Monday, February 7, 2011

Bertrand Russell on Aggregates

Picture taken and copyrighted by Terry Cryer, and posted here on the basis of fair use.
"It is important to realize that a whole is a new single term, distinct from each of its parts and from all of them: it is one, not many (i.e. - it is of the same logical type as its simple parts), and is related to the parts, but has a being distinct from theirs. The reader may perhaps be inclined to doubt whether there is any need of wholes other than unities; but the following reasons seem to make aggregates logically unavoidable, (1.) We speak of one collection, on manifold, etc., and it would seem that in all these cases there really is something that is a single term. (2.) The theory of fractions, as we shall shortly see, appears to depend partly upon aggregates. (3.) We shall find it necessary, in the theory of extensive quantity, to assume that aggregates, even when they are infinite, have what may be called magnitude of divisibility, and that two infinite aggregates may have the same number of terms without having the same magnitude of divisibility; this theory, we shall find, is indispensable in metrical geometry. For these reasons, it would seem, the aggregate must be admitted as an entity distinct from all its constituents, and having to each of them a certain ultimate and indefinable relation."

- Bertrand Russell, The Principles of Mathematics, 1903

A lot of my discussion with Jan Helfeld yesterday centered around the nature of "society" as a unit of analysis, with Jan holding the view common to a lot of libertarians that society is just the thing we call a bunch of individuals, but that only individuals have agency. That only individuals have "agency" may be a specific proposition I could accept, but I couldn't simply accept the assumption that aggregates like "society" are lacking in an independent meaning. Agency implies some conscious direction of action, which is obviously an odd way to think about "society". But surely we can think about non-conscious actions, right? We are composed, after all, of "selfish genes" which evolutionary biologists consider to be the appropriate unit of analysis. From the perspective of biology, it is the organism itself that is a somewhat incidental aggregate of the true unit of evolutionary action: genes. But of course, the aggregate that is the organism is not an insignificant aggregation for biologists at all! For some reason, aggregating up from individuals causes people more trouble than aggregating up to individuals.

John Dewey wrote that "Society in its unified and structural character is the fact of the case, the non-social individual is an abstraction arrived at by imagining what man would be if all his human qualities were taken away. Society, as a real whole, is the normal order, and the mass as an aggregate of isolated units is the fiction". I shared this with Jan and his reaction was interesting - he thought that I was saying (through Dewey) that individuals were fictions, which obviously wasn't what Dewey said at all. Dewey simply said that this view of atomized individuals with independent agency who just happened to find themselves in groups every once in a while is a fiction. I suggested that the way he understands individuals is a fiction. But of course that's not saying individuals are a fiction.

This is all very hard to conceptualize, though, because our brains are individual brains so they've evolved to understand us as individuals. We still have a tough time accepting Dawkins' selfish gene concept and selection at the genetic level for precisely this reason. The very way we've come to define meaningful units of analysis is based on an understanding of agency grounded in the human brain. But of course there's no obvious reason why this unit of analysis should take precedent, and in lots of cases we find that the world simply doesn't make sense unless we look at the world from a different unit of analysis. A lot in evolutionary biology didn't make sense until we started looking at the gene. A lot in social science didn't make sense until we started looking at society.

But it's nevertheless very hard to talk about. It's not clear to me, though, that the solution is that that which is hard to talk about isn't real or significant. Society seems to have a very real independent significance. Does anyone know anyone who has treated this issue in a useful way? I know several of the prominent Austrians, for example, who insist that the only appropriate unit of analysis is the individual. I know that case and I'm not especially interested in that.

14 comments:

  1. I do think that there are a lot of "Austrians" (mostly amateur economists) who have stressed the importance of the individual, and who have discarded aggregation as a product of the Keynesian macroeconomic revolution. In fact, there may be professional Austrians would feel similarly. I think I've been pretty consistent in arguing that in reality the Austrian focus is neither entirely on the individual nor on the aggregate. Austrians argues that aggregates are composed as individuals, but that in order to understand the impact of the individual you need to consider the aggregate.

    As a closely related metaphor, take Hayek's point in P&P that in order to understand a piece of the (economic) pie you need to incorporate it into the whole, but Hayek nevertheless studied a piece of that pie (price theory).

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  2. And its not just the amateurs - Mises and Rothbard talk a lot about this too. They will say that only humans act, when we say the government "does something", we really mean that certain individuals do things.

    On a superficial level, I'm not contesting this at all. Insofar as human aggregates "act" they (1.) don't do so consciously, and (2.) appear to do so through the agency of individuals. It's not an amateurish observation - but I don't think it's a complete observation either, and I just not interested in being furnished with those claims because for one thing I agree with them, and for another thing they miss my point.

    The question for me is, are these aggregates (and perhaps its better to talk of "institutions" rather than things like "society") significant actors and units of analysis. Jan Helfeld responded to this claim of mine by saying "Have you ever seen society ride a bicycle? Have you ever seen society eat an apple?", to which I responded "no, but I haven't seen a bunny rabbit ride a bicycle either". Helfeld, I think, focused on some incredibly superficial things and tried to leverage a claim out of it. I don't think that was legitimate. But in making that attempt, he does clearly highlight how hard it is to talk about these non-tangible things, or to talk the way Dewey does about the social as co-terminous with the invidivual (and that there is no invidivual apart from society). It's very hard to do, and I'm curious if anyone else has sufficiently navigated these problems.

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  3. "They will say that only humans act, when we say the government "does something", we really mean that certain individuals do things."

    Would you disagree? My professors always talk about assuming the state as an actor, but then contradict themselves when they focus on the corruption of certain individuals within that bureaucracy. The fact is that a bureaucracy is made of individuals, and that bureaucracies as a whole don't act, and so it's absurd to call the state an actor.

    However, neither Rothbard nor Mises avoided the state as an aggregate. In fact, the fact that they consistently refer to the "state" is evidence enough that they do consider this aggregate relevant.

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  4. No, definitely not - that's what I was trying to make clear. I don't disagree with this view.

    What I think is much harder is answering questions like:

    1. Are these acting individuals atomistic or are they somehow co-terminous with an aggregate like "society"?

    2. Are these acting individuals indeed atomistic, but are they acting as an agent of legitimate aggregate like "society"

    etc. etc.

    So no, the whole point is I'm totally fine with this point, but I would not extend that to other claims (ie - I would not use that to try to answer those two questions). I would not use that, as Jan Helfeld does, to rule out the idea of an aggregate as a meaningful entity appart from its constituent parts.

    That does not mean I am well equipped to talk about it as an entity. But it's not surprising we're not well equipped - our brains our maintained within individuals. It's not surprising we have trouble thinking and talking about other units of analysis.

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  5. I think that part of the point of saying that governments don't act is to highlight that *information is lost* when you assume some kind of unity of purpose among all of the people who hold government jobs. You don't want to forget that individuals have private motives that they give expression to as they carry out official duty.

    That said, obviously you're right that 'society' is a meaningful concept, and one that (if well-defined) can be the basis for analysis. I think the definition part is lacking - and for good reason because it's hard to know what to leave out and what to include. The notion of 'society' is enormously complex. Way more complex than, say, conceptualizing the gravitational interactions among n bodies...

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  6. Ooh, this brought to mind a good article (that I might have already posted here or you might have already seen, its a few months old and I don't remember) by Julian Assange. His outline of individuals thinking and acting as connected graphs is spot-on, I think, and it gives a good perspective of what his goals with Wikileaks really are (or at least were, in 2006):

    http://cryptome.org/0002/ja-conspiracies.pdf

    And an analysis of it:
    http://zunguzungu.wordpress.com/2010/11/29/julian-assange-and-the-computer-conspiracy-%E2%80%9Cto-destroy-this-invisible-government%E2%80%9D/

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  7. Wonderful, nickn - thanks. I'm going to digest this and perhaps post on it tomorrow.

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  8. Interesting topic and quotations. I agree with much that has been said above, but would also emphasise that much of my interest in what constitutes "society" is derived from the fact that we can't necessarily extrapolate from the individual to the whole... Indeed, they may even be in direct conflict.

    Because these aggregate results (i.e. not averages) can differ from what we might guess simply by looking at individual behaviour or motivations, they warrant a higher level of analysis. (That being said, the advances in agent-based modelling make it a particularly interesting way to scale up the analysis from the individual to society as a whole.)

    Lastly, there are also some important phenomena that are only relevant in the context of larger groups, e.g. identity theory and crowd psychology. Using current events as an example, I don't think you couldn't understand what is happening in North Africa by looking only at individual grievances... Clearly, its a big part but you have to understand the dynamics of group psychology to get an idea of why the uprisings occurred so explosively.

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  9. The difference, I believe, comes from perspective.

    I am inclined to believe a market economy is a network of individuals, and the functions and derivations of it can be studied via methodological individualism (yes, even things like the interest rate and money).

    You, on the other hand, for reasons inscrutable to me, seem to view a market economy as a process or a system - one that is explained by reference to parts but somehow transcends them. You have never given me a good reason why you hold this position.

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  10. Mattheus -
    First, I'm not caught up on language - I think networks can be descriped as processes or systems if they follow a process or are systematic in some way (which the market is). I've told you several times in the past I see the market as a network. This is the whole point of the division of labor, after all - integrating a greater number of distinct units more than proportionally increases the efficiency of the system. That's the behavior of a network.

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  11. I go with the argument that the rise of the modern nation provides for an intellectual framework for individualism. That's the real contribution of Hobbes in a way.

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  12. The photo of Bertrand Russell on this web site is my copyright, what makes you think you can you can just rip it off, do you not realise that this is theaft of property. get it off the site. as proof of my ownership consult the Corbis web who have sole commercial rights to this image. Terry CRyer

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    1. It's hard to take an anonymous commenter seriously on an issue like this. I post material on here under the assumption of fair use. This blog is for education and the dissemination of research. I specifically don't allow advertisements here so that "fair use" status is maintained.

      If you could actually demonstrate you are who you claim to be - say, by emailing me - I'm happy to take it down if that's really what you prefer, even though I am using it well within the bounds of fair use. Of course what would be better for both of us, I think, is for you to just acknowledge the fair use of the photo and grant permission to use it.

      In future correspondence, I'd prefer you not accuse me of trying to "rip it off".

      re: "as proof of my ownership consult the Corbis web who have sole commercial rights to this image."

      I am not using the image commercially.

      Delete
    2. I also meant to mention - please note the caption I added to the photo.

      Delete

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