Nicholas Funari Voltani

20260202 O Capital e Teoria de Categorias (Espaço Comum de Organizações)

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up:: 099 MOC Anotações // 010 MOC Marxism // 027 MOC Category Theory

Preliminary remarks

Motivation: common conceptual frame to deal with political economy and political organization (!)

References:

“Theory of social worlds”, from CSO (Common Space for Organizations/Espaço Comum de Organizações).

Modeling

System models system if all morphisms can be written as

for some (where is the concatenation operator in categories).

The advantage that can be gained is that elements in can be retroducted to , i.e. we can ask whether it makes sense in as it makes sense in or not.

Embedding yields an allegory (mathematical concept [!]). The importance of this is to prove ontological statements, not merely in the “representational” space.

A convergence of theories

  • Category Theory
  • Tektology (Bogdanov): general theory of natural/social/political organization theories
  • Objective Phenomenology (Badiou): “Reason of Worlds”, a theory of phenomena/appearances

Immanent critique: not for seeing from the outside, but from seeing more from the inside, seeing inside more thoroughly.

Interpreting “objective phenomenology”: analysing some object not by “looking from the outside”, but by HOW IT APPEARS to OTHER PARTS OF the system.

E.g.: money can only see what is equal to it in value and what isn’t. Capital sees things as what can valorize itself and what can’t.

E.g. 2: the labor process can be seen differently:

  1. A worker sees things changing and being created
  2. Money sees value coming in and coming out greater
  3. capital sees constant and variable capital combining into commodities

Fetichism and light example: to understand why light appears with different wavelengths is to understand why different retinas see them differently. Using a microscope allows for a more thorough analysis of the phenomenon of light, but not on why it differently appears to us! A fetichistic understanding is to try to understand this difference within the very phenomenon (?).

Artificial restriction of evaluation space: fetichism goes away when it is seen from outside its usual restricting/mistifying scope; a flattening of perspectives.

A natural question is: when do we know we’re having a limited, “fetichistic” point of view? The general answer is: when you are seeking to “leave no stone unturned”.

Evaluating whether two commodities are equivalent or not:

So they start beyond assuming that commodities are all comparable, and retrieving results that are valid for equivalent commodities from this more general statement.

Mentions of categorical terms:

Commodities are produced such that they are comparable to other things (commodities)! A “defective” product is one that is not like the other products within a same production process.

A use value of something is the “intersection” of its use and the use value kernel (?). So the “use” of a thing is distinguished from its “use value”.

Evaluating from some domain towards a space of values , . Coming back through , as in a Preimage of Function, the composition yields “bigger” elements — somehow dialectics arises here!

For capital to be a consistent value relation, it either

  • Breaks its own logic, and only sees equivalence
  • Breaks equivalence somehow

In this sense, it is “needed” to have different degrees of evaluation between commodities, since Ciclo D─M─D’ produces something that is not equivalent to what was spent: transitivity is broken, at least formally!

Value is an intuitionistic relation!!!

Referências

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