I’m doing some writing on the concept of numerical identity at present, so I thought it might be interesting to consult Google to see what others have said about it. I can usually rely on the contributors to the Standford Encyclopedia of philosophy, but this time somebody (Harold Noonan), I daresay (and I say it cautiously!), got it wrong. He writes:
To say that things are identical is to say that they are the same. “Identity” and “sameness” mean the same; their meanings are identical. However, they have more than one meaning. A distinction is customarily drawn between qualitative and numerical identity or sameness. Things with qualitative identity share properties, so things can be more or less qualitatively identical. Poodles and Great Danes are qualitatively identical because they share the property of being a dog, and such properties as go along with that, but two poodles will (very likely) have greater qualitative identity. Numerical identity requires absolute, or total, qualitative identity, and can only hold between a thing and itself. Its name implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical (Geach 1973).
I agree with most of this. Yes, there is a fundamental distinction between numerical identity and qualitative identity. Two things can have all the same qualities (e.g. two rubber balls made on the same production line) and so be mostly qualitatively identical, but because there are two balls sitting side by side and not one ball, they are not numerically identical. If they had all their qualities in common (including their position in space and time) then there would be only one thing, and in fact they would be numerically identical, but in this case, there are not. When you’re counting how many balls there are, you have to count two, or you’ve missed one.
But let me go out on a limb (again, cautiously) and say that when Noonan (and the many who agree with him) says that “Numerical identity requires absolute, or total, qualitative identity,” the claim is at best incomplete, and wrong as it stands. It is true in one sense, but not true in another. Recall the ball example: Yes, if they have all things in common including space and time, then we’re talking about the same ball, so there is numerical identity. But consider for example the following scenario, especially the question: “Martha says this is my long lost husband. He looks so different. Could he really be the same man I knew ten years ago?” The question clearly makes sense, and it is clearly a question about identity. But it is not a question about qualitative identity. The questioner already knows that the man she now sees and the man she was married to ten years ago are not qualitatively identical. The man she sees before her looks different, so he has different qualities. The question is whether or not this man is numerically identical with the man she once knew. And this question is one that could quite conceivably be answered in the affirmative: Yes, this is the same man, even though his qualities are now different. This is because – as is perfectly obvious once we see what the distinction between numerical and qualitative identity is – numerical identity over time does not require qualitative identity.
It’s possible that Noonan would grant this claim if it were pointed out to him, and qualify his statement somewhat to say something like: “At any fixed point in time, not allowing for qualitative change, a thing’s being numerically identical with something requires that it have qualitative identity with it as well.”
The reason I was doing the search in the first place was because I’m preparing a piece on the abortion issue where I explain that even though I am not qualitatively identical with a fetus (I’m obviously a lot bigger, I have much more brain function etc), I am numerically identical with a fetus from the past (from 1975 actually). The very same human creature who is now typing this, was a fetus, but this human creature doesn’t have all the same qualities as a fetus.
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