## Marx's Value Theory

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I've decided to revisit Marx's value theory after a long absence of dealing with it. The central features of Marx's value theory are presented in Capital Vol 1 Chapter 3. I'm assuming that readers of this thread are sufficiently familiar with basic Marxist concepts that I don't need to introduce them. First I'm going to go through the text, annotating and summarising. Second I'll condense what I've written into some summaries and exegesis.

Unlike the exegesis of Marx inspired value theory you find in the literature, I frame things mathematically where appropriate. So here we go.

Throughout this work, I assume, for the sake of simplicity, gold as the money-commodity.

I've seen it claimed that Marx's value theory no longer works because we transitioned from gold to paper money. You can see from the start that this is based on a misreading (though you can find Marxists that reject the value theory because of its reliance on the gold standard). Marx thinks of the gold as an exemplar of the money-commodity rather than its essential constitution.

The first chief function of money is to supply commodities with the material for the expression of their values, or to represent their values as magnitudes of the same denomination, qualitatively equal, and quantitatively comparable. It thus serves as a universal measure of value. And only by virtue of this function does gold, the equivalent commodity par excellence, become money.

It's quite easy to pass this over without noticing some subtleties. Money supplies commodities with the material for expression of their values. Contained in this statement is the underlying assertion that the expression of the values of commodities must always have a physical form, even if value is an ideal category; real abstraction in the jargon.

Reading with a Deleuzian lens, a real abstraction can be thought of as composite series correlated over different ontological strata. EG: The attribution of Tesla's stock tanking (even more) to Elon Musk smoking a blunt with Joe Rogan couples: (social norms of competence and leadership in business) with (the physical consumption of a particular good; pot), (the aggregate of those two sub processes to a negative opinion), (the negative opinion being expressed in the 'animal spirits' of the stock market), which finds its economic expression in the selling of Tesla stock and their subsequent reduction in value. The metaphysics of capital regularly couples processes with different 'substances', and this metaphysics occurs as part of the development of capital.

Much could be said about the use of 'expression' as a substitution for dealing with how one ontological stratum pulls others with it, suffice to say for now that the analysis works so long as the bracketed events are (strongly) correlated and did indeed happen; in absence of any metaphysical guarantees.

It is not money that renders commodities commensurable. Just the contrary. It is because all commodities, as values, are realised human labour, and therefore commensurable, that their values can be measured by one and the same special commodity, and the latter be converted into the common measure of their values, i.e., into money. Money as a measure of value, is the phenomenal form that must of necessity be assumed by that measure of value which is immanent in commodities, labour-time. [1]

A commodity is equivalent to its price as expressed in money. This equivalence is as much an ideal equivalence of numerical equality as it is a social arrangement drives that numerical agreement. Spelling out this duality and claiming that it was recognised as a real feature of capital is essentially what footnote (1) does:

The question — Why does not money directly represent labour-time, so that a piece of paper may represent, for instance, x hours’ labour, is at bottom the same as the question why, given the production of commodities, must products take the form of commodities?

The ability for a money price to signal the equivalence of commodities in value is recognised to require the equivalence of commodities in value. This requires that productive activity be organised socially in a manner that produces values as well as useful goods and ties the two together (in the above sense of creating and reinforcing a real abstraction). This references the previous chapters in Capital where Marx develops his distinction between use and exchange values, and tries to show that the money price of a commodity tracks the socially necessary labour time for its production.

Note that the claim here is as much empirical as it is metaphysical, Marx says that production under capital really is the production of values which are ultimately commensurable due to being products of labour. This sets the stage for the analysis of surplus value extraction.

It's also often said that the extraction of surplus value is what ensures that a capitalist mode of production creates value. While it's true that the extraction of surplus value creates a numerical excess of values there still needs to be an account of the conformability of the commodities in terms of their value; this requires both a historical and a logical component, Marx accounts for both of these later.

An under appreciated feature of surplus value extraction is that value must be calculable, which is facilitated by the most developed value forms.

The expression of the value of a commodity in gold — x commodity A = y money-commodity — is its money-form or price. A single equation, such as 1 ton of iron = 2 ounces of gold, now suffices to express the value of the iron in a socially valid manner. There is no longer any need for this equation to figure as a link in the chain of equations that express the values of all other commodities, because the equivalent commodity, gold, now has the character of money. The general form of relative value has resumed its original shape of simple or isolated relative value. On the other hand, the expanded expression of relative value, the endless series of equations, has now become the form peculiar to the relative value of the money-commodity. The series itself, too, is now given, and has social recognition in the prices of actual commodities. We have only to read the quotations of a price-list backwards, to find the magnitude of the value of money expressed in all sorts of commodities. But money itself has no price. In order to put it on an equal footing with all other commodities in this respect, we should be obliged to equate it to itself as its own equivalent.

Imagine we've stepped back in time before the capitalist mode of production was widely adopted, we still have trade networks. Networks of trade provide (somewhat location specific) series of equivalences of possible trades. Like 2 sheep = 1 cow, say. Cows could be traded for others things, say 2 cows for 5 pigs, and the total set of pairs of goods which will be traded is termed the 'expanded form' of value. This does not require that we say 1 cow is equal to 2.5 pigs as a matter of concrete history, but it does contain within it the logical (and real) possibility of commensurating these goods as expressions of an underlying value.

As Marx points out, though:

On the other hand, the expanded expression of relative value, the endless series of equations, has now become the form peculiar to the relative value of the money-commodity. The series itself, too, is now given, and has social recognition in the prices of actual commodities

the commensuration of the trade networks and the expression of each network as a specific value is a feature of value in the capitalist mode of production.

The different forms of value operative in Marx's analysis are simultaneously logical determinations about trade and the social embodiment of those logical determinations. Assume we have a set of all goods X, and we have a relation T on X which codifies which specific goods can be traded for other specific goods.

The simple form of value is the mere establishment that an amount of a good is as valuable as itself; and of the equivalence of that good to another in a specific trade. This means T consists of all pairs of goods which have actually been traded, in absence of any merely ideal equivalences. This means that the simple form of value has T consisting of all pairs of goods with themselves, and the various concrete trades which have happened. It is the minimal reflexive relation on the set X with some unstructured (read, historically specific to specific barter economies) bumf. This is more of a logical assumption about value than the description of a historical circumstance of value, even as it is contained in trade from barter economies up.

The relative form of value is the establishment that an amount of a good x and another good y are as valuable as each other. This means that T consists of all pairs of goods which can be traded, and of each good with itself as a pure marker of the existence of commensurability. When we have the relative form of value, we can take an amount of a good x and construct the set:

$\{ y \in X | xTy \}$

also noting that if xTy then yTx logically and concretely as modelling the stance agents holding those goods and trading them take. This establishes for the first time the symmetry of the value relation. It is now symmetric and reflexive.

Note at this point that there is no guarantee of transitivity, this means that the following implication does not yet apply:

$xTy \& yTz \rightarrow xTz$

due to the local specifities of trade. It might be that 1 cow here is 3 sheep, but in a colder place perhaps 2 sheep are 1 cow. The form of value here has various non-commensurable trade networks built in as a feature.

The price or money-form of commodities is, like their form of value generally, a form quite distinct from their palpable bodily form; it is, therefore, a purely ideal or mental form. Although invisible, the value of iron, linen and corn has actual existence in these very articles: it is ideally made perceptible by their equality with gold, a relation that, so to say, exists only in their own heads. Their owner must, therefore, lend them his tongue, or hang a ticket on them, before their prices can be communicated to the outside world. [2] Since the expression of the value of commodities in gold is a merely ideal act, we may use for this purpose imaginary or ideal money. Every trader knows, that he is far from having turned his goods into money, when he has expressed their value in a price or in imaginary money, and that it does not require the least bit of real gold, to estimate in that metal millions of pounds’ worth of goods. When, therefore, money serves as a measure of value, it is employed only as imaginary or ideal money. This circumstance has given rise to the wildest theories. [3] But, although the money that performs the functions of a measure of value is only ideal money, price depends entirely upon the actual substance that is money. The value, or in other words, the quantity of human labour contained in a ton of iron, is expressed in imagination by such a quantity of the money-commodity as contains the same amount of labour as the iron. According, therefore, as the measure of value is gold, silver, or copper, the value of the ton of iron will be expressed by very different prices, or will be represented by very different quantities of those metals respectively.

Combining the previous 2 things I bolded highlights the non-transitivity of the expanded value relation due to an insistence on concrete capacities for trade as relative values. In reverse order:

The price or money-form of commodities is, like their form of value generally, a form quite distinct from their palpable bodily form; it is, therefore, a purely ideal or mental form. Although invisible, the value of iron, linen and corn has actual existence in these very articles: it is ideally made perceptible by their equality with gold, a relation that, so to say, exists only in their own heads.

There is no longer any need for this equation to figure as a link in the chain of equations that express the values of all other commodities, because the equivalent commodity, gold, now has the character of money.

And inversely, it caricatures the money form thusly: the money form consists in applying this transitivity condition in the abstract (which was always a real possibility of the expanded form) and in the aggregate agreeing to and applying this transitivity condition. It is only at this point that value as a universal equivalent emerges in the analysis. Everything becomes commensurate with gold, just as gold becomes commensurate with everything. This universal commensurability is a precondition for the development of any money commodity, and the universal commensurability becomes a concrete social practice to the extent that one commodity is really used for the expression of value for all things in the expanded form.

Note that pre-capitalist trade networks, when exposed to trade which features the universal equivalent form of value can be forced to adopt this valuation partly because the universal equivalent is both a logical and real possibility of any trade network (as characterised by the expanded form). A good historical example here is the Jicarilla War and the subjugation of the Apaches for the extraction of gold, which in turn imposed gold as the money commodity through its facilitation as a differential trade advantage bought in blood.

Edit: the 'myth of barter' is somewhat of a given in Marx, and should be criticised. However, criticising it doesn't do too much to the rest of the analysis: it doesn't matter that barter economies in the 17-1800s and contemporary bourgeoise economic textbook myth sense didn't really exist. This is because the myth of barter is just a conceptual stepping stone for Marx to get to more of the meaty bits.

Edit2: It's also somewhat artificial to aggregate all elements of simple barter into a relation T at that point, since the aggregation of such barters is what gives the first expression of the relative and equivalent forms of value as a trade network. The reflexivity condition could be included later, as Marx would probably see it as a bad retrojection. Regardless, I'll leave it as it is.
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Another feature to highlight is that value is a real abstraction, it's tightly coupled with the commodity and 'comes along with it'. This is why you can't dissect a commodity to ascertain its value from its constituent parts (even though those constituent parts can be valued to the extent they are commodities, eventually, in the aggregate, yielding values of production as expressed in direct price).

So long as the money commodity functions in a manner modelled well by Marx's descriptions, it doesn't matter what it is.

If, therefore, two different commodities, such as gold and silver, are simultaneously measures of value, all commodities have two prices — one a gold-price, the other a silver-price. These exist quietly side by side, so long as the ratio of the value of silver to that of gold remains unchanged, say, at 15:1. Every change in their ratio disturbs the ratio which exists between the gold-prices and the silver-prices of commodities, and thus proves, by facts, that a double standard of value is inconsistent with the functions of a standard.

This is to say that so long as silver and gold remain in a constant ratio of value, the transitivity condition of T isn't violated. If I could spend 1 gram of gold to obtain 2 grams of silver, but then 2 grams of silver to obtain 2 grams of gold, silver would then be worth the same as gold, but at the start it wasn't. Being able to make the final conclusion that 'silver would then be worth the same as gold' but that it also was worth half of gold is simultaneously an insistence on the general equivalent as a transitive standard of price and the failure of this standard as a real event.

We have (1g gold T 2g silver), (2g silver 2g gold), in order to say 'oh shit 1g silver = 1g gold' we need to be able to insist on the transitivity condition, and this also allows us to insist that 1g of gold is worth 2g of gold. So long as the fluctuations in these commodities are sufficiently slow and the relative value fluctuations are relatively minor this doesn't cause issue. However sufficiently variable fluctuations of the values of representative commodities; those which serve as a standard of price; give rise to all kinds of madness in a capitalist economy. A contemporary issue related to this is the Venezuelan hyper-inflation; the value of money is decreasing far more rapidly than any change in median/lower quartile wage can adjust to. Footnote [4] is a historical example of this internal problem of capitalism:

“Wherever gold and silver have by law been made to perform the function of money or of a measure of value side by side, it has always been tried, but in vain, to treat them as one and the same material. To assume that there is an invariable ratio between the quantities of gold and silver in which a given quantity of labour-time is incorporated, is to assume in fact, that gold and silver are of one and the same material, and that a given mass of the less valuable metal, silver, is a constant fraction of a given mass of gold. From the reign of Edward III. to the time of George II., the history of money in England consists of one long series of perturbations caused by the clashing of the legally fixed ratio between the values of gold and silver, with the fluctuations in their real values. At one time gold was too high, at another, silver. The metal that for the time being was estimated below its value, was withdrawn from circulation, mated and exported. The ratio between the two metals was then again altered by law, but the new nominal ratio soon came into conflict again with the real one. In our own times, the slight and transient fall in the value of gold compared with silver, which was a consequence of the Indo-Chinese demand for silver, produced on a far more extended scale in France the same phenomena, export of silver, and its expulsion from circulation by gold. During the years 1855, 1856 and 1857, the excess in France of gold-imports over gold-exports amounted to £41,580,000, while the excess of silver-exports over silver-imports was £14,704,000. In fact, in those countries in which both metals are legally measures of value, and therefore both legal tender, so that everyone has the option of paying in either metal, the metal that rises in value is at a premium, and, like every other commodity, measures its price in the over-estimated metal which alone serves in reality as the standard of value. The result of all experience and history with regard to this equation is simply that, where two commodities perform by law the functions of a measure of value, in practice one alone maintains that position.” (Karl Marx, l.c., pp. 52, 53.)

When people say 'internal contradictions of capital', this is an example of what they mean. Capital has a logic, but that logic isn't completely consistent with how capital actually operates.

Commodities with definite prices present themselves under the form: a commodity A = x gold; b commodity B = z gold; c commodity C = y gold, &c., where a, b, c, represent definite quantities of the commodities A, B, C and x, z, y, definite quantities of gold. The values of these commodities are, therefore, changed in imagination into so many different quantities of gold. Hence, in spite of the confusing variety of the commodities themselves, their values become magnitudes of the same denomination, gold-magnitudes. They are now capable of being compared with each other and measured, and the want becomes technically felt of comparing them with some fixed quantity of gold as a unit measure. This unit, by subsequent division into aliquot parts, becomes itself the standard or scale. Before they become money, gold, silver, and copper already possess such standard measures in their standards of weight, so that, for example, a pound weight, while serving as the unit, is, on the one hand, divisible into ounces, and, on the other, may be combined to make up hundredweights. [5] It is owing to this that, in all metallic currencies, the names given to the standards of money or of price were originally taken from the pre-existing names of the standards of weight.

We're now in a position to look at T again and see what properties it has: it is reflexive (all things can be traded for themselves), symmetric (if x can be traded for y then y can be traded for x) and transitive (if x can be traded for y and y can be traded for z, then x can be traded for z). This characterises T as an equivalence relation; the canonical example of an equivalence relation is of numerical equality. 1+1=2=3-1=4-2. With the establishment of T as an equivalence relation this facilitates trade with the logical structure of representatives.

A brief detour into mathematics. Representatives are an important part of the algebra of addition and multiplication of fractions. There are so many fractions representing equal values: 1,2/2,3/3,4/4..., what allows us to substitute one for the other; to do calculations with them? Well, we could do before the axiomatisation of the rationals, but the conceptual character of substituting equal things into equations is what is captured by the idea of an equivalence class. An equivalence class of a number is the set of all numbers equal to it; similarly the equivalence class of a fraction is the set of all fractions equal to it. The equivalence class of a number is denoted by putting square brackets around it. Explicitly this gives:

$[1]=\{1,2/2,3/3,4/4,...\}$

and the algebra of fractions is then defined on the equivalence classes. Since everything in an equivalence class is equal it gives the collection of things which can be substituted for it verbatim in any expression. If we define addition, subtraction, multiplication and division on the equivalence classes of fractions, then we can do all the algebra with fractions that we learn in school. This lets you say things like:

$[1]+[2]=[1+2]=[3]$

Equivalence classes are also either equal or share no common elements. This is to say that if we have something like (4-3)/2=2/4, we immediately have [(4-3)/2]=[2/4]; the relation of the elements entails the equality of the equivalence classes. Similarly 1/2 != 1/3 ensures [1/2] and [1/3] share no common elements. This allows us to define the idea of a representative of an equivalence class; which is just a canonical element we elect somewhat arbitrarily to denote that class.

Look at how Marx introduces an algebra of values (divisions into hundredweights) just after he invoked the transitivity condition! He's performing manipulations of (nominal) trade networks (the expanded form) by dealing with numerical and concrete divisions of a representative commodity. This works to characterise a trade network because gold is the money commodity...

The money commodity is that commodity which serves as the canonical representative for a network of trades of equivalent value. Moreover, the potential for a trade network to develop a money commodity is always there when that trade network functions in accordance with the expanded form, simply by requiring the transitivity of trade relations as a valuation of goods, and a convenient commodity to serve as the representative.

The impact of this is quite large; if a supposedly post-capitalist, post-revolution economy can interface with a capitalist economy through trades of equivalent value, it will still be a subjected to some of the process of capital; as the economies will couple. This is a good reason not to be a Leninist.
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I'm beginning to think it might be worthwhile to go back and do Chapter 2 afterwards, since that introduces the different forms of value. Anyway:

As measure of Value, and as standard of price, money has two entirely distinct functions to perform. It is the measure of value inasmuch as it is the socially recognised incarnation of human labour; it is the standard of price inasmuch as it is a fixed weight of metal. As the measure of value it serves to convert the values of all the manifold commodities into prices, into imaginary quantities of gold; as the standard of price it measures those quantities of gold. The measure of values measures commodities considered as values; the standard of price measures, on the contrary, quantities of gold by a unit quantity of gold, not the value of one quantity of gold by the weight of another. In order to make gold a standard of price, a certain weight must be fixed upon as the unit. In this case, as in all cases of measuring quantities of the same denomination, the establishment of an unvarying unit of measure is all-important. Hence, the less the unit is subject to variation, so much the better does the standard of price fulfil its office. But only in so far as it is itself a product of labour, and, therefore, potentially variable in value, can gold serve as a measure of value.[6]

Money functions as a measure of value since it renders a network of commodities as an exchangeable network of commodities; it is a standard of price inasmuch as that exchangeable network has a canonical representative as an amount of a money commodity. The commodities must be partly composed of exchange values in order for those exchange values to be commensurable under the banner of value (as congealed labour in the abstract, as effortful time expenditure). Their numerical commensurability (being members of the same equivalence class) is logically prior to their representation as a specific amount of a representative commodity, but once a representative (money)commodity is established it prefigures all goods as commensurable (buyable) in specific amounts.

It's also sometimes assumed that Marx can't account for deviations from the socially necessary labour time as expressed in direct price, but he contains such deviations as part of his account. He is fully aware that fluctuations of prices and of values occur, and constrains those fluctuations explicitly as part of the usual functioning of money as the standard of price. For Marx, amounts of labour required for production are the basis for which different amounts of the same commodity attain different values (but note, explicitly, not different prices alone, my bolding at the end). Prices can decouple from values, this is a feature of the analysis, not a bug.

This is another of those contradictions of capital people harp on about. The possibility of decoupling of value and price tout court gives the real possibility of large decouplings and pathologies. These invariably result in social tensions. This is why Marxists think it is important to look at the 'internal contradictions of capital'; like the pathological ways price and value can diverge; because those structural tensions in how capital works produce social tensions in the real world.
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It is, in the first place, quite clear that a change in the value of gold does not, in any way, affect its function as a standard of price. No matter how this value varies, the proportions between the values of different quantities of the metal remain constant. However great the fall in its value, 12 ounces of gold still have 12 times the value of 1 ounce; and in prices, the only thing considered is the relation between different quantities of gold. Since, on the other hand, no rise or fall in the value of an ounce of gold can alter its weight, no alteration can take place in the weight of its aliquot parts. Thus gold always renders the same service as an invariable standard of price, however much its value may vary.

I'm going to go off on a bit of a digression/rant here.

This has a mathematical representation in terms of the cancellation of fractions. If x gold is worth 5 cows is worth 10 pigs, then if x decreases 5 cows is still worth 10 pigs. Changing x doesn't change the amount of each commodity that each other commodity is worth, it just changes the overall standing of that equivalence class with respect to others.

Another mathematical note at this point: increases and decreases of commodity money price only make sense on the background of an ordering relation of values and prices. This ordering comes from two places; first there is an ordering in terms of the measure of value, which is a value expression of the different amounts of labour congealed in the commodities. Then there is the ordering on the standard of price; which is an ordering of the amount of the money commodity fixed to each equivalence class. That the money commodity is the representative of the first gives the ability to evaluate the different equivalence classes in terms of the raw amount of their representative. When we speak about the self valorisation of capital; capital appearing to the capitalist (and itself) as M-C-M' where M'>M this is what gives the logical structure under which that comparison is made.

The expansion of values and its concomitant concentration of values makes sense upon the background of the algebraic structure of value, that it forms a duality of calculable structures of labour times and money prices that jointly constrain each other without solely determining the other. The formal name for this calculable structure is an ordered field, the most common example of which is the real line (which, conveniently, is the numerical system for the representation and modelling of values). The requirements of perpetual valorisation destroy even the physical form of the money commodity, as more and more value is created the amount of value exceeds any limit; thus as a practical consequence paper moneys and then information moneys come to dominate.

In the second place, a change in the value of gold does not interfere with its functions as a measure of value. The change affects all commodities simultaneously, and, therefore, caeteris paribus, leaves their relative values inter se, unaltered, although those values are now expressed in higher or lower gold-prices.

This is a restatement that a change in gold doesn't change the relative value of commodities, but it changes how much a set of commodities of equivalent value are worth. The 'spending power' of the money commodity has its origin here.

Just as when we estimate the value of any commodity by a definite quantity of the use-value of some other commodity, so in estimating the value of the former in gold, we assume nothing more than that the production of a given quantity of gold costs, at the given period, a given amount of labour. As regards the fluctuations of prices generally, they are subject to the laws of elementary relative value investigated in a former chapter.

The elementary relative form of value is sort of like direct barter. Imagine if you took the previous conception of the elementary form from a previous post but instead made that trade as a trade of equivalent exchange values rather than through a utility comparison. When Marx says the fluctuations obey the elementary value form it's important to see what there isn't in the elementary form in a capitalist economy that there is in the dual standard of price and measure of value form.

This comes down to the possibility of the failure of the symmetry condition due to non-negligible fluctuations in short time periods of the prices; buy now get a lot more for it later! Or a lot less. It also removes the transitivity condition, as the infinity of imagined conduct of the same no longer occurs due to these instabilities. A commodity is, however, still worth exactly the same amount of itself, so reflexivity persists through time. The instabilities curtail the possibilities of trade at a given time period, so the trade relation T becomes more subject to local effects and interventions. It is no longer behaving much like the model, but the logic of capital can still exert social forces despite (and sometimes because of) the concrete failure of its mechanisms.
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This is awesome. Please, keep going ;-)
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There are many problems with Marx, but here I guess the problem is that Marx takes the classical view of money while in todays World money is debt.
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There are a couple of bits I want to address in in what's come so far. The first is of how use and exchange values intermingle as part of capitalist production, the second is in how the value form itself is the ur form of commodity fetishism (rather than treating commodity fetishism as a purely social phenomena).

In chapter 2 of capital Marx writes:

What chiefly distinguishes a commodity from its owner is the fact, that it looks upon every other commodity as but the form of appearance of its own value. A born leveller and a cynic, it is always ready to exchange not only soul (exchange value), but body (use value), with any and every other commodity, be the same more repulsive than Maritornes herself. The owner makes up for this lack in the commodity of a sense of the concrete, by his own five and more senses. His commodity possesses for himself no immediate use-value. Otherwise, he would not bring it to the market. It has use-value for others; but for himself its only direct use-value is that of being a depository of exchange-value, and, consequently, a means of exchange.[3] Therefore, he makes up his mind to part with it for commodities whose value in use is of service to him. All commodities are non-use-values for their owners, and use-values for their non-owners. Consequently, they must all change hands. But this change of hands is what constitutes their exchange, and the latter puts them in relation with each other as values, and realises them as values. Hence commodities must be realised as values before they can be realised as use-values.

The use value of labour in the relation C-M-C', the non-capitalist perspective, is to obtain goods and services. The use value of the commodity in M-C-M', the capitalist perspective, is to obtain more money. The latter is an essential component of capitalist production tout court; things are produced not for their use values, but for their (exchange) values. The dual nature of the commodity in use and exchange also mirrors the dual nature of the stand points that agents can have toward capital. Marx explicitly contrasts this to Aristotle in the third footnote in chapter 2:

“For two-fold is the use of every object.... The one is peculiar to the object as such, the other is not, as a sandal which may be worn, and is also exchangeable. Both are uses of the sandal, for even he who exchanges the sandal for the money or food he is in want of, makes use of the sandal as a sandal. But not in its natural way. For it has not been made for the sake of being exchanged.”

Secondly, commodity fetishism. The 'Marxism for dummies' way of summarising it in a bunch of buzzwords is that 'The social relations between people become the material relations between things'. While it has lots of mediating steps with labour and its social organisation, the commensurability in terms of value of a wage labourer's work with the money they receive is a manifestation of money as the representative of value equivalence classes. Think of how different the world would be if different equivalence classes of values held; how different the features of industry are, changes in the extent of mechanisation and the global demography of the labour force. All of this manifests in money. And money has that power because it's the canonical representative of trade networks!

Commodity fetishism is a real possibility as soon as an economy's value form becomes an expanded trade network.
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Money has always been intimately tied to debt. EG, owing the ruling body taxes in terms of raw goods. I'm going to sidestep this for now.
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Money functions as a measure of value since it renders a network of commodities as an exchangeable network of commodities; it is a standard of price inasmuch as that exchangeable network has a canonical representative as an amount of a money commodity.

Having a gold standard limits the money supply and reinforces confidence in the currency. And that's what money basically is made of: confidence. That's why it's tied to a political entity that can establish social order and enforce merchant law.

As for the roller coaster that starts with the abandonment of a standard: it's all psychology.
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The next paragraph is essentially a bit of bookkeeping.

A general rise in the prices of commodities can result only, either from a rise in their values — the value of money remaining constant — or from a fall in the value of money, the values of commodities remaining constant. On the other hand, a general fall in prices can result only, either from a fall in the values of commodities — the value of money remaining constant — or from a rise in the value of money, the values of commodities remaining constant. It therefore by no means follows, that a rise in the value of money necessarily implies a proportional fall in the prices of commodities; or that a fall in the value of money implies a proportional rise in prices. Such change of price holds good only in the case of commodities whose value remains constant. With those, for example, whose value rises, simultaneously with, and proportionally to, that of money, there is no alteration in price. And if their value rise either slower or faster than that of money, the fall or rise in their prices will be determined by the difference between the change in their value and that of money; and so on.

This is just saying that if the commodities in an equivalence class in general increase in in value then the value of the representative required to facilitate those trade relations also increases. Similarly (but not entirely symmetrically!), if the value of the representative increases without a concomitant increase in the commodity values then you can buy more with less.

Note that interventions that change the relative values of different commodities are quite a lot different from interventions that change the value of the money commodity. EG, Keynes diagnosis that (if his economics were followed more accurately...) quantitative easing produces some inflation. Or that hyper-inflation without a concomitant increase in wages impoverishes wage labourers.

This highlights something that's often missed: Marx's analysis is of capital ceteris paribus, he knows it doesn't live up to the abstraction sometimes. Failing to live up to the abstraction can have real effects (see previous posts).

A metaphor I think is useful here is to think of Marx's capital mostly as the analysis of an attractor in a dynamical system. If capital is functioning without weird shit going on, Marx thinks it will look like his model. If capital is dealing with some weird shit, it doesn't have to look exactly like the model.

Insert debate here about how capital makes use of crises and other radical interventions (like the introduction of railways). Another metaphor I find useful is of capital as an ecological generalist. It can thrive in a wide variety of conditions, so long as they are not sufficiently different to the abstraction Marx is analysing.

By degrees there arises a discrepancy between the current money-names of the various weights of the precious metal figuring as money, and the actual weights which those names originally represented. This discrepancy is the result of historical causes, among which the chief are: — (1) The importation of foreign money into an imperfectly developed community. This happened in Rome in its early days, where gold and silver coins circulated at first as foreign commodities. The names of these foreign coins never coincide with those of the indigenous weights. (2) As wealth increases, the less precious metal is thrust out by the more precious from its place as a measure of value, copper by silver, silver by gold, however much this order of sequence may be in contradiction with poetical chronology. [7] The word pound, for instance, was the money-name given to an actual pound weight of silver. When gold replaced silver as a measure of value, the same name was applied according to the ratio between the values of silver and gold, to perhaps 1-15th of a pound of gold. The word pound, as a money-name, thus becomes differentiated from the same word as a weight-name. [8] (3) The debasing of money carried on for centuries by kings and princes to such an extent that, of the original weights of the coins, nothing in fact remained but the names. [9]

Harken back to the first sentence in the chapter.

Throughout this work, I assume, for the sake of simplicity, gold as the money-commodity.

Marx is aware that something which for all intents and purposes counts as the value representative is the value representative. The debasement of currency 'saves money' by shaving off bits of value from the coin by changing is material constitution, while remaining something which counts as the coin. Of course, reality eventually catches up and the coins reduce in value as their material composition changes; coming to reflect the value of the constituents. We then have the introduction of paper money, which eases trade by not having to lug around loads of metal, but more importantly it can't be debased by changing its material constitution. It either counts as a paper money or it doesn't, you need other ways of controlling what it's worth.

In terms of the composition of global money now, though, the majority of it is information money; marks in digital ledgers. It appears as entirely divorced from anything material, but nevertheless functions in the way it does because it's still a real abstraction; it still has the social function of money.

As for the roller coaster that starts with the abandonment of a standard: it's all psychology.

Yes. If everyone just stopped using that worthless piece of paper it wouldn't have any value! The psychology of treating it, and information money, as the representative of value equivalence classes is only part of what makes it work. There's the level of heritable tradition which also needs to be analysed, and also that paper money still has a use as a means of circulation of relatively small amounts of money. It's not just psychology, paper money and information money are a self-reinforcing system that occurs in reality, not just in the minds of us plebs.

Edit: Also, ironically, abandoning the gold standard occurred after so many 'reclaimable bonds' (money) were issued that their total value far outstripped any gold reserves. Capital grew until it expanded past a limitation, then it kept functioning in much the same way ceteris paribus - though it's no longer beholden to manifesting in any currency denomination's paper money (because it's now a real valued variable, like it always wanted to be in the ordered field), that's part of what was undermined before the switch. It doesn't care about the physical process of division of the money commodity any more.
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Self indulgent coincidence:

The rational numbers, which serve as the numerical representation of the money commodities like gold, when they must be able to be physically split into smaller valued pieces, stopped being the appropriate ordered field to think about money values in the second economic analysis and forecasts were internalised as part of capital. The rational numbers can be used to arbitrarily approximate any real number, but the real numbers are what facilitate the mathematical machinery that represents capital to itself as an intellectual abstraction. This was mostly written so I could write the following sentence:

The extension of the needs of value past the representative capacity of fractions coincided with the extension of the field of fractions to the reals as the algebraic structure of value.
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the value of any currency is what the world's consensus of its value is. Value "jiggles" up and down continuously. Currency is connected to real stuff through what? Trade. A country which has (practically) nothing to sell is going to have a virtually worthless currency. If you sell stuff then you can buy stuff, and if you pay your bills, your money is good. Stop paying your bills and your currency might turn into cat litter. Value comes from the market.

The value of fiat currency comes from real production and trade. The cartoon desert island has nothing to sell, nobody wants to go there, and the two people there very much want to leave. "It" could declare a fiat currency but it could not be worth anything. But suppose the two castaways discovered that the desert island was composed of nothing but pockets of pure rare earths (lanthanum, praseodymium, neodymium, gadolinium, terbium, dysprosium,, ytterbium, and so forth). Now the desert island would have something to sell that was in demand, and with the income from selling it's ore they could buy stuff. It's fiat currency would be welcome everywhere.

"Having stuff to sell" doesn't guarantee that everything will work out just fine. Look at Venezuela. Even though Venezuela has stuff to sell, it was able--through centralized gross mismanagement--to end up in an economic shithole.
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The value of fiat currency comes from real production and trade.

It does, but precisely how Marx thinks this works comes later in Capital. His theory of value is inseparable from the rest of the account IMO, even though some people do Marxist analysis without it.
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Money has always been intimately tied to debt. EG, owing the ruling body taxes in terms of raw goods. I'm going to sidestep this for now.
Fine, sidestep it, but just to note that Marx has basically a theory of commodity money (just as you put it, taxes in terms of raw goods, and elsewhere) and this is very important to notice. This commodity money was a typical theory for the 19th Century as the gold standard reigned back then. Marx was obviously a child of his era at least in this case.

Yet money today is basically created as debt and the central banks themselves account just for a small portion of the money supply. Money supply of M1 is also just a small percentage of the whole money supply.

If everyone just stopped using that worthless piece of paper it wouldn't have any value! The psychology of treating it, and information money, as the representative of value equivalence classes is only part of what makes it work. There's the level of heritable tradition which also needs to be analysed, and also that paper money still has a use as a means of circulation of relatively small amounts of money. It's not just psychology, paper money and information money are a self-reinforcing system that occurs in reality, not just in the minds of us plebs.
Well, people are using less and less of paper money anyway. Try going to a bank a getting a larger sum in cash: it's difficult. But as long as governments make it legal tender and do make people to pay taxes, there is a credibility behind that fiat money. Now we don't even have to have that as we have all these various invented cryptocurrencies.

Also, ironically, abandoning the gold standard occurred after so many 'reclaimable bonds' (money) were issued that their total value far outstripped any gold reserves. Capital grew until it expanded past a limitation, then it kept functioning in much the same way ceteris paribus - though it's no longer beholden to manifesting in any currency denomination's paper money (because it's now a real valued variable, like it always wanted to be in the ordered field), that's part of what was undermined before the switch. It doesn't care about the physical process of division of the money commodity any more.
Yes, but the question is that why hasn't then money lost it's value? Or (perhaps this is ventures way off from the topic) why didn't we get a massive inflation after all the pumping up that happened after the last financial crisis?
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Yes, but the question is that why hasn't then money lost it's value? Or (perhaps this is ventures way off from the topic) why didn't we get a massive inflation after all the pumping up that happened after the last financial crisis?ssu

The quantitative easing that occurred as a result of the financial crisis in 2008 almost all ended up in the coffers of the very rich. It didn't influence the effective demand for most goods very much; people still needed what they needed. Nevertheless the story goes that due to the increased money supply for investment, the economy grew and prices increased as is usual; but the rising tide didn't raise all boats, as it usually does not. Keynes' idea came along with a lot of wealth redistribution*, and that wasn't implemented at all in the global financial crisis.

It's a complicated story to try and tell; money only loses most semblances of its value due to inflation when the inflation rate goes through the roof. I imagine this is a question of degree. Regardless, precisely how the recent financial crisis arose and how it effected things resists easy summary, like most events in economics.

*edit: Well, it did, but in the wrong direction. Rich got richer, poor got poorer.
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Marx then highlights some themes in the evolution of the money commodity. One part of this is to show that the debasement of currency, rather than simply being a historical accident of the development of capitalist economies; a bug; is actually the manifestation of a feature of money in capitalist economies. Money tends toward greater and greater abstraction from the productive organisation that conditions it and in the final instance determines how it expresses value.

These historical causes convert the separation of the money-name from the weight-name into an established habit with the community. Since the standard of money is on the one hand purely conventional, and must on the other hand find general acceptance, it is in the end regulated by law. A given weight of one of the precious metals, an ounce of gold, for instance, becomes officially divided into aliquot parts, with legally bestowed names, such as pound, dollar, &c. These aliquot parts, which thenceforth serve as units of money, are then subdivided into other aliquot parts with legal names, such as shilling, penny, &c. [10] But, both before and after these divisions are made, a definite weight of metal is the standard of metallic money. The sole alteration consists in the subdivision and denomination.

It begins by noting a transformation in the money commodity's physical form and social constitution of its value, but throughout the transformation it still serves the social function of the money commodity and so operates in essentially the same manner as the money commodity. The literal meaning of, say, 'a pound', being a redeemable token of a pound weight of a precious metal, becomes a figurative meaning again while maintaining the same socio-economic functions. The rest is book-keeping.

However, one part of the book-keeping is extremely important.

Since the standard of money is on the one hand purely conventional, and must on the other hand find general acceptance, it is in the end regulated by law. These aliquot parts, which thenceforth serve as units of money, are then subdivided into other aliquot parts with legal names, such as shilling, penny, &c. [10] But, both before and after these divisions are made, a definite weight of metal is the standard of metallic money. The sole alteration consists in the subdivision and denomination.

Ensuring that the money commodity functions as the money commodity under arbitrary transformations of its physical form necessitates the intervention of the ruling classes to enforce the rules. This is foreshadowing of the critical role governing bodies play in maintaining the function of capital. A law that a paper token or information token, no longer redeemable as any physical good, is a codification of that which counts as money by fulfilling its social function. A necessary constituent of the organisation of money in a capitalist economy is the rule of law.

This is a good reason not to be an anarchocapitalist.

The prices, or quantities of gold, into which the values of commodities are ideally changed, are therefore now expressed in the names of coins, or in the legally valid names of the subdivisions of the gold standard. Hence, instead of saying: A quarter of wheat is worth an ounce of gold; we say, it is worth £3 17s. 10 1/2d. In this way commodities express by their prices how much they are worth, and money serves as money of account whenever it is a question of fixing the value of an article in its money-form. [11]

The loss of the ability to redeem a currency in terms of its correspondent amount of a precious metal serves to abstract the money commodity's social function from the social relations that make sense of the money commodity and the social function of the money commodity itself. This is another time Marx foreshadows the account of commodity fetishism and grounds it in his theory of value.

Another thing to keep track of here is his introduction of money of account, which is the price form expression of the value of an asset in a ledger.

Marx completes his tracing of the tendency of the money commodity to greater and greater abstraction (fetishism) with the next paragraph:

The name of a thing is something distinct from the qualities of that thing. I know nothing of a man, by knowing that his name is Jacob. In the same way with regard to money, every trace of a value-relation disappears in the names pound, dollar, franc, ducat, &c. The confusion caused by attributing a hidden meaning to these cabalistic signs is all the greater, because these money-names express both the values of commodities, and, at the same time, aliquot parts of the weight of the metal that is the standard of money. [12] On the other hand, it is absolutely necessary that value, in order that it may be distinguished from the varied bodily forms of commodities, should assume this material and unmeaning, but, at the same time, purely social form. [13]

The situation with fiat money, in both paper and information forms, is even more mystifying; but would be essentially the same. The value of a mass of fiat money, rather than being redeemable in a physical commodity, is still redeemable in terms of every buyable good. The social relations underpinning production, which vouchsafe the social function of money, are essentially the same in fiat currencies; just their regulation differs somewhat. And purely fiat moneys facilitate even more abstract representations of money amounts, just as they respond to the needs of value after it has evaporated what was presumed to be its physical basis.

What this reveals is that value; including currency; is not chiefly a physical relation of commodity amounts; it is a social function which enforces and represents exchange ratios of commodities and quantifies them irrelevant of any physical or numerical bounds on the magnitude of value. The money form was destined to be a real valued variable with a currency stamp on it.
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I'm impressed by the scholarship, but my upbringing in Marxism always stressed the unity of theory and practice. I am left, in my later years, to be just a person who knows a little about the subject, but no longer a Marxist because I am cut off from action. What, fdrake, would you see as the implications for practice?
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Price is the money-name of the labour realised in a commodity. Hence the expression of the equivalence of a commodity with the sum of money constituting its price, is a tautology, [14] just as in general the expression of the relative value of a commodity is a statement of the equivalence of two commodities.

The abstraction that comes with the application of a money-name as a measure of value is present here too. Labour is baptised in value and emerges converted to money as the price of that labour. This is to say that just as commodities can be split into constituent parts, like the iPhone into its electronic schematics, it can be split into the labours that produce those parts. The sum total of the labours in the production of the commodity gives it an initial valuation; a direct price which closely tracks the measure of the total value of labour within that commodity.

But although price, being the exponent of the magnitude of a commodity’s value, is the exponent of its exchange-ratio with money, it does not follow that the exponent of this exchange-ratio is necessarily the exponent of the magnitude of the commodity’s value.

This harkens back to something Marx wrote at the very start of the chapter:

The first chief function of money is to supply commodities with the material for the expression of their values, or to represent their values as magnitudes of the same denomination, qualitatively equal, and quantitatively comparable.

the values must have a material expression; but carefully reading this shows that the material expression of value in direct price is not facilitated by the identity of the magnitude of value with the magnitude of price. Just as values and prices can diverge, so can the value of labour and its direct price. Marx develops this notion further:

Suppose two equal quantities of socially necessary labour to be respectively represented by 1 quarter of wheat and £2 (nearly 1/2 oz. of gold), £2 is the expression in money of the magnitude of the value of the quarter of wheat, or is its price. If now circumstances allow of this price being raised to £3, or compel it to be reduced to £1, then although £1 and £3 may be too small or too great properly to express the magnitude of the wheat’s value; nevertheless they are its prices, for they are, in the first place, the form under which its value appears, i.e., money; and in the second place, the exponents of its exchange-ratio with money. If the conditions of production, in other words, if the productive power of labour remain constant, the same amount of social labour-time must, both before and after the change in price, be expended in the reproduction of a quarter of wheat. This circumstance depends, neither on the will of the wheat producer, nor on that of the owners of other commodities.

The value of labour and the manifestation of that value in the price tightly constrain each other numerically but are not identical; and that tight numerical constraint still allows room for social deviations. If workers act together and manage to obtain an increase in their wages, the price of their labour increases but the socially necessary labour time for the production of the commodities does not have to change.

Again we see an awareness of internal tensions within the mechanisms of value Marx diagnoses of capital; a friction between its own regulative ideal and its material comportments.

Marx's Capital is one of those inexhaustible books. Whenever I see a direct tension between my exegesis (which is more 'fdrake's Marx' than Marx's Marx) and a political ideology (like Leninism or anarchocapitalism so far) I will highlight it.

I think it's pretty important to understand things before trying to change them.
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This is awesome.

Second that. As is this: https://thephilosophyforum.com/discussion/3111/society-of-the-spectacle/p1

Which is high on my list for a reread. :clap:
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ftd - it seems to me that, since capitalism and class relations are constantly in change and development, we are, alas, not given any 'before' in which to consider. So it goes - at present, very badly!
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I'm much happier with this than with Debord. Marx is much more straightforward a writer, too. It's easy to get somewhere in the vicinity of his intentions, whereas I was spending most of my time clamouring for examples and applications with Society of the Spectacle. I did enjoy trying to ape Debord's poetic, exaggerated style though.

Society of the Spectacle also had a definite mood to the writing, there was a sense of despair and confinement and a real existential dread permeating the whole thing. Marx is a lot dryer, and he even uses examples. There weren't many examples in Society.
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What can I say? It worked for me. Of course, that's pretty much smack on the type of thing I'm interested in, so I may be biased. :)
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The next paragraph is pretty dense, requires a lot of unpacking, and is very revealing over how Marx thinks about capital and precisely how Marx thinks his account holds of capital.

Magnitude of value expresses a relation of social production, it expresses the connexion that necessarily exists between a certain article and the portion of the total labour-time of society required to produce it.

This is a statement of the ceteris paribus relationship between the magnitude of value of a commodity amount and the (socially necessary) portion of total labour time over all production it takes to produce that commodity. Again, remember that this equality is approximate, and deviations from the equality far from being a bug in Marx's theory are treated as a real feature of capital. Marx is explicit about the deviation of capital in reality from the model he develops.

As soon as magnitude of value is converted into price, the above necessary relation takes the shape of a more or less accidental exchange-ratio between a single commodity and another, the money-commodity. But this exchange-ratio may express either the real magnitude of that commodity’s value, or the quantity of gold deviating from that value, for which, according to circumstances, it may be parted with.

This distinction makes use of the previous distinctions between the magnitude of value and the money expression of that value. The two, again, only are close to coinciding when all deviating forces are sufficiently small. It's also worth highlighting a metaphysical subtlety in the modality of this coincidence too:

As soon as magnitude of value is converted into price, the above necessary relation takes the shape of a more or less accidental exchange-ratio between a single commodity and another, the money-commodity.

The coincidence of the amount of socially necessary labour time in a commodity with its correspondent value magnitude is a necessary feature of capital: a law. But nevertheless capital can accidentally deviate from this law. What does this mean for the status of the law? How can the law be a law if it doesn't hold for all times?

I think of it as a law of statistical tendency. Just like how it is the law of a fair coin flip to produce half heads and half tails, this still allows deviations from samples which have exact proportions of half heads half tails. The properties of a coin that give it this statistical property are no more incidental to the coin than its approximate fairness: a coin needs to have approximate symmetry in mass distribution and sufficient flatness over its sides for it to have this statistical regularity. The concordance of the coin flips with the law of their sides' equiprobability is no more a contingent feature of the coin than the real possibility of deviation from that law in the finite realisation of coin flip sequences. Its laws and the bugs are built into the coin.

In a similar way, the realisation of capital can be close to or far from its statistical laws while still being consistent with those statistical laws. Even the deviations of the reality of capital from its ideal/expected tendencies can be interpreted as part of the description of capital; just as a distribution has a mean, it also has a variance. Like the seasonal variations in temperature; the specific temperature of each day does not refute the rule that summers tend to be warmer than winters.

This can be summarised with the metaphor I used before, of Marx's model of capital as a model of an attractor for some dynamical economic system; what its expected function is from the regularities of its mechanisms; and the deviations from that attractor; what fluctuations occur and from which internal tensions of capital do they arise from.

The possibility, therefore, of quantitative incongruity between price and magnitude of value, or the deviation of the former from the latter, is inherent in the price-form itself. This is no defect, but, on the contrary, admirably adapts the price-form to a mode of production whose inherent laws impose themselves only as the mean of apparently lawless irregularities that compensate one another

He says it a lot better than I do.
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Mathematical aside: on central limit theorems and emergent, yet inherent laws.

This is no defect, but, on the contrary, admirably adapts the price-form to a mode of production whose inherent laws impose themselves only as the mean of apparently lawless irregularities that compensate one another

The final part of the paragraph, which I bolded and italicised above, is extremely suggestive of the mathematical machinery of central limit theorems (which are sometimes called statistical attractors). What a central limit theorem does is take a bunch of processes that spit out (realise) numbers with much different laws, add them together, and show that the sum of such realisations obeys an aggregate law that the individual elements, and indeed small, finite subsets, need not follow.

The most well known example of this in mathematics is the Lindberg Levy central limit theorem. Many central limit theorems assume that the individual elements constituting them do not provide any information on any other individual elements (statistical independence), but there are lots of cases where you can relax this assumption; you allow the processes to depend on each other in some specified way.

Is tempting to think that because the collection of processes in a central limit theorem need to be constrained in some manner before they obtain their aggregate law (central limit) that this central limit has little influence on the collections of processes that satisfy it. This isn't true though; the usual result of a central limit theorem is that the series of processes when iterated converges to the law of its aggregate, its central limit; this is to say that the law begins constraining the processes from the start and the more items in your collection the more accurately that collection's statistical regularities approximate the law. The law, as an emergent order, is already baked into the finite realisations of these processes; just as the individual collections constrain the law, the law constrains the individual collections.

I believe we should think of Marx's analysis as diagnosing something like this law; in the aggregate, when all is behaving ceteris paribus, it approximates the law well. In the aggregate, when all is not behaving ceteris paribus as assumed, it need not obey the law very well at all.
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I guess I do have something to add here after all. I think that the difference between absolute value and price or exchange value is what allows surplus-value and the rate of exploitation to be calculated as well. It sets the stage for the structural flow of value from one class of persons to another. Price isn't value because the price has to be higher than the value in order for their to be surplus-value, and then surplus-value has to be owned by persons who aren't producing it to make capitalism. The capitalist owns capital, which in turn allows him to set the price for both labor -- which is held in check by necessity, the capitalist needs workers still of course -- and the commodity being produced.
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I'm in agreement, and I think the point can be made more generally. I think, for Marx, capital doesn't just deviate from its laws through its internal tensions, it utilises those internal tensions to regulate its own functioning. As a process, it iterates from its pathologies and its mundanities alike. So far I've been trying my best to highlight the distinctions between the various expressions of value; and how their non-identity facilitates/constrains life under capital, and your comment is another part of this.

Another point which jives well with this is that value essentially is surplus value in terms of its numerical composition. The self valorisation of capital occurs in the difference between the money expression of socially necessary labour time for a commodity and the price of purchase for that commodity. That is, off the worker's back and from the worker's brow.
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I should say, if anyone wants to comment or ask questions please do. It's always more fun to have a discussion than to monologue.
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Marx notes that the divergence between value and price has some radical implications; the commodification of everything.

The price-form, however, is not only compatible with the possibility of a quantitative incongruity between magnitude of value and price, i.e., between the former and its expression in money, but it may also conceal a qualitative inconsistency, so much so, that, although money is nothing but the value-form of commodities, price ceases altogether to express value.

Objects that in themselves are no commodities, such as conscience, honour, &c., are capable of being offered for sale by their holders, and of thus acquiring, through their price, the form of commodities. Hence an object may have a price without having value. The price in that case is imaginary, like certain quantities in mathematics. On the other hand, the imaginary price-form may sometimes conceal either a direct or indirect real value-relation; for instance, the price of uncultivated land, which is without value, because no human labour has been incorporated in it.

Roughly how this works is that a price can be attached to everything regardless of its value. The untethering of the magnitude of the value in terms of labour and the magnitude of the value in terms of price takes an extreme form in which a price can be attached to an entity or attribute which is not an product of (social) labour.

What should be noted is that in this particularly abstract application of price, the amount of value that price expresses cannot mirror a socially necessary amount of labour in the commodity; but nevertheless what price actually obtains has its value in relation to the value of commodities. A psychologist does not produce a commodity through their labour, but nevertheless their labour has a price and they can be payed a wage for their labour. Their labour consists in the administration of therapy, which produces no physical item. Nevertheless the product; the treatment of a mental condition; has utility; but this utility is not tied to the duality of use and exchange even as the price of that product is associated with the expenditure of labour and the dynamics of value which find their money expression in the price of the shrink's service.

Again, that price makes sense upon the production of commodities and their trade networks. The ostensible arbitrariness of the assigned price to their labour does nothing to undermine the overall structure of value production; it actually expresses the inner torsion of price and value in capital. That torsion here is so great that it occludes the relationship between labour and value; and that occlusion is another manifestation of the fetishism of commodities.

Marx expands on divergence next, in the final paragraph of the chapter (or section, depending on how the book is split up). It also summarises/references the main themes of the chapter.

Price, like relative value in general, expresses the value of a commodity (e.g., a ton of iron), by stating that a given quantity of the equivalent (e.g., an ounce of gold), is directly exchangeable for iron. But it by no means states the converse, that iron is directly exchangeable for gold.

That amount X of gold is worth amount Y of iron doesn't mean that gold can be traded directly for iron as goods, goods will be tradable for gold only insofar as gold functions as the universal equivalent; which is to say, insofar as it functions as money.

In order, therefore, that a commodity may in practice act effectively as exchange-value, it must quit its bodily shape, must transform itself from mere imaginary into real gold, although to the commodity such transubstantiation may be more difficult than to the Hegelian “concept,” the transition from “necessity” to “freedom,” or to a lobster the casting of his shell, or to Saint Jerome the putting off of the old Adam. [15]

This is to say that for a commodity to be traded in terms of its exchange value, it simply must serve the social function of being of the right magnitude of value in trade. By treating the commodities as such we elide their physicality and utility for their social function in exchange.

Though a commodity may, side by side with its actual form (iron, for instance), take in our imagination the form of gold, yet it cannot at one and the same time actually be both iron and gold. To fix its price, it suffices to equate it to gold in imagination. But to enable it to render to its owner the service of a universal equivalent, it must be actually replaced by gold. If the owner of the iron were to go to the owner of some other commodity offered for exchange, and were to refer him to the price of the iron as proof that it was already money, he would get the same answer as St. Peter gave in heaven to Dante, when the latter recited the creed —

The replacement of a commodity by gold is just its purchase; and value must find its expression in a physical form to count as value in principle. This by no means stops working for information/digital money, it has become that the recorded marks signifying values of definite magnitudes serve exactly the same social function as a definite weight of gold. The digitalisation of money has not changed its social function; just as the removal of the gold standard did not, the (almost complete) removal of our 'paper' standard did not either.

A price therefore implies both that a commodity is exchangeable for money, and also that it must be so exchanged. On the other hand, gold serves as an ideal measure of value, only because it has already, in the process of exchange, established itself as the money-commodity. Under the ideal measure of values there lurks the hard cash.

The fungibility of real abstractions; like money; requires that they piggyback on physical processes with physical representatives irrelevant of how complex the social functions surrounding them are. This is to say that all the dynamics and semantics of value Marx has hitherto developed appear to us simply as good exchanges and purchases; as their embodiment in their marks. Perhaps the capacity for all these internal tensions is then no surprise, as all qualitative distinctions in the processes which together function as procedural components of value (labour time, socially necessary labour time, relative form, equivalent form, universal equivalent, money commodity, money names, the inexhaustible numerosity of trade networks and their value equivalence classes...) are forced to cohabit as uneasy roommates in the innocent home of their representation; the hard cash.

Collapsing all of these social processes into the money commodity then facilitates Marx to analyse the circulation of money and commodities.

That's the end of the section. I'll reflect on it a bit then post some more. Comments/questions?
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The fungibility of real abstractions; like money; requires that they piggyback on physical processes with physical representatives irrelevant of how complex the social functions surrounding them are. This is to say that all the dynamics and semantics of value Marx has hitherto developed appear to us simply as good exchanges and purchases; as their embodiment in their marks. Perhaps the capacity for all these internal tensions is then no surprise, as all qualitative distinctions in the processes which together function as procedural components of value (labour time, socially necessary labour time, relative form, equivalent form, universal equivalent, money commodity, money names, the inexhaustible numerosity of trade networks and their value equivalence classes...) are forced to cohabit as uneasy roommates in the innocent home of their representation; the hard cash.

I flubbed a bit here, and the use of 'physical processes' as a category of description doesn't really fit the bill. As I highlighted in the first post, events can have significance (expressions) in multiple ontological registers; the physical is but one. For example, debasing a currency is a chemical processes, but it has socio-economic effects. The appropriate vocabulary here is to use 'real abstraction' again, but pair it with 'real event' or something similar.

Regardless, the metaphysical function of my use of 'physical process' is I believe essentially correct; what it highlights is a certain collapse/codification of Marx's account of value into concrete events of exchange. In order for Marx to be right, his model of capital must be occurrent; what he describes in the (real) abstract has to actually play out.

Marx returns in the final two paragraphs to what started it all in the chapter; the exchange of commodities. The dynamic abstraction of money, value, and the attended social circumstances of trade must be embodied in the real relations of exchange in order for his account to be correct. Presciently, Marx uses all the abstractions he developed and collapses them into their already established representative; exchange as an exchange of equivalent values of the money commodity.

This then facilitates him to describe how this process reproduces itself; firstly with an account of the circulation of commodities - a model of exchange networks, purchases, wages and industrial ownership - then with an account of alienation and the extraction of surplus value. That Marx folds his account, at the end of every major section, back into the realities it deals with allows him to take a systemic approach to the reproduction of capital through circulation, and the self valorisation of capital through exploitation.

You can read this as something like as utilising commodity fetishism backwards; if it really is the case that exchange relations are the site of all these features of his account, he has to be able to use exchange relations as the real representation of his account of them. As much effort as he puts into explicating the hidden structure within commodities, he has to be able to treat the structure as hidden again when dealing with processes that operate regardless of his elucidation.
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I'm pretty pleased with myself. I had the mathematical components sketched out a while ago, but it turns out that a few more years of reading other things gave me the ability to give a much deeper account of what's going on in the chapter.

Chapter 2 and 3 have a pretty bad reputation for complexity; I remember being told that, though it may be apocryphal as I've never managed to find the reference again after checking it, Althusser cautioned his students around the chapters; take them with a pinch of salt, they're inessential to the account.

Since reading Vol 1 through the first time I really disagree with this, Marx's value theory sets the stage for so much in his later account. He also seemed to be somewhat of a prophet about the development of capital; as he takes great pains to present things as generally as possible. It's amazing to go through it again and find his analysis cognisant of the historical contingencies of capital of his day - like gold and fiat currencies just being examples of the money form.
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This is cool, about halfway through. Thanks for this.
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