A is numerically identical to B) then: every property that A has, B also has to have, and vice versa.

Does Leibniz's Law Imply That It's Impossible for Things To Change?

Suppose in 1980 we spend a pleasant afternoon sitting underneath a little tree--call it Junior. In 2006 we return to the same location and find a much taller, fuller tree--call it Senior. People living nearby tell us that no tree was ever cut down or removed from that spot. Does Leibniz's Law allow us to say that Junior and Senior are one and the same tree? It looks like the trees have different properties. Junior was little, but Senior is very tall and full. Since they don't have the same properties, how can they be one and the same tree?

Intuitively, we want to say that Junior is the same tree as Senior, even though Senior is much taller and fuller than Junior. That is, Senior is NOW much taller and fuller than Junior WAS. Perhaps this is important. After all, can't we say:

So we have to pay attention to the time at which things have various properties. Senior isn't just tall, period. He's tall in 2006. But it also seems true to say that Junior is tall in 2006. There was a time when Junior wasn't tall. That was back in 1980. But Senior wasn't tall then, either.

So Junior and Senior do have all the same properties, after all--if we pay attention to the time at which they have them. Neither of them has the property of being tall in 1980. Both of them have the property of being tall in 2006. So Leibniz's Law permits us to say that Junior and Senior are one and the same tree, after all.

If we like, we can build this reference to time into Leibniz's Law, as follows:

If A is one and the same thing as B, then: for every time t, if A exists and has certain properties at t, then B also has to exist and have those properties at t, and vice versa.

As we proceed into our discussion of personal identity, it will be crucial for you to keep these points firmly in mind:


To illustrate once more: The clock on the wall right now is numerically identical to the clock that was on the wall five minutes ago, even though some of its properties have changed (its hands have moved).

A thing's identity conditions are the facts about that thing in virtue of which it is one and the same object over time, and a different object from its neighbors. When we come back after twenty-some years and look at the grown-up tree Senior, what makes it one and the same tree as the tree we sat under back in 1980? What makes it a different tree from the trees in the neighbors' yards (which may be qualitatively very similar to it)? To answer questions like that is to say what the tree's identity conditions are.