Section 1: The Two Factors of a Commodity: Use-Value and Value

There are two essential components of the commodity, value and use-value.

1. Use-value is the concrete, natural form of the commodity; its physical or measurable characteristics. Quality and quantity are determined by direct physical observation.
2. Value is the abstract, social form of the commodity. Its quality or substance is homogeneous, abstract human labor. Its quantity is socially necessary labor time (SNLT).

We infer value through exchange value, the relationship between two commodities such as "one shirt is worth two hats."

Mass and weight provide an almost 1-to-1 analogy to value and exchange value, respectively. Objects have mass, but we do not measure absolute mass. We always measure relative mass by comparing the mass of two objects. One of these objects might be a standard kilogram weight. So weight expresses mass, it allows us access to it, but only through relative measurements of different massive objects. When weighing a mass, all other properties besides mass are ignored; color, volume, texture, etc. do not affect the weight. All other qualities except mass are "abstracted" away, and the objects are considered only insofar as they are masses.

Like the above, exchange value expresses value, but only after abstracting away all the distinct characteristics (use value) of the commodities. When we abstract from the use-value of a commodity, we also abstract from the concrete kind of the labor that produced it. This leaves a "residue" of abstract labor, human labor as such. This is the substance that forms value, common to all commodities.

Exchange value tells us about equivalence in terms of both quantity and quality. It is only logical to compare two quantities if they are of like quality. Think of it like converting to the right "units" to add two lengths: You can't directly add 5 inches + 3 centimeters, so you convert one into the units of the other in order to add them as quantities of the same substance.

Section 2: The two-fold Character of the Labour Embodied in Commodities

When we abstract from the use-value of a commodity, we also abstract from the concrete kind of the labor that produced it. This leaves a "residue" of abstract labor, human labor as such. This is the substance that forms value, common to all commodities.

This is a small point, but this dichotomy between concrete/natural, abstract/social continues throughout Capital in various forms.

Marx's method is not like the modern scientific method in which one test an arbitrary hypothesis. Here, the hypothesis (or thesis, more properly) is identified by the internal logic of the object of analysis (here, the commodity). This immanent critique is one example of Hegel's influence on Marx. The reason this is important: Chapter 1 is not a hypothetical or a final model to accept or deny (like a marginal utility theory, e.g.). It is a set of observations first and foremost, with logical inferences in tow.

okay this was a lot more work than I expected, let me know if you want more, otherwise I'm probably gonna stop

Your summaries are very helpful!

Section 3: The Form of Value or Exchange Value

The purpose of section 3 is to trace the "genesis" of money, from exchange value to "the dazzling money-form."

In all subsections, a value relation is any relation that manages to express, or reveal, the value of a single commodity.

A. Elementary or Accidental Form Of Value

x commodity A = y commodity B

The left side of the equation is the relative form, the commodity that has its value expressed. The right side of the equation is the equivalent form, the commodity that expresses value by acting as an equivalent.

This elementary form of value is symmetrical, so reading it either direction is equally valid and merely a different perspective; but in either case, only one or the other commodity expresses its value.

The equation implies equivalence of both quantity and quality. The word for this ability to compare quantity, by virtue of identical quality, is commensurability. The value of the relative-form commodity takes on an existence in the bodily form, in the use value, of the equivalent-form commodity. This sounds really odd, but think of it like mentally substituting "y commodity B" everywhere you see "x commodity A", not just in quantity, but in quality too. The physical body of commodity B gives a physical, independent existence for the purely social value-substance from our analysis which is imprisoned inside the use value of commodity A.

Think about the consequence of value taking on the physical form of the equivalent-form commodity (the coat in Marx's example). If the physical body of a commodity is value itself, in the context of a single elementary value relation, can you guess what commodity might be universally recognized as value?

Finally, because value relations are relative, they do not tell us the absolute amount of value in a commodity. If commodities A and B both dropped in value by half, they would still happily exchange at a rate of x to y respectively.

Section 4: The Fetishism of Commodities and the Secret Thereof

Honestly this is one of my favorite sections of the entire book, and it's right at the start. Many Marxists, and even some non-Marxist, humanist types, have noted the significance of commodity fetishism and more broadly Marx's theory of alienation. It goes beyond capital, but it is certainly interesting in regard to capital too!

Definition of commodity fetishism:

"In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with the products of men’s hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseparable from the production of commodities."

In other words,

"the relations connecting the labour of one individual with that of the rest appear, not as direct social relations between individuals at work, but as what they really are, material relations between persons and social relations between things."

I think the name "fetish" is perfect. It refers to religious fetishes — think voodoo dolls and other idols — which humans consciously produce, yet they believe that the objects take on a supernatural character once produced.

The name is perfect for two reasons. First, it very precisely describes what is happening with commodities and the illusions they produce in the mind. Second, because it is a jab at the colonizing European societies that believed themselves to be so culturally and intellectually superior to the peoples they colonized, many of whom used fetishes in their religious practices.

"... the mutual relations of the producers, within which the social character of their labour affirms itself, take the form of a social relation between the products."

This line reminds me of one of Marx's letters to his friend Ludwig Kugelmann in which he strongly defends his identification of labor as the substance of value. For Marx, the procedure for this determination is backward from the political economists. The political economists started from the commodity in order to identify the determinants of commodity prices. From this point of view, labor is just one speculative guess at one such determinant among many, such as energy, utility, etc.

Marx starts from the other direction. For him the big question is not what forms price magnitudes? but rather how does capitalist society distribute labor? And, as he says in the letter, it is clear that the way that the total social labor is distributed in capitalism is through the exchange of commodities. From this perspective it is no longer a mystery why labor is the essence of value.

To digress a tad. Alienation occurs when a human power or ability is placed onto an object. This occurs with labor being objectified (i.e. placed into an object) as value. But it can occur in other ways, such as placing our legal-political power into liberal institutions. We are alienated from our ability to affect political decisions and only have access to that ability through electoral institutions.

The same is true for the "human essence" which I won't spend time exploring here; but in Marx's early, pre-communist 20s and 30s, when he was involved with the Young Hegelians, he spent a lot of time thinking about materialism and religion in works like Theses on Feuerbach, The German Ideology, and Critique of Hegel's Philosophy of Right. In the intro to the last one, where Marx makes his famous "opiate of the people" line (this intro is my favorite of all of Marx's writing) he talks about "inverted consciousness" in an "inverted world". This inversion is due to alienation, and in that way is linked to commodity fetishism.

Section 3 (continued): The Form of Value or Exchange Value

B. Total or Expanded Form of value

z Com. A = u Com. B or = v Com. C or = w Com. D or = Com. E or = &c.

Generalization of the elementary form of value from subsection A. Each singular commodity A has an elementary form of value with each other commodity B, C, D, etc. and vice versa. It's unwieldy to state an infinite series, but at this point it is the only way to adequately express the value of a commodity.

C. The General Form of Value

Since the expanded form of value is unwieldy, simply flip it around, since we already knew in subsection A that reading the equations backward is equally valid. Instead of each commodity requiring an infinite series of elementary value relations to express its value, read it as all commodities being able to express their value universally in one special commodity Z. This one commodity takes on a special social function of embodying value universally. This becomes its use value.

The universal equivalent commodity only emerges insofar as all other commodities are practically excluded from direct exchange. Although as a logical prerequisite all commodities are directly exchangeable with each other, in practice they exchange only directly with the universal equivalent, and it the mutual exchangeability of all commodities is apt to be "forgotten". Thus we perceive exchangeability to be unique to that one commodity, as if there is something inherently special about that one commodity in itself, when its specialness is precisely because of it being "just" a regular commodity, at first.

D. The Money-Form

Same as form C, but note that historically gold has been chosen as the universal equivalent commodity.