Marx continues his argument for the externality of value to the commodities in an exchange.

A simple geometrical illustration will make this clear. In order to calculate and compare the areas
of rectilinear figures, we decompose them into triangles. But the area of the triangle itself is expressed by something totally different from its visible figure, namely, by half the product of the base multiplied by the altitude. In the same way the exchange values of commodities must be capable of being expressed in terms of something common to them all, of which thing they represent a greater or less quantity.

This time through an analogy. Updating the analogy somewhat is useful. Say we have a square and a circle and the two are equal in terms of area. This means that the square of side h, of area $h^2$ and the circle of radius r, with area $\pi r^2$, are equal. We can say that the square and the circle are of equal area because $h=\sqrt{\pi}r$. The only reason we can make this equation is that the two are already posited as equal in area; and the idea of 'equal area' is no more contained in the square than the circle. That they are of equal area follows from the application of the abstraction of area; which nevertheless can be read as an inherent/intrinsic property of both the circle and the square. The analogy functions by mapping 'are of equal area' to 'are of equal value' and of mapping 'circle, square' to 'commodity 1, commodity 2'. 'This size' and 'that size' become commensurable through 'area'. This commodity and that commodity become commensurable through exchange value.

This common “something” cannot be either a geometrical, a chemical, or any other natural property of commodities. Such properties claim our attention only in so far as they affect the utility of those commodities, make them use values. But the exchange of commodities is evidently an act characterised by a total abstraction from use value. Then one use value is just as good as another, provided only it be present in sufficient quantity. Or, as old Barbon says,“one sort of wares are as good as another, if the values be equal. There is no difference or distinction in things of equal value ... An hundred pounds’ worth of lead or iron, is of as great value as one hundred pounds’ worth of silver or gold.”[8]

Again, the emphasis here is that value is a (real) abstraction that operates on commodities in an exchange and isn't essentially constituted by material properties of either commodity. Since the use values of commodities depend entirely on their material constitution, this means that exchange value is essentially different from use value. A more striking way to use Barbon's equivalence is to suggest that because, say, 1 mole of iron is worth 1 mole of copper, 1 atom of iron is worth 1 atom of copper - the raw proportion of the two is all that matters in determining their relative value, irrespective of every everyday use of both being destroyed by the amounts present.

Since there was interest, I'm going to continue giving my exegesis of the book, and take a break from the mathematical modelling above. I'll return to it once I've done more exegesis. I'll be going through chapter/section 1, which stretches from the opening page to the end of the section on the fetishism of commodities.

The wealth of those societies in which the capitalist mode of production prevails, presents itself as “an immense accumulation of commodities,”[1] its unit being a single commodity. Our investigation must therefore begin with the analysis of a commodity.

This is pretty straightforward. Capitalist production makes a lot of stuff, and people have bought that stuff; making capitalist production appear as the accumulation of stuff people have bought. Note that the analysis begins from something worldly; Marx has noticed that capital accumulates a lot of stuff that people have bought; it isn't a purely philosophical assumption.

A commodity is, in the first place, an object outside us, a thing that by its properties satisfies human wants of some sort or another. The nature of such wants, whether, for instance, they spring from the stomach or from fancy, makes no difference.[2] Neither are we here concerned to know how the object satisfies these wants, whether directly as means of subsistence, or indirectly as means of production.

Commodities satisfy human wants and needs. The only thing which matters for analysis is that they satisfy human wants and needs, not how. This is an important methodological technique as it abstracts from the particular nature of commodities; how commodity x satisfies needs y; to their general structure; that commodities always satisfy wants and needs.

Every useful thing, as iron, paper, &c., may be looked at from the two points of view of quality and quantity. It is an assemblage of many properties, and may therefore be of use in various ways. To discover the various uses of things is the work of history.[3] So also is the establishment of socially-recognized standards of measure for the quantities of these useful objects. The diversity of these measures has its origin partly in the diverse nature of the objects to be measured, partly in convention.

Qualities of iron/paper etc are what wants and needs they satisfy and how they satisfy them; this is why studying human behaviour as it regards those commodities reveals the uses, and is a historical endeavour. How much of a given thing there is is also a function of the raw physical amount and the systems of measurement which have been developed. EG, cows come in whole number lots, iron comes in grams, paper can come in notepads or pieces etc.

The utility of a thing makes it a use value.[4] But this utility is not a thing of air. Being limited by the physical properties of the commodity, it has no existence apart from that commodity. A commodity, such as iron, corn, or a diamond, is therefore, so far as it is a material thing, a use value, something useful.[/b]

This is simply to state that how an item satisfies certain wants and needs depends on the material properties of that commodity (and how those properties are made use of). Corn satisfies hunger by being a food, specifically a hardy, insect resistant crop full of carbohydrates and nutrients.

This property of a commodity is independent of the amount of labour required to appropriate its useful qualities. When treating of use value, we always assume to be dealing with definite quantities, such as dozens of watches, yards of linen, or tons of iron.

This is to say that iron, as a construction material for munitions and boats, does not have the ability to be used for that construction if it comes in the quantity of a microgram. So Marx takes the dependence of use values on the amount of a commodity as something largely irrelevant; so long as we ascribe a use value to a thing, that can only be done insofar as there is enough of that thing for the use value. This ties in neatly with:

The use values of commodities furnish the material for a special study, that of the commercial knowledge of commodities.[5] Use values become a reality only by use or consumption: they also constitute the substance of all wealth, whatever may be the social form of that wealth. ||| In the form of society we are about to consider, they are, in addition, the material depositories of exchange value.

the bolded part. Use values are only use values insofar as they are used. Unprocessed iron in the ground, or an iron repository in a closed factory, do not strictly speaking have use values since they are not being utilised. There is still the []potential of use[/i] in those items afforded to them by their material properties. To put it another way, the formal character of a use value is to be expended through use.

Another feature of use values is that their accumulation constitutes wealth. Someone would be wealthy in virtue of having all they want and need forever. Wealth, as related to use values alone, is constituted by the fulfilment of a wants and needs; and having access to sufficient resources for it requires a certain availability and accumulation/storage of use values.

The sense of wealth in the previous paragraph doubtlessly seems very twee compared to the one we have now; but this is because the sense of wealth as the accumulation and availability of useful resources does not reflect the structure of wealth now; wealth under capitalist societies. In those societies, the family home of the commodity, goods also have exchange value and serve as its material depositories. Similar to previous discussion, commodities in certain amounts serve as a material expression of a social structure.

Exchange value, at first sight, presents itself as a quantitative relation, as the proportion in which values in use of one sort are exchanged for those of another sort,[6] a relation constantly changing with time and place. Hence exchange value appears to be something accidental and purely relative, and consequently an intrinsic value, i.e., an exchange value that is inseparably connected with, inherent in commodities, seems a contradiction in terms.[7] Let us consider the matter a little more closely.

bolded bit is the first reference to the 'lawless irregularities' that are the concrete acts of trade; exchange. Nevertheless Marx insists that there is, regardless, a social form of exchange which embeds itself in each exchange; constraining them, mediating them and ultimately reproducing itself as a social form in those concrete acts; which nevertheless is not a purely material property of the commodities themselves. From the previous vocabulary, Marx's reference to exchange value as intrinsic to the commodities sets up the value form as a real abstraction. It is intrinsic to the social significance of the commodity and the social form which uses them as such, not to the good stripped of all context and left as a barren composite of matter.

A given commodity, e.g., a quarter of wheat is exchanged for x blacking, y silk, or z gold, &c. – in short, for other commodities in the most different proportions. Instead of one exchange value, the wheat has, therefore, a great many. But since x blacking, y silk, or z gold &c., each represents the exchange value of one quarter of wheat, x blacking, y silk, z gold, &c., must, as exchange values, be replaceable by each other, or equal to each other. Therefore, first: the valid exchange values of a given commodity express something equal; secondly, exchange value, generally, is only the mode of expression, the phenomenal form, of something contained in it, yet distinguishable from it.

Marx points out that in order for exchange to occur as it usually does, the commodities which are exchanged must be equivalent in some manner. This is not necessarily to say that they are equal in all respects, like a numerical identity or both being rigidly designated by the same name; but to say that they count as one another in a sortal sense of equivalence. And just like such sortals, counting as one another is ultimately a consequence of the social organisation of trade.

I will highlight it again because it's important; exchange value is embedded in the commodities, but is distinct from every commodity. The mathematical structure of this embedding is what I've been wrestling with in a lot of these posts.

Let us take two commodities, e.g., corn and iron. The proportions in which they are exchangeable, whatever those proportions may be, can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron: e.g., 1 quarter corn = x cwt. iron. What does this equation tell us? It tells us that in two different things – in 1 quarter of corn and x cwt. of iron, there exists in equal quantities something common to both. The two things must therefore be equal to a third, which in itself is neither the one nor the other. Each of them, so far as it is exchange value, must therefore be reducible to this third.

This is an interesting argument; a kind of transcendental deduction. If all the properties of x and all the properties of y are held equal in some sense, what renders that equality must be external to the properties of both; and instead is a feature of the relation of the two. Because changing the quantity of one commodity changes the quantity of the other that may exchange with it, the commensurability of x and y must be expressed in terms of an abstract quantity with which they are both equal.

Contained in this argument are the germs of the relative form and equivalent form of value, and of the universal equivalent. That we exchange x for y doesn't tell us why we can exchange x for y; we say that we can exchange them when they are of equivalent value, but this equivalence as a numerical property must be abstracted from the material properties and relative uses of both in the trade.

That was one reason I put it in scarequotes.

Have a sketch of how to decompose a commodity into its constituents while still satisfying the above algebraic relationships, but it's more based on things from chapters 1 and 2.

If you take an iPhone and split it into the commodities which are used to assemble it, the socially necessary labour time of the iPhone will be equal to the sum of the socially necessary labour times for the composite of commodities which make it plus the assembly time. If we define a function D that takes a commodity and splits it into the sources of socially necessary labour time that together constitute the total for that commodity we'd end up with something like:

SNC(D(iPhone)) = SNC(C1 + C2 + C3 + ... +Cn)+SNC(assembly of iPhone)

where SNC is the socially necessary labour time. But we know from how direct prices and labour times work - they're additive/associative/commutative, this results in:

SNC(D(iPhone)) = SNC(D(C1 + C2 + C3 + ... + Cn)) + SNC(assembly of iPhone)
implies
SNC(D(iPhone))=SNC(D(C1))+SNC(D(C2))+SNC(D(C3))+...+SNC(D(Cn))+SNC(assembly of iPhone)

similarly, C1 through Cn will consist of commodities which have a socially necessary labour time for production and an overall assembly time for each commodity from its constituents. The trick here is to notice that this procedure of the iterative application of D bottoms out in raw goods, which have not been subject to labour and therefore have no exchange value. This makes D partition the commodity into the raw goods which constitute it - which do not contribute to the value - and the socially necessary labour times for transforming raw goods into the commodities. The consequence of this is that just as value consists essentially in (abstract) labour times, the socially necessary labour time consists of sums of abstract labour alone; transformative activities on raw goods, and transformative activities on bought commodities. So long as commodity labels remain in the the expression for D(x), the procedure iterates down to labour times, which are already isomorphic to direct prices.

What remains to be shown, though I think it's quite obvious, is that D as defined above agrees with the direct price decomposition as defined previously.

In 2200 people are going to be looking to Gibson for 'essential insights into the nature of humankind' more than Dostoevsky and Tolstoy.

Appreciating 'the classics' is fine, reducing good literature to them is silly. In 200 years perhaps people will be lamenting that not enough people read Danielewski and Palahniuk. There's already something similar happening with Borges and Eco, last time I spoke to literature snobs anyway.

It might be, but over 8 times reduced revenue due to piracy in music looks like a stretch to me. Even if you double the amount of people who admitted music piracy according to that study and assumed that people who pirate music only pirate music that still leaves extra revenue for books. Music revenue/0.3 is still 2-3 times less than books.

Regardless, there's no evidence people are reading comparatively less books. The death of literature as a position has to come from a (somewhat conservative) cultural stance; something about digital books being worse than paper ones.

I do prefer paper books personally, especially ones that you study and return to. Over years of use the deterioration of pages opposing the spine gives you a good measure of which parts are most important and most difficult for you.



Such a conservative stance is being taken by Number2018. I see no reason to believe artistic merit dies with increasing popularity of the art form - absent a well developed theory of artistic merit and its relation to digitalisation and increasing popularity. So far, we're just sneering.

https://thenewpublishingstandard.com/global-book-market-valued-at-143bn/

https://en.wikipedia.org/wiki/Global_music_industry_market_share_data

Global revenue for books is about 8 times more than music in 2017.

Principle (1), the ability to decompose commodities into constituent commodities and assembly prices is tricky. Might take some time to model it.

Mathematical note: the algebra of commodities and the algebraic structure of value.

A tacit assumption in the mathematical model I've made so far is that commodity direct prices for a specific amount of that commodity are a real or rational multiple of the per unit price or per unit socially necessary labour time. Often, however, an exchange consists of multiple commodities for multiple commodities of equivalent value or of multiple commodities for their real price.

Given the previous sketch on the relationship of direct to real prices, I'm going to deal solely with the mathematical relationship between multiple commodities being traded for their direct price. This is because the manifest real prices of commodities are chaotic and impossible to map consistently, but the minimal price they could be sold for profit is more well behaved (at least in principle). I am making an assumption that the socially necessary labour time for the production of a given batch of commodities is constant here, and this means the analysis will not hold when the socially necessary labour time is changing due to innovation in production.

Say someone buys an iPhone with an iPhone case. The direct price of the sum is the sum of the direct prices. Similarly with the iPhone, the direct price of the iPhone is the sum of the direct prices of its components. So by writing:

iPhone + iPhone case = (component 1 of iPhone + component 2 of iPhone + ... + final component of iphone) + price of assembly of iPhone + iPhone case

I mean to say that the two sides are of equivalent direct price. There are two principles here:

(1) The direct price of a commodity is the sum of the direct price of its components plus the direct price of that commodity's assembly (as determined from the socially necessary labour time of assembly).
(2) The direct price of a set of commodities is equal to the sum of the direct prices of each commodity.

I think it's appropriate, when talking about the direct price or socially necessary labour time of a single commodity, to fold the price of assembly into the direct price. However when looking to compose commodities into other commodities the assembly price must be added on; adding it on keeps track of the money expression of the socially necessary labour time. The direct price must reflect the total conditions of production for that commodity.

How does this tie in with the algebraic structure of value? This is mostly book-keeping as the mathematical machinery developed with the ordered field isomorphism does the work of translating labour times to direct prices. The only thing to construct is a mapping from collections of commodities to their socially necessary labour times - the above construction maps this to direct price (and then the sketch maps it to real price). I'll deal with point (2) first then come back to point (1)

The meat of this is translating the meaning of addition of commodities to a trade to the meaning of adding socially necessary labour times. So when Apple produces an iPhone and an iPhone case, writing this as:

iPhone+iPhone case

means that Apple has produced one iPhone and iPhone case.*

Writing it in terms of direct prices we have the same thing:

Value of (iPhone) + Value of (iPhone case)

We also have that if there were 2 iPhones and 2 iPhone cases produced, we have:

2 iPhones + 2 iPhone cases

becoming

(A) Value of (2 iPhones) + Value of (2 iPhone cases)

which is equal to

(B) 2*Value of (iPhone) + 2*Value of (iPhone case)

there is a subtlety here. The algebraic structure of commodities differs from that of values - we can't make -1 apples, but we absolutely can subtract the value of 1 apple from a trade to reduce the value in accordance with removing a commodity from the trade. This means that the above way of composing commodities into multi-commodity trades through addition is not immediately an ordered field, since there's no sense of subtraction of raw commodities.

If we have a list of all commodities C={C1, C2, ... , Cn}, the set of multi-commodity trades which can be made from that list is just the collection of all sums of commodities in the sense of *. If C1=iPhone and C2=iPhone case this just gives C1+C2 as the items available in the trade. This makes the set of all trades the set of all (finite) such sums.

C1+C2 is clearly the same as C2+C1, and C1+(C2+C3) is clearly the same as (C1+C2)+C3, only which goods are on the table matter at all, not how they are presented. This means that the + operation in sense * is associative and commutative. This means that the set of all possible trades is (isomorphic to) the free commutative monoid on C. It also comes equipped with the multiplicative group action of the whole numbers on it. EG C1+C1=2*C1 even though 2 is not a commodity. IE If N of the same commodity P are produced, this can be written as P*N (like 2 iPhones + 2 iPhone cases = iPhone + iPhone + iPhone case + iPhone case).

Now we can return to principle 2:

(2) The direct price of a set of commodities is equal to the sum of the direct prices of each commodity.

This states that the direct price of a multicommodity trade is just the sum of the direct price of each commodity. Now there's some extra formalism developed, principle 2 is equivalent to this:

the mapping from a set of commodities in a trade to its socially necessary labour time is homomorphism of commutative monoids (with 0 as the identity element), which are fields that have forgotten the idea of additive and multiplicative inversion (there's no such commodity as 1/iPhone or -iPhone). (A) and (B) as labelled above demonstrate the required properties of a commutative monoid homomorphism. Specifically, this mapping takes the above algebra of commodities and maps it to the additive part of the ordered field of values.

However, in this case it is not an isomorphism (and moreover one cannot exist). This is because the value of two distinct amounts of different commodities can be equal (so the mapping is not injective).

This then allows elements of (C,+) to be ordered by mapping them to their values. EG, if C1+C2 costs less (direct price) than C3+C4, C1+C2<C3+C4). Also, the equivalence classes of value take their form here as the preimage of a direct price. EG, if the value of C1 = C2 and both have price 2, C1 and C2 would be in the set of all elements that have price 2 - the inverse image of 2 under the homomorphism.

Edit: regarding the action of the whole numbers on the commodities. More generally, multiplication by fractions and reals should be allowed. EG, if a 1 g of diamond had a direct price of 1 unit, 1/sqrt(2) g of diamond has a direct price of 1/sqrt(2) units. It may be more appropriate to model a multicommodity trade as a vector space over the reals with a certain mapping to the reals that corresponds to the evaluation of direct price. I'll sketch this out later.

Edit2: the vector space idea doesn't work.

Sketch for later: one feature of the relationship between direct and real price.

As highlighted before, direct and real prices can (and usually do) diverge. This is pretty much a fact. A good requires a minimal cost to produce, but Bunnpris and Rema might sell it for different prices. This means that any supposed function mapping direct to real prices wouldn't actually be a function at all: it would be one-to-many. If Bunnpris sells Eldorado Tuna for 8.3NOK and Rema sells it for 8.2 NOK, it's the same commodity in the same amount, so both socially necessary labour times are equal. But the prices aren't. This means that direct price and price cannot have a direct mapping even when evaluating at precisely the same time.

A sketch of how to make a monotonic relationship between direct prices and prices might proceed as follows:
(1) Real prices are there to produce profit.
(2) It would be impossible to profit on the immediate sale of a commodity if the prices of production equalled the real price of the good in exchange.
(3) This means that the direct prices of production are a lower bound for the prices of sale.

So instead of associating the direct price of a commodity with a real price, we should associate the direct price of a commodity with a range of real prices. The range of sale prices for any commodity will have the direct price its greatest lower bound assuming sale is always sale for profit.

This means the function g that maps direct to real prices maps specific direct prices to intervals of real prices. EG, say the direct price of production for Eldorado Tuna is 3NOK, then any sale above 3 NOK is consistent with sale for profit. That means we can map:

direct price x->(direct price x, infinity)

And set up an ordering on the intervals (x, infinity) in terms of their greatest lower bound. EG, if direct price x < direct price y, then the corresponding order on real price intervals would be (direct price x, infinity) < (direct price y, infinity). This can be equipped with a distribution of real prices obtained from real sale data, which is the only way to represent all the different real prices that the same commodity can have.

One consequence of this is that while direct prices are essentially deterministic, real prices are essentially stochastic; the features of the distribution depending on where and when you are, and only easily summarised as an aggregate.

Mathematical note: the isomorphism of the measure of value and the standard of price.

I've been trying to understand the connection between value and price a bit better. If they're usually very similar but have the possibility of diverging in various circumstances that leaves some work in spelling out how the two relate quantitatively when things are going normally. In what sense is value as measured in the amount of abstract labour in the commodity the same as the price expression of that value?

I wrote before about labour times and values necessarily being calculable, and that the algebraic structure of value (and labour times) is that of an ordered field. There are a few things that characterise this relationship in terms of their socially necessary labour time and their direct price. Let commodity one in some amount x have direct price P1 and socially necessary labour time T1, and commodity two in some amount y have direct price P2 and socially necessary labour time T2.

(1) If we have two distinct commodities in two different amounts, x and y, the value of x and y together as measured in (socially necessary) labour time will be the sum of the labour times. T1+T2
(2) Under the same set up, if we take x and make it A times, it will have the same socially necessary labour time as A times x; A*T1
(3) Under the same set up, if we make y B times, the socially necessary labour time is B*T2.
(4) From (1), you can aggregate (2) and (3) to get the total amount of socially necessary labour time from the production of batches of commodities; giving the total socially necessary labour time as A*T1+B*T2.


Restating (1)->(4) in terms of prices just for explicitness:

(1) If we have two distinct commodities in two different amounts, x and y, the value of x and y together as measured in direct price will be the sum of their direct prices. P1+P2
(2) Under the same set up, if we take x and make it A times, it will have the same price as A times x; A*P1.
(3) Under the same set up, if we make y B times, the price is B*P2.
(4) From (1), you can aggregate (2) and (3) to get the total price from the production of batches of commodities; giving the price as A*P1+B*P2.

Let f be the function that maps a commodity's direct price to its socially necessary labour time. The first thing to notice is that this f is invertible; if things are going normally, any direct price is commensurate with a corresponding socially necessary labour time, and vice versa. For a given price, there is a certain amount of human labour in the abstract which that price expresses. This is to say that at a given time, there is a unique price for any amount of socially necessary labour time.

From (1) to (4) in both lists, you can see that the following relationships hold:

(1) f(P1+P2)=f(P1)+f(P2)=T1+T2
(2) f(A*P1)=A*f(P1)=A*T1

this means that the mapping from socially necessary labour times to direct prices is an isomorphism of fields. The two are so tightly coupled that socially necessary labour time and direct price are just different names for the same thing. However: this relationship between socially necessary labour times and their direct price expressions does not necessarily preserve the ordered structure of both of them. This is a useful distinction, as it is a substantially weaker form of the relationship between direct price and socially necessary labour time that Marx uses. You can find in Chapter (1):

Some people might think that if the value of a commodity is determined by the quantity of labour spent on it, the more idle and unskilful the labourer, the more valuable would his commodity be, because more time would be required in its production. The labour, however, that forms the substance of value, is homogeneous human labour, expenditure of one uniform labour power. The total labour power of society, which is embodied in the sum total of the values of all commodities produced by that society, counts here as one homogeneous mass of human labour power, composed though it be of innumerable individual units. Each of these units is the same as any other, so far as it has the character of the average labour power of society, and takes effect as such; that is, so far as it requires for producing a commodity, no more time than is needed on an average, no more than is socially necessary. The labour time socially necessary is that required to produce an article under the normal conditions of production, and with the average degree of skill and intensity prevalent at the time. The introduction of power-looms into England probably reduced by one-half the labour required to weave a given quantity of yarn into cloth. The hand-loom weavers, as a matter of fact, continued to require the same time as before; but for all that, the product of one hour of their labour represented after the change only half an hour’s social labour, and consequently fell to one-half its former value.

Marx uses direct proportion here (which still produces an isomorphism of fields). But direct proportion has one property that the above account does not; direct proportion is a monotonic increasing relationship between socially necessary labour time and direct price. This means it also produces an isomorphism of ordered fields ( it is an order preserving map ).

We can weaken Marx's assumptions (based on cotton loom prices) here and end up with much the same algebraic relationship; we don't need direct price and socially necessary labour time to be proportional to one another, we just need direct price to be a monotonic increasing function of socially necessary labour time.

One reason that such a weakening might be useful is in the analysis of the relationship between inflation and the minimum wage. If the minimum wage increases, we can expect an increase in the direct prices associated with any amount of social labour; labour becomes more valued. If inflation occurs, then the amount of each commodity that the same minimum wage as before buys is decreased; labour becomes less (relatively) valued. These two forces can (and usually do) operate at the same time, but I would be very surprised if the two had a linear relationship; this is what would occur when increases in the minimum wage were a constant multiple of inflation - that the graph between them is a straight line. This doesn't happen often (look at any real wage graph).

This means that f, the mapping from direct prices to socially necessary labour times, is a time varying function. The above relationship between the fields works at any specific time point, but the isomorphism breaks down for similar reasons to the ideal equivalence between real price and socially necessary labour time. That is, rapid fluctuations in the value of commodities or money undermining the stability of (equivalently valued) trade (exchange).

If I can be so intrusive, I'd recommend listening to Manuel De Landa's lectures on Youtube. De Landa sees things from a very Deluzian perspective, but his lectures are far less dense than reading Deleuze (or Deleuze and Guttari).

Would people be interested in me continuing through the book too? I have a couple of summary posts of what's happened so far planned, and some ideas for extra mathematical formalism to investigate. So there will be a delay due to the latter taking a decent amount of time.

NP. I've said elsewhere, I don't think it's 'Marx's Marx', I think it's very much 'fdrake's Marx'.

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.

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. — fdrake

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.

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?

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.

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.

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.

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.

Do you think this metaphysics of expression admits of different degrees of expression?

The star is shiny -> The star shines -> the star luminesces with brightness X and frequency spectrum Y.

Or are expressions only discretised into the presence or absence of a modality?

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.

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.

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.

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.

The value of fiat currency comes from real production and trade. — Bitter Crank

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.

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.

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. — frank

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.

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.

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.

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.

Felicity and infelicity would serve as an interesting topic for epistemology. Instead of analysing how propositions connect to truths through justifications, we could analyse what makes certain speech acts good or bad in accordance with their function. This, roughly, is what I see as the big picture behind Ray Brassier's 'Concepts and Objects' (after the critical component), what he imagines as a renewed purpose of epistemology:

Unless reason itself carries out the de-mystification of rationality, irrationalism triumphs by adopting the mantle of a scepticism that allows it to denounce reason as a kind of faith. The result is the post-modern scenario, in which the rationalist imperative to explain phenomena by penetrating to the reality beyond appearances is diagnosed as the symptom of an implicitly theological metaphysical reductionism. The metaphysical injunction to know the noumenal is relinquished by a post-modern ‘irreductionism’ which abjures the epistemological distinction between appearance and reality the better to salvage the reality of every appearance, from sunsets to Santa Claus

To refuse correlationism’s collapsing of epistemology into ontology, and of ontology into politics, is not to retreat into reactionary quietism but to acknowledge the need to forge new conditions of articulation between politics, epistemology, and metaphysics. The politicization of ontology marks a regression to anthropomorphic myopia; the ontologization of politics falters the moment it tries to infer political prescriptions from metaphysical description. Philosophy and politics cannot be metaphysically conjoined; philosophy intersects with politics at the point where critical epistemology transects ideology critique. An emancipatory politics oblivious to epistemology quickly degenerates into metaphysical fantasy, which is to say, a religious
substitute. The failure to change the world may not be unrelated to the failure to understand
it

The distinction between the object’s conceptual reality and its metaphysical
reality has an analogue in the scholastic distinction between objective and formal reality.
Yet it is not a dogmatic or pre-critical residue; rather, it follows from the epistemological
constraint that prohibits the transcendentalization of meaning. The corollary of this critical constraint is the acknowledgement of the transcendental difference between meaning and being, or concept and object. Contrary to what correlationists proclaim, the presupposition of this difference is not a dogmatic prejudice in need of critical legitimation. Quite the reverse: it is the assumption that the difference between concept and object is always internal to the concept—that every difference is ultimately conceptual—that needs to be defended.

Reading the distinction between noumena and phenomena as part of the speech act (not merely 'confined to language' or correlation), by which the objective features of (philosophical?) speech acts could be analysed on their merits of noumenal exhibition, would regardless be an interesting project.

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.

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.

I do actually think that time presents a coherent set of problems, though. The problem of presentism isn't 'Can we say the past and future exist in the same sense as now?', it's 'Does only the present exist?'. I think some things which evince that the debate isn't just a problem of language are:

(1) the problem that the present isn't temporally extended.
(2) Whether presentism requires there to exist a unique ordering of all events.
(3) The equivalence of the ordering in (2) with time.

Admittedly there's a lot of baggage which can be brought to the table. 'Temporal extension' reads a lot like the Cartesian sense of extension, which applies to substance, and time alone doesn't seem to be substantial. Regardless, intervals of time are well understood, the present understood as a duration 0 event makes it pretty hard to defend. This alongside whether presentism requires a single unique now or a plethora of unique nows depending on the spacetime geometry of the universe.

I think the interaction of the debate around presentism with the problem of future contingents is suspiciously 'language addled' so to speak. If I say 'it will rain tomorrow' now, and it does rain on the next day, 'it will rain tomorrow' is true. If presentism is true tomorrow doesn't exist, which (arguably) doesn't allow the lining up with the state of affairs which happens tomorrow with my statement. Then it can be analysed as 'It will rain tomorrow' will be phrased as 'It will rain (for some subinterval of time within the next 24 hours)'. I think once we start doing the conceptual analysis of phrases to dodge objections using our folk understanding of terms it should raise suspicions that what we're doing is moving language around rather than anything substantive.

I would also like to highlight that it's probably the case that it's easier to take a bad approach to a complicated problem, making 'language run idle', than it is for the problem itself to have 'must be treated with language on idle' as a property.

Presentism and the problem of future contingents:

But what if dog didn't do way instain mother? Dog is would be, maybe. But definitely dog wasn't. Would be isn't is and wasn't isn't is, can talk that. But only is is is! Therefore wasn't isn't is and isn't isn't was, and would be isn't is and isn't isn't would be. But isn't is maybe would be some of the time. Would be and wasn't isn't is.

I hope that you don't think that I would suggest that a definition correctly understood would somehow solve the problems that Wittgenstein is referring to. I would suggest that some philosophical problems do go away once one understand some of Wittgenstein's points. And even in the example above one could apply Wittgensteinian methods to help clarify concepts. — Sam26

No, I don't think you take such a reductive view of philosophy. What issues do you think are dissolved, or nearly dissolved, by looking at them through your preferred lens? I don't have a view of philosophy of language in general, but I am rather prejudiced against ordinary language philosophy because at its worst it thinks there are no substantive philosophical issues and because it espouses a kind of 'first philosophy' which is to be done through the analysis of word use.

With reference to the other desired kind of response you wanted, I can think of a few things which reading Wittgenstein left me with.

(1) Pay a lot of attention to how the thing you're looking at works.
(2) Using language with a purpose always has some background upon which it makes sense.

(1) and (2) together form a maxim: once you have a description you have a model.

(3) Rule following is a non-deliberative** component of language use; the 'way of following a rule which is not an interpretation'. As @StreetlightX put it, language is extra-linguistic.
(4) Highlighting the importance of aspect shifting (seeing as).

The interaction of (3) and (4) has been influencing my thoughts and philosophical studies for some time. It's difficult for me to articulate without jargon, but the rough idea is that nature is suggestive. (3) highlights that we're always in the world with the stuff at our fingertips and (4) highlights that the world springs out into structures when we have both language and the stuff at our fingertips.*

As somewhat of a consequence of (1),(2),(3),(4), though the theme is also present in the contrast of early vs late Wittgenstein in terms of the realism of the language he studies.

(5) Good presuppositions facilitate insight, bad ones impede it.

Don't you think that depending on how you define the word creates many philosophical and maybe even scientific confusion? — Sam26

There's a debate, now mostly settled as far as I know, in feminist theory. It began as an internal tension in feminism; why was it that feminist activity mostly excluded women of colour? This gave rise to theoretical and practical emphasis on 'intersectionality', a view that paying attention to how different marginalised groups interact on a personal (like black transgender) and interpersonal (corporate hierarchies like black women are cleaners, white women are secretarial, white dudes are managerial) level is important in addressing political marginalisation as a whole.

The idea that any of this could have been resolved through supplying an appropriate definition, or impeded forever by supplying inappropriate definitions, is really far off the mark. It was mostly worked through by people hashing it out, and was enabled by the civil rights movements for people of colour and women. Political problems don't arise or go away through the analysis of language, they arise and go away through targeted change of social systems and behavioural change on a large scale. The analysis of these problems and the activity of addressing them concern real social systems, not words.

The story's a bit less clear cut for time, I imagine.