Numerical and Qualitative Identity and Radical Flux

Philosophers often use 'numerically' in contrast with 'qualitatively' when speaking of identity or sameness.  If I tell you that I drive the same car as Jane, that is ambiguous: it could mean that Jane and I drive one and the same car, or it could mean that Jane and I drive the same make and model of car, but not one and the same car. To take a second example, six bottles of beer in a typical six-pack are numerically distinct but qualitatively identical. Suppose you want a beer from the six-pack. It won't matter which bottle of the six I hand you since they are all qualitatively the same (qualitatively identical) in respect of both bottle and contents, at least with regard to the properties that you would find relevant such as quantity, taste, inebriatory potential, etc. If I hand you a beer and you say you want a different beer from the same six-pack, you mean a numerically different one. If I reply by saying that they are all the same, I mean they are all qualitatively the same.

If A and B are numerically identical, it follows that they are one and the same. A and B are one, not two.  If A and B are qualitatively identical, it does not follow that they are one and the same. But they might be.  For if A and B are numerically identical, then they share all properties, in which case they are qualitatively identical.  Furthermore, if A and B are qualitatively identical, it does not follow that they share every property: it suffices that they share some properties.

To see this, suppose that you and I both order the 'monster chimichanga' at the local Mexican eatery. We have ordered the same item, qualitatively speaking.  But it turns out that the one served to you is slightly more 'monstrous' (a wee bit bigger) than mine. That doesn't change the fact that they are qualitatively the same or qualitatively identical as I use these phrases.  The chimis are two, not one, hence numerically different.  They are the same in that they share most properties.

I suppose we could nuance this by distinguishing strict from loose qualitative identity.  Strict implies indiscernibility; loose does not. 

Can One Step Twice into the Same River?

Stephen Law (HT: Sed Contra) thinks one can make short work of a Heraclitean puzzle if one observes the numerical-qualitative distinction:

If you jump into a river and then jump in again, the river will have changed in the interim. So it won't be the same. But if it's not the same river, then the number of rivers that you jump into is two, not one. It seems we're forced to accept the paradoxical - indeed, absurd - conclusion that you can't jump into one and the same river twice. Being forced into such a paradox by a seemingly cogent argument is a common philosophical predicament.

This particular puzzle is fairly easily solved: the paradoxical conclusion that the number of rivers jumped into is two not one is generated by a faulty inference. Philosophers distinguish at least two kinds of identity or sameness. Numerical identity holds where the number of objects is one, not two (as when we discover that Hesperus, the evening star, is identical with Phosphorus, the morning star). Qualitative identity holds where two objects share the same qualities (e.g. two billiard balls that are molecule-for molecule duplicates of each other, for example). We use the expression 'the same' to refer to both sorts of identity. Having made this conceptual clarification, we can now see that the argument that generates our paradox trades on an ambiguity. It involves a slide from the true premise that the river jumped in the second time isn't qualitatively 'the same' to the conclusion that it is not numerically 'the same'. We fail to spot the flaw in the reasoning because the words 'the same' are used in each case. But now the paradox is resolved: we don't have to accept that absurd conclusion. Here's an example of how, by unpacking and clarifying concepts, it is possible to solve a classical philosophical puzzle. Perhaps not all philosophical puzzles can be solved by such means, but at least one can. 

Problem Solved?

Not so fast.  Although superficially plausible, the above solution/dissolution of the puzzle begs the question against the doctrine of Heraclitean flux. Law goes at Heraclitus with the numerical-qualitative identity distinction.  But this distinction presupposes a distinction between individuals and qualities.  Given this distinction one can say that one and the same individual has different qualities at different times.  Thus one and the same river is stepped into at different times. But on a doctrine of Heraclitean flux, there are no individuals that remain self-same over time.  There is no substrate of change.  Change cuts so deep that it cannot be confined to the properties of a thing leaving the thing, as the substrate of change, relatively unchanged.  For Heracliteans as for Buddhists, it's flux all the way down.

Law taxes Heraclitus with an illicit inferential slide from

The river jumped into the second time is not qualitatively the same

to

The river jumped into the second time is not numerically the same.

But there is no equivocation on 'same' unless we can sustain a distinction between the thing and its properties.  Is this distinction unproblematic?  Of course not. It reeks with problems. Just what is a thing in distinction from its properties?  A Bergmannian bare particular? An Armstrongian thin particular? An Aristotelian primary substance? There are problems galore with these conceptions. Has anyone ever really clarified the notion of prote ousia in Aristotle? Nope. Is a thing a bundle of its properties? More problems. And what is a property? An abstract object? In what sense of 'abstract'? A universal? A trope?  Will you say that there are no properties at all, only predicates?  And what about the thing's HAVING of properties? What is that? Instantiation? Is instantiation a relation? If yes, does it sire Bradley's Regress?  Are properties/concepts perhaps unsaturated in Frege's sense?  Can sense be made of that?  Is HAVING some sort of containment relation? Are the properties of a thing ontological constituents of it? And what could that mean? And so it goes.

We are presented with a puzzle and a seeming absurdity: There is no stepping twice into the same river. The Moorean rebuttal comes quickly: Of course, there is! Common sense, convinced that it is  right, attempts to dissolve the puzzle by making a simple distinction between numerical and qualitative identity.  The dissolution seems to work — but only if we remain on the surface of the troubled waters. Think a little more and you realize that the distinction presupposes a deeper distinction between thing and properties. But now we are launched into a labyrinth of ontological problems for which there is no accepted solution. The unclarity of the individual-property distinction percolates back upwards to disturb the numerical-qualitative distinction. 

Law has not definitively solved the Heraclitean puzzle.

The Numerical-Qualitative Distinction is Valid at the Level of Ordinary Language

We need to make the distinction, of course: it is fallout from, and exegesis of, ordinary usage.  'Same' is indeed ambiguous in ordinary English. The distinction does useful work at the level of ordinary language. The Heraclitean, however, need not be taken as contesting, at that level, the truth that one can step twice into the same river.  He is making a metaphysical claim: there is in reality, below the level of conventional talk and understanding, radical flux. If so, there is nothing that remains self-same over time, such as a river,  into which one can step twice.

Summary

To think clearly and avoid confusion one must observe the distinction between numerical and qualitative identity. But this distinction, which is serviceable enough for ordinary purposes, rests on a distinction, that of individual and property, which is metaphysically murky. Therefore, the common sense distinction cannot be used to dispatch the Heracliteans' metaphysical claim.

The deep metaphilosophical issue here concerns the role and status of Moorean rebuttals to seemingly crazy metaphysical claims. The illustrious Peter van Inwagen famously denies the existence of artifacts.  But he is not crazy, and you won't be able to blow him out of the water with some simple-minded distinction.

See Peter van Inwagen, Artifacts, and Moorean Rebuttals 

Comments

[Josh]

Thanks for the post. I think you're spot on regarding Law's question-begging "refutation" of Heraclitus. Would you countenance a further metaphilosophical distinction between "Moorean facts" and something like a quasi-religious philosophical intuition? This is off the top of my head, but I'll try to clarify.

It seems that Moorean facts are marked not only by the fact that they are indemonstrable and "obvious," but also by the fact that they seem to be the objects of convictions that are more or less "neutral" with respect to larger metaphysical programs considered as wholes. For example, the numerical-qualitative distinction seems like it is open to a wide variety of big-picture metaphysical theories.

The quasi-religious philosophical intuitions that I'm thinking of seem similar to Moorean facts in the sense that they are indemonstrable and "obvious," but differ in that they amount to foundational motivations suffusing a metaphysical program in its entirety. For example, one could be a Heraclitean about change not due to some isolated skepticism about the numerical-qualitative distinction, but rather due to some implicit or explicit commitment to the utterly tragic nature of human intellectual striving, or something like that.

I hope this isn't too opaque.

[Thomas]

I am reminded here of Aristotle when he says that we may never know what substance is (I cannot for the life of me remember where he said this, but it is in the metaphysics somewhere). For such a man to say a thing like that is, I think, remarkable. But it does get me down sometimes. With so many competing theories and no consensus, what is one to do? Simply pick the one he likes best or the one which aligns most closely with his own convictions? Perhaps, BV, you would agree with Aristotle here that we can only gain as much precision as the subject matter will allow? What is one to do then?

[Valeriu]

Two objects that are numerically identical are also qualitatively identical (and surely they are one and the same object). By way of consequence, two objects that aren't qualitatively identical aren't numerically identical. So, if R1 (river at first jump) is qualitatively different from R2 (river at second jump), then R1 is numerically different from R2.

You say:

"Law taxes Heraclitus with an illicit inferential slide from

'The river jumped into the second time is not qualitatively the same'

to

'The river jumped into the second time is not numerically the same'."

But this is perfectly licit as long as we affirm "if A and B are numerically identical, then they share all properties, in which case they are qualitatively identical".

The problem is, of course, as you suggest, that we usually admit that one and the same object can have different qualities at different times. It seems to me that Stephen Law's "solution" is based on a different understanding of the distinction between the two senses of identity (and on this different understanding is primarily based your disaccord). By this understanding, we must admit that two numerically identical objects may be or not be qualitatively identical.

[BV]

Thomas,

One should not pursue false precision. The Stagirite is right: one cannot expect the precision of mathematics in the field of ethics.

The problem, however, is not that philosophy lacks precision, but that there are no solutions, acceptable to all competent practitioners, to any of its problems.

What philosophy teaches us, above all, are the limits of our understanding and the infirmity of finite, discursive reason. This humbles us, which is good. When we penetrate the depth and insolubility of the problems of philosophy we come to appreciate, among other things, how stupid are the scientistic solutions offered by people like Jerry Coyne and other scientisticists -- to coin an ugly name for an ugly animal.

Law's essay is about scientism.

[Opponent]

How does this engage with Law’s claim that ‘philosophical questions are for the most part conceptual rather than scientific or empirical and the methods of philosophy are, broadly speaking, conceptual rather than scientific or empirical’? The Heraclitus example is meant to support that.

Your discussion suggests you have a broader disagreement, yes?

[Opponent]

Sorry, just spotted your comment immediately above. Right, so philosophical problems are not like Law's other example, i.e. the 4 people and the family relationships, which he rightly says has a clear solution, although conceptually difficult. You are saying that philosophical problems are essentially of a different nature from these mind-puzzles, I think.

[BV]

Yes, phil. problems are not like the family relationships puzzle. One reason is that the latter has no specifically philosophical content. A second reason is that it is not clear that puzzles about change and identity over time are conceptual. What is clear is that they are non-empirical. But one can't assume that what is non-empirical must be conceptual.

There are conceptual truths, e.g. 'A triangle is a plane figure but a sphere is not.' The truth -- if it is a truth and I think you will agree that it is -- that nothing can have properties unless it exists is not a conceptual truth, but a substantive truth of metaphysics. After all, there is nothing in the concept of a thing having properties that requires that such things exist! You can't refute Meinong that easily.

Obviously, much depends on what a concept is. Consider the question: What is a concept? That's not an empirical question. Is it a conceptual question? Not obviously.

[BV]

My working hypothesis is that the problems of phil are genuine but insoluble by us.

So I tested my hypothesis against Law's solution of the Heraclitean puzzle he describes. (By the way, I am not concerned with the historical question of what the Sage of Ephesus actually maintained.) I found Law's sol'n to be no sol'n at all. It is superficially plausible but doesn't stand up to scrutiny.

[BV]

Valeriu writes,

>>Two objects that are numerically identical are also qualitatively identical (and surely they are one and the same object). By way of consequence, two objects that aren't qualitatively identical aren't numerically identical. So, if R1 (river at first jump) is qualitatively different from R2 (river at second jump), then R1 is numerically different from R2.<<

This is tricky. We have to distinguish the synchronic from the diachronic cases. Your first and second sentences are true. The first is a version of the Indiscernibility of Identicals; the second its contrapositive, the Discernibility of the Diverse.

These principles undoubtedly hold at a time. But what about over time?

Let's consider a simpler example, a nice British example. Apparently, the Brits use pokers to stir up the fires in their 'rooms.' Or at least they used to.

Suppose poker P is hot at t1 but cold (not hot) at t2 later than t1. You may be arguing that Hot Poker (P at t1) is qualitatively different from Cold Poker (P at t2) and that therefore that Hot Poker and Cold Poker are numerically different. But then you have an argument for temporal parts, an argument that supports a quasi-Heraclitean position. P on such a scheme would be a diachronic bundle of temporal parts, each num. distinct from every other one such that there is no one poker that remains numerically self-same over the temporal interval.

Is that what you have in mind?

[BV]

Josh,

Thanks for the comment, but you need to be clearer. Are you suggesting that the data of Revelation could be taken as Moorean facts within the purview of say, Christianity?

E.g., that we are fallen beings is not, strictly speaking, a Moorean fact, but it is obvious to many, and a kind of datum, a datum of Revelation which is abundantly confirmed in the horrific events of human history.

[Opponent]

Why is this a Brit example? What implement do Americans use to stoke up their fires? And do you not have 'rooms' like us?

[Valeriu]

BV,

Not exactly. What I have in mind is that Law sees the numerical identity as only overlapping the qualitative identity, such that num.id. doesn't imply qual.id. In this understanding, one object can remain the same over time, even if its qualities change.

[Thomas]

Dear BV,

I find that interesting that you think the problems of philosophy are genuine but insoluble by us. Do you know of any thinkers of who wrote about this idea, or have you published anything on it? I would love to read more about it.

[BV]

Thomas,

Benson Mates maintained the thesis, and I am trying to finish a book on the topic. I marshall inductive evidence for the thesis and then try to work out a conception of what philosophy is good for should the thesis be true.

[BV]

Sorry, Opponent. No offense intended. I was thinking of McTaggart's poker example, and the book *Wittgenstein's Poker* -- yes I know Ludwig was an Austrian -- and L. W.'s brandishing of a poker in his debate with Karl Popper, and the expression which sounds slightly odd to my ears, of say 'visiting so-and-so in his rooms at King's College' whereas we would say 'in his office.'

[Astute opponent]

Ah right! Not an expert on Oxbridge terminology but always thought 'rooms' were what we call a 'flat', US 'apartment', or 'suite'.

A bedroom or two and facilities, plus a living room with a desk and an armchair and a fire. Gilbert Ryle lived most of his life in his college 'rooms'.

[Thomas]

I look forward to your upcoming book!