Numerical identity does not require Qualitative identity

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.

Glenn Peoples

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16 thoughts on “Numerical identity does not require Qualitative identity

  1. The claim that numerical identity requires qualitative identity is simply entailed by Leibniz’s law (the indiscerniblity of identicals), which seems to me as as self-evident a truth as any. I don’t think that you have provided a genuine counterexample.

    I agree that I am numerically identical to the boy I was ten years ago. But who does the description ‘the boy I was ten years ago’ refer to? It can’t refer to someone who is numerically distinct from me (because we both agree that I am numerically identical to the referent of that description). So it must refer to me. But, of course, I have all the properties that the referent of any description that refers to me has. So I have all the properties that the boy I was ten years ago has.

    The boy I was ten years ago now has the property of being 31 years old, being married, having children, etc. The boy I was ten years ago is sitting in this chair typing right now; he has grown up. Since he is me, he has all the same qualitative properties that I have and I all of the same qualitative properties that he does.

  2. Arg. That should have been something like “the boy I was twenty years ago” (what was I thinking; oh well; it’s one of those kind of days). I don’t think that my 21 year old self would appreciate being called a boy. But, oh well, I suppose I lot of people back then would have thought that the description is appropriate 🙂

  3. “So I have all the properties that the boy I was ten years ago has.”

    Kenny, the problem is that you obviously don’t. That boy was shorter than you are now, and height is a property.

  4. No Glenn, I do have all the properties that the boy I was 20 years ago has. I’m him, grown up. It’s true that he was once shorter than me. But, over 20 years, he’s grown to my height (of course, in speaking of “him” I’m simply speaking of myself in the third person).

    Suppose you wanted to put a sticky note labeled “Kenny” on the person who is numerically identical to the referent of ‘Kenny’. Where would you put it? Well, on me, of course. And then, if you wanted to know what properties the referent of ‘Kenny’ has, you would just have to look at see what properties I have. Now, suppose you wanted to put a sticky note labeled “the boy Kenny was 20 years ago” on the referent of ‘the boy Kenny was 20 years ago’. Where would you put that sticky note? Not on some boy (there’s no boy around who is referred to by that description). The only person around for you to put it on is me (and I’ll do, since I’m numerically identical to the referent of that description). If you want to know what properties the referent of that description has, again, you must look at me.

    The referent of ‘the boy Kenny was 20 years ago’ is no longer a boy, but that’s no more problematic than its being the case that the referent of ‘the greatest basketball player of all time’ is no longer a basketball player. The boy Kenny was 20 years ago has changed what properties he has over time and he has acquired all of the properties that I now have (which is just a round about way of saying that I have changed over time and have acquired the properties that I now have, since ‘I’ and ‘the boy Kenny was 20 years ago’ are coreferential).

    May I commend to you (if you haven’t read it already) Peter van Inwagen’s article “Plantinga on Transworld Identity”. The subject is what the title indicates, but van Inwagen spends a lot of time talking about the issue of trans-temporal identity as well (I borrowed the sticky-note thing from him). And when I read that article, a lot of confusions I had about the notion of numerical identity faded away. Of course, you may disagree that they did. You may think I’m displaying confusions that I acquired from the article instead. 🙂

  5. Kenny, I can see what you are saying, it’s lucid enough. You’re saying (my paraphrase) “there is no ‘me of 20 years ago,’ and the only me that there is is the me who exists now. Therefore in order for anything to have numerical identity with me, something must be the present incarnation of me, and so must have all the qualities that I now have.”

    Of course, everyone agrees that in order to be the current incarnation of you, a thing must have the qualities that you now have. The question I’m discussing, however, is whether it can be said that something’s qualitative identity has changed while it remains numerically the same thing.

    I think that contained in what I have said already is adequate reason to continue to maintain that Kenny at t1 can have different qualities from Kenny at t2 (where t2 is 20 year after t1), and yet still have numerical identity with Kenny at t2. Ergo in the sense that I am obviously talking about, I dogmatically affirm that numerical identity does not require qualitative identity.

    You can change your qualities, but you cannot change your (numerical) identity.

  6. I do hold there is a “me of 20 years ago”. He’s sitting in this chair right now. He’s lived another 20 years since 20 years ago.

    I agree that I can change qualities without ceasing to be numerically identical to the individual that I was. But that does not entail that numerical identity does not require qualitative identity. If I start out having property F, then I am numerically identical to something that has F. If I subsequently lose property F, then I am numerically identical to something that lacks F. But it is never the case that I am numerically identical to something that has F and to something that lacks F. Again, this last part is just the indiscernibility of identicals, which, to my knowledge, is an almost entirely uncontroversial principle.

    Let me put the following dilemma to you: Either (1) the boy I was 20 years ago presently exists or (2) the boy I was 20 years ago does not presently exist.

    If (1), then since there is no boy answering to the description ‘the boy I was 20 years ago’, if that description presently refers to anything at all, it presently refers to me (this adult, sitting in this chair). So, if (1), that description does presently refer to me. But if ‘the boy I was 20 years ago’ presently refers to me, then it does not presently refer to anything that is qualitatively different from me. So we have no counterexample to the claim that numerical identity entails qualitative identity.

    If (2), then nothing presently exists that is identical to the boy I was 20 years ago. Since I presently exist, it follows that I am not numerically identical to the boy I was 20 years ago. So, again, we have no counterexample.

    As for phrases like ‘Kenny at t’, I think that Peter van Inwagen is right to call such phrases examples of “adverb pasting”. Consider the sentence ‘Kenny at t is thirsty’. What does ‘at t’ modify in that sentence? I think that the appropriate answer to that question is not ‘Kenny’ but ‘is’. I.e. the same proposition is also expressed by the sentence ‘Kenny is thirsty at t’. But if you want to stipulate that ‘Kenny at t’ is to be taken as a referential phrase, then the only candidate available (at least so says my presentist self) to be the referent of phrase is me (the guy sitting here, in this chair, right now).

  7. Kenny, it’s obvious that our main disagreement is about whether or not “Kenny at t1,” where t1 was 20 years ago is qualitatively identical to Kenny at t2. I gratuitously suggest that the fact that different qualities exist at t1 and t2 settles this.

    Obviously the individual who was you 20 years ago still exists. That’s not the disagreement. What I’m talking about is the fact that this individual is no longer you 20 years ago. Really I think you’re objecting to a way of saying things, rather than the substance of what is said. We are both stating and agreeing with the same facts of the matter. You’re just preferring to name them differently.

  8. Glenn, if the substance of what you are saying is that it is possible for something to continue to be numerically identical to itself through qualitative change, then I do agree. But you have said more than that.

    You have said, for instance, that Noonan was wrong to say that numerical identity requires qualitative identity. But he wasn’t wrong. And the claim that something can remain numerically identical to itself through qualitative change does not entail that he was wrong.

    What Noonan said is entailed by a (in my opinion) self-evident and almost entirely non-controversial principle (the indiscernibility of identicals). The principle just boils down to the claim that a thing can’t have different properties than itself. I don’t see how that claim can be reasonably denied. But the claim that numerical identity does not entail qualitative identity entails the denial of that principle.

    The claim that it is possible for something to retain numerical identity with itself through qualitative change does not entail that numerical identity does not require qualitative identity. At no point is a thing that changes its properties numerically identical to something it is not qualitatively identical to.

  9. Kenny, the key in your last post is the phrase “at no point.” Sure, “at no point” will a relationship of numerical identity exist without qualitative identity. As you’ve seen by now, that’s not the disagreement.

    The other key is that you use language that makes it impossible to talk about Kenny at t1 AND ALSO Kenny at t2. You refer to it as just Kenny. I (rather self servingly, no doubt), consider my use of language more precise and nuanced, which is why Noonan should (in my view) have added a time reference in his claim, as suggested in my blog post.

    If we can’t agree that this is what is happening, then it ends there. Once we agree that this is what’s happening, then we agree that two things can be numerically identical and also not be qualitatively identical. This is why I say you language use is the root of the disagreement.

  10. Glenn, *if* ‘Kenny at t1’ refers to something that is in fact numerically identical to ‘Kenny at t2’, then ‘Kenny at t1’ does not refer to anything different than does ‘Kenny at t2’. And if those phrases both refer to the same thing, they don’t refer to things with different properties. These claims are all just trivial consequences of the concept of numerical identity.

    There are philosophers who think that ‘Kenny at t1’ refers to something other than ‘Kenny at t2’. Some philosophers think, for example, that those phrases refer to two distinct stages of a temporally extended four dimensional space-time worm. But those philosophers do not believe that Kenny at t1 is numerically identical to Kenny at t2.

    I’m not aware of any major metaphysician that would grant, however, that qualitative change affords a counterexample to the claim that numerical identity entails qualitative identity. That numerical identity entails qualitative identity, rather, is something that is usually taken as a given at the outset of debates about what happens in qualitative change. Some philosophers (e.g. perdurantists) deny that things change qualitatively while persisting numerically through time. Others (e.g. endurantists) affirm that instead. But both parties are in agreement that numerical identity entails sameness of properties.

    I think, maybe, the closest you might get to your position is that some philosophers advocate a doctrine of temporary identity and insist that the principle of the indiscernibility of identicals requires temporal qualifiers. There’s also, I suppose, advocates of the notion of relative identity who deny that there is any such thing as absolute numerical identity who allow that two things can be e.g. the same cat as one another but have different qualitative properties. But all parties agree that these are non-standard views of identity.

  11. Well Kenny, I take the normative claim that “the indiscernibility of identicals requires temporal qualifiers” to be such clearly good common sense that I think anyone who neglects it should be more careful, ergo my issue with the claim that numerical identity requires qualitative identity.

    I am also aware – as I am sure you are also – that there exist what you call “non-standard” views in philosophy that do in fact represent good commons sense that many philosophers neglect.

    A pox on the house of anyone who thinks that numerical identity requires qualitative identity.

  12. Well Glenn, I think that even if we go with some of the temporary identity folks (which I don’t) and say that the indiscernibility of identicals requires temporal qualification, it is still, at best, a confusion to say that numerical identity does not require qualitative identity. I say that, in any case, a thing can’t be different than itself (and that’s what I take to be good common sense! :smile:)

    Of course, I realize that often what one philosopher takes to be confusion, another takes to be insight (that’s the nature of the field). But I think we’ve talked the issue through enough here. So I’ll sign off.

  13. Fair enough Kenny.

    For those who were reading and not entirely sure about the “indiscernability of identicals” and what Kenny and I were talkig about, here’s what it was about: The indiscernability of identicals means that if something is identical to something, then the “two” things are indiscernable from each other, being the same thing.

    What I’ve said about “temporal qualifiers” means this: That the above principle should really be stated like this: “At any specified point in time, if something is identical to something, then the “two” things are indiscernable from each other, being the same thing.”

    Given this version of the principle, we can put a photo of me taken in 1975 when I was born side by side with a photo of me taken today and say that in one sense the individuals depicted in each photo are identical. They are numerically identical, because one person IS the other person.

    However, my version of the principle also allows us to say that the two individuals, while they do indeed retain numerical identity between 1975 and now, are still discernable. The two are not qualitatively identical.

    I think my version is more plausible to those of us who agree that we can discern differences between a newborn baby and a 33 year old man even though it’s the same person. And that is why the principle of the indiscernability of identicals is incorrect if left without temporal qualifiers, and that is why numerical identity doesn’t require qualitative identity.

  14. Kenny got it wrong.
    Leibniz’s law is not the indiscernability of identicals. It’s the reverse – the identity of indiscernibles. http://en.wikipedia.org/wiki/Leibniz%27_law
    If two things are indiscernable in every sense (to the point of occupying the same space in time), then they are identical (i.e. they are not two things but one). That’s Leibniz’s law.

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