Paul Cockshott wrote: > The points you raise about vector spaces get to the heart of the issue. > There exists no unique ordering on a vector space of dimension greater >than 1, and since many economic configurations can be represented as > vectors : vectors of different material inputs, vectors of consumer goods, > vectors of labour distributed into different tasks this immediately poses > problems as soon as you want to make a choice between configurations. Such > a choice requires the existence of an ordinal scale and thus a mapping > function from the vector space onto a numeric scale. A system of > multipliers like prices is one way to do it, but in principle a non linear > function can be used as is done in some more recent algorithms for linear > programming or in some computable general equilibrium models.
Yes indeed, we've reached agreement that whether a multi-dimensional measurement can be reduced to a single number is a crucial issue. But no, there is *no* reasonable way to map a two or more dimensional vector space onto an ordinary numerical scale without losing essential information. Period. That's the end of the story. It isn't a matter that this is a complicated problem. It isn't a matter that one can use fancy methods of linear programming to do this. Or shadow prices. Or Lagrange multipliers. Or non-linear functions. Or whatever. It simply isn't possible. A two-dimensional vector space, for example, obeys different laws than a simple numerical scale. That's no way around this. Or, to put it another way, if one reduces a two-dimensional vector to a single number, one loses essential information. Back, for a moment, to the example of a flat two-dimensional map. The location can be represented by a vector of two numbers, say, <3,4>, representing 3 miles north and 4 miles east. Suppose one tries to reduce these two numbers, 3 and 4, to one number. One way of doing it is by considering the distance of the location from the origin, which is 5 miles. Or, mathematically speaking, the length of the vector <3,4> is 5 (equals the square root of 3 squared plus 4 squared). Thus the vector <3,4> has been correlated to a single number, 5. This number 5 does represent something real -- the distance from the origin. But the reduction of the vector <3,4> to a number means one has lost the direction. The location is 5 miles from the origin, but in any direction. There is no way to know, from the distance 5, which direction to go. So it is impossible to plan a route to get to the location just using the single number 5. If all one knows is the 5, one is lost. There are other ways to reduce the vector <3,4> to a number. One could, for example, simply take the first number, 3 and forget about 4. The 3 tells us how far north to go, but by dropping the second number we have no idea how far east or west the location is. So that's no good either. No matter how one reduces the vector to a number, one ends up losing information. Translated into economics, when one reduces a specification of what it takes to produce something to its labor content, one loses most of the information we need to plan its production. We know a total value, such as 5 labor-hours, but don't know if this represents so much steel or so much plastic or so much carpentry labor or so much steelworking labor etc. The same figure, 5 labor-hours, could represent steel plus steelworking, with no carpentry at all, or wood plus carpentry, with no steel, or even simply 5 hours of a service. And it doesn't tell us if the labor was done in New York City or Antarctica, although the available of workers in New York City tells us nothing about whether workers are willing to go to Antarctica. So too much information has ben lost for the labor-content to be a natural or rational tool of economic calculation. -- Joseph Green [email protected] > ________________________________________ > From: [email protected] [[email protected]] On > Behalf Of Joseph Green [[email protected]] > Sent: Monday, July 18, 2011 6:27 PM > To: Progressive Economics > Subject: Re: [Pen-l] Ingo Elbe: Between Marx, Marxism, and Marxisms, Part I.3 > > >From Paul Cockshott: > > > > > [JG] No, you are wrong. You are confusing concrete human labor, which > existed > > >prior to commodity-producing society, and will continue to exist as long > as > >> human beings exist, with abstract human labor. Marx wrote in volume I of > > >"Capital" that the amount of abstract labor-time embodied in a product is > a > > >"non-natural property" of the product, something that is "purely social". > > --------------------------- > > [PC] I would be interested in exactly which passage you mean, but in > general the labour time in a product > > is something social, since it depends on the social productivity of labour, > > but that does not make human > > labour in the abstract something specific to capitalism. He says is is > > something specific to societies > > in which there is a division of labour, going to some length to illustrate > > this with non capitalist examples > > as well. > > I gave the quote immediately on in my comment when I wrote that Marx: > > ----------------------------------------------------------------------------- > wrote that when exchange equates a definite quantity of one product > with a definite quantity of another, the result "represents a non-natural > property of both, something purely social, namely, their value." (Capital, > Kerr edition,vol. I, Chapter I, section 3, Subsection 2.2.3, p. 66.) > ---------------------------------------------------------------------------- > > And Marx writes repeatedly elsewhere that equating commodities on the basis > of their labor-content means ignoring all their material properties. I've > written about this elsewhere in detail, see > www.communistvoice.org//00LaborHour.html. > > But regardless of quotes from Marx, it's clear in itself. If one equates two > things on the basis they both represent the same amount of abstract labor, > one ignores or negate their material differences, their use-value, and any > other particular aspect of them. One ignores their color, their weight, their > size, how they compare to similar products, and on and on. Some of the things > ignored may not be important, but some are. The labor content ignores many of > the things which are absolutely necessary for economic planning, and the > things that aren't ignored are aggregated together in a near-useless fashion. > > > And in particular, the labor content ignores environmental factors. If one > plans on the basis of the abstract labor-hour, one creates environmental > havoc. The "wealth" given us by nature has zero labor-content. > > Does abstract labor exist outside capitalism? Sure, it exists. The question > is whether it is a natural economic measure. > > One can define the labor content if one knows the average amount of labor > used in producing products, all the inputs (not just direct labor) that goes > into making a product, the amount of the products produced, etc. You, Prof. > Cockshott, have put a good deal of care and effort into showing how to > calculate the labor-content, and have written extensively on this. It > definitely could be done. > > The question is not whether one could calculate the labor-content in a > communist, marketless, moneyless economy, but what, if any, significance the > labor-content would have for that economy. The question isn't whether > abstract labor exists, but whether it is the major category that explains > what goes on in that economy. Or, to put it another way, the question is > whether it is the natural unit of economic calculation for that economy. > > One could weight all material products (not services). The mass of a product > is a definite measure. The mass of a product exists in any economy. But is > the mass meaningfull to explain what goes on? > > Well, the word "natural" has several different meanings. One meaning refers > to being of the material or physical world. Another meaning refers to whether > something is significant in a certain context -- for example, whether one > enjoys movies is a natural consideration for deciding whether to go to a > movie theater. > > The weight or mass of an item is a natural property in that it refers to a > material, physical property of an object. It is not, however, natural with > respect to explaining how economic exchange takes place. A diamond weighs > very little, and yet costs more than a computer. > > The labor-content is not a material property of an object. It abstracts away > from any of the physical or material properties of an object. It is a social > property of a commodity system. Social properties are actual properties.. But > it's not a material property. And since rational economic planning requires > taking account of material properties, the labor-content is an un-natural > property with respect to rational economic planning. > > One could calculate the labor-content in a future communist society. But the > main thing it is suitable for, which is being a social property in a > commodity system, is no longer relevant. > > > ---------------------- > > Joseph > > He wrote that when exchange equates a definite quantity of one product with > > a > > definite quantity of another, the result "represents a non-natural property > > of both, something purely social, namely, their value." (Capital, Kerr > > edition,vol. I, Chapter I, section 3, Subsection 2.2.3, p. 66.) > > > > The value being referred to is, of course, the amount of abstract labor > > contained in a product. If the value is a non-natural property, then so is > > the amount of abstract labor. > > ------------------------------------------------------- > > Paul > > That is true since the amount of labour contained in a product is a > relationship between the product and its conditions of production in human > society, but that is true of any society in which there is a division of > labour not specifically a capitalist society. In les " états sociaux dans > lesquels le même homme est tour à tour tailleur et tisserand" the coat would > still have required a definite amount of human energy and time, even if all > of this was done in turn by one person. > > Yes, it is true that the amount of abstract labor is a non-natural property > of a product in any society, not specifically a capitalist society. I agree. > It is not a natural unit for economic planning om any system. One of the > contradictions of capitalism is that it runs according to the law of value, > and yet value is not a natural property. > > It's true, by the way, that a coat requries a definite amount of human energy > and time, even if produced by one person. So what? You are implying that so > long as human energy is required, then the labor content is supreme. What's > what you want to prove, so you can't use it as the premise of your argument > unless you want to keep engaging in a big vicious circlle. > > Yes, labor is used in producing coats. But that doesn't make the labor > content into a natural unit. > > a) making a coat requires not just a definite amount of human energy and > time, but a specific type of human labor. The labor of brain surgery won't > create one. The labor of making a house won't create one. So it is not > abstract labor that makes a coat, but concrete labor. > > b) Making a coat requires raw materials too. > > c) Making a coat requires certain tools. > > d) Making a coat presupposes that the environment is still suitable to human > life on this planet. > > > > ---------------------------- > > Joseph > > Marx even states that this is "purely social". Well, the amount of abstract > > labor usually has some connection to the amounts and types of concrete labor > > involved, although you can't measure concrete labor simply by a number. > > -------------------------- > > Paul > > That is because a quantity of concrete labour is what is called a > > dimensioned > > type it has the type hours * coat making for example, by abstracting from > > the > > concrete character of the labour you project it down onto the sub space of > > simple > > time. > > Multi-dimensional types are very different from simple scalars. For example, > a two-dimensional vector can indicate location on a flat map (without > height). So the location might be designated as (3,4), three miles north of > here, and four miles east. The vector (3,4) is very different from the single > numbers, 3 and 4, that appear in it. The laws governing how vectors work, > and those governing how single numbers, work, are quite different. > > It is a gross mathematical error to ignore the differences between vectors > and simple numbers (scalars). In essence, this is the error repeatedly made > when concrete labor is confused with abstract labor. > > [Paul, continuing] > >This is conceptually the same operation as we perform when we abstract > > from the substance of something and consider only its weight. A we can have > > the dimensioned quantity 5 kg sugar or 3 kg salt in order to add them we > > consider > > them just as weight, put them both on the scales and find we have 8kg of > > mass > > ignoring the substance. The abstraction operation for obtaining 8 hours > > labour time in > > general from 5 hours of coat making and 3 hours of spinning is conceptually > > identical. > > The problem is that you start this analogy, but you don't finish it. > Yes, you can combine 5 kg of sugar and 3 kg of salt to end up with 8 kg of > stuff. But is that a meaningful figure? > > Let's see. Suppose you are going to the grocery store. Does your shopping > list only specific that you need 8 kg of stuff, or does matter whether you > buy salt and sugar, or apples and oranges? > > Suppose someone is baking a very very big cake for salt addicts. Does the > recipe only specify 8 kg of stuff, or does it specific 5 kg of sugar and 3 kg > of salt? > > Suppose a patient is taking medication. Over a year, does the patient simply > take 8 kg of any tablets that happen to be in the pharmacy, or 5 kg of a > specific medication and 3 kg of another medication. > > The 8 kg figure is a non-natural figure for grocery shopping, for recipes, > and for medications. > > It may be a natural figure for certain other purposes. For example, if one > is trying is lift something, it is important to know how much it weighs. > > So it isn't enough to say that it is possible to abstract from the material > properties of an object and get a single figure. The point is -- is that > single figure useful and natural? > > > > ------------------------- > > Joseph > > So > > what Marx is the stressing is that the very process of reducing concrete > > labor to abstract labor, and hence measuring it with a single number (the > > amount of abstract labor, the value), is something that is "non-natural". > > ------------------ > > Paul > > Where exactly does he state that or is it an inference you are making? > > In general such a reduction of the concrete to the abstract is not > > unnatural, > > the equivalence of gravitational mass is a natural instance of such an > > abstraction process. > > The process of abstraction means ignoring certain things. Whether the result > is natural or unnatural, depends on whether it makes sense to ignore those > things. I just gave you various examples of that with respect to the weight > of things. > > Of course, if you want to calculate the gravitational attraction of two > things, then the mass is a very natural quantity. (It is natural in two > distinct senses: it is natural to the problem of gravitational attraction, > and it is natural in that it refers to a physical, natural property of a > thing.) If one wants to deal with a certain social phenomenon, the economic > weight of a product in the marketplace, then the labor-content is very > important, and the mass is not. > > The law of labor-content (the law of value) shows how capitalism operates. So > Marx doesn't say that the labor-content is a chimera. On the contrary, it is > very important, but it is a social property of a product. In an economy > without marketplaces and commodities, this social significance is gone. The > labor-content can still be calculated, if one wants to, but it loses most of > its significance, because it is a non-natural property. (I say "most" here, > because in my article on the labor-hour, I show how a *modified* labor- > content might retain a certain subordinate role in a communist economy. But > even handling that role correctly requires realizing that it is an un-natural > measure.) > > > But in the case of the products of human labour > > you can argue that the labour embodied in them is always a social > > rather than a natural reality since the labour is always done in the context > > of some form of human society. > > Yes, there always is a social aspect to products of human labor. But there > are lots of social properties aside from the labor-content. It's an > elementary logical flaw to conclude from the fact that the labor-content is a > social property, that all social-properties are the labor-content. > > But of course coats or spun linen are > > very un-natural objects anyway. > > Oh ha, ha, ha. You've gone post-modernist, have you? > > Coats and spun linen have a physical reality and physical, material > properties. They are natural in that sense. > > Coats and spun linen are important for economic planning for the needs of the > people. They are natural for that problem as well. > > Coats and spun linen are produced for human use. In that sense they are > social. But actually, that doesn't make them un-natural. > > > > > > > Paul Cockshott wrote: > > > The claim that only a capitalist market allows the measure of abstract > > > socially necessary labour time turns Marx onto his head and reads him > > > without his advocacy of communism. > > Joseph > > One could,in any society, seek to define and measure the amount of abstract > > labor in a product, but what one would obtain is a "non-natural property" of > > a product. This "non-natural property" could be defined, but it would have > > lost its significance. > > ------------------ > > Paul > > Not at all, for example you can construct aircraft out of titanium or > > aluminium, but > > it requires much more labour to manufacture them out of titanium, this fact > > will > > be significant to any aircraft industry whether socialist or capitalist. > > What matters is the total resources used for the production of aircraft, the > environmental affects of the aircraft and of the production processes > (including mining, smelting and refining the metals), and the affects this > has on the workers themselves. The labor-content is an un-natural measure of > this. It ignores totally the environmental issues; it ignores a number of > issues concerning the affect on the workers; and, with respect to the many > things which it does take account of it, it aggregates them together in a way > that is unnatural. > > At times, you admit much of this. You yourself write of the environmental > havoc that would be created by planning simply on the basis of the labor- > content. But then, in theory, you ignore it. > > Joseph Green > [email protected] > _______________________________________________ > pen-l mailing list > [email protected] > https://lists.csuchico.edu/mailman/listinfo/pen-l > > The University of Glasgow, charity number SC004401 > _______________________________________________ > pen-l mailing list > [email protected] > https://lists.csuchico.edu/mailman/listinfo/pen-l ----------------------------------- Joseph Green [email protected] ------------------------------------ _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
