A very quick note to complement my last reply to Jim. Pile of term papers to mark.
Today, I believe, the most general and powerful way to think of social agency/structure (e.g. valuation/value or "society" for short) at each point in time is as a "fixed point" -- or, if you prefer, as a "fixed set." It must be so; otherwise society would not jell. And societies exist at each point in time, until they don't. They retain their "quality," though their "quantity" stretches and stretches until it makes the "quality" snap. Therefore, they are f(x)=x type of thingies. Again, until they are not, but exclude that possibility for now. In his own way, it seems clear to me that Marx had this much down in his brain. The real difficulty is of course describing the stuff that happens within x, which is what physicists call a "functional model" or a "functional system" (a functional is a function of functions). The arguments in the functional model x are the individual actions (e.g. individual allocations a.k.a. individual valuations), where the model describes specifically how these individual actions impinge on one another. The reproduction scheme in volume 2 is a simple case of this, where time is discrete, we have "representative agents" (the "capitalists" and the "workers" from each department) rather than individuals, there's perfect foresight, etc. Not bad for a guy who'd have been 195 just yesterday. This fixed point convergence is necessarily true for society as a whole, and it must also be true for each concrete individual social structure (and for each one of us), to the extent it keeps up with the world. So, if you ask me what would be the most profitable avenue for a young man to truly grasp Marx's value theory today, I'd say study Marx but also study duality: Slutsky, Hicks, Roy, Shephard, et al. Mind Marx's advice: the key to our ape ancestor's anatomy lies in today's human anatomy. And please, do *not* take any of these people literally. They do not have to know all they're talking about. But you should try to know it. You have the benefit of hindsight. Quantities $q$ (discrete chunks of wealth) and their measures of "social importance" (e.g. values, $\lambda$) are dual to each other: q(~ x) = ~ \lambda(x) = productive force of labor(x). Something like that. Again, x is the functional model, where the game is played. Humanity is all about producing humans by means of humans, society is all about producing social structures by means of social structures -- and social structures are the forms (mathematical transformations, measures) of the productive forces of labor. I am trying to figure out ways to explain this to my students in the simplest terms. Because, once we grasp this (and the only way to truly grasp it is by staging social revolutions that get us closer and closer to our unity as producers) we'll realize that our power (or freedom) to produce and redesign our social structures is much but much greater than we ever thought. fwiw. _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
