In a series of blog posts I have written, and probably in more that I will write in the future, I explain my understanding of Marxist ideas in partially mathematical terms.

There are a few reasons I am doing this, and there are also a few reasons I am aware of for why this might not be a good ideas.

Speaking mathematically means restricting one’s language to a subset of the full range. As a result, the meanings and associations present in ordinary language are not available when writing mathematically. This has upsides and downsides.

Upsides:

• Mathematical language can be more precise than the full range of human language, and so the correctness of mathematical arguments is easier to appraise. This has many potential benefits. For example, it may make it possible for consensus on the validity of one’s arguments to be reached more quickly amongst readers. This can help settle arguments more quickly, and help in keeping those struggling against capitalism more aligned in their actions, and thus make the struggle more effective overall. It also helps writers themselves develop their thoughts more effectively, by forcing them to be more explicit about their assumptions and by allowing them to check their own arguments more easily.
• Mathematical language is geographically and culturally translatable (assuming a base level of familiarity with math). Because mathematical language is restricted, mathematical writing relies less on culturally and geographically specific implicit knowledge, which makes it more culturally translatable (assuming that the reader knows math). This is why it is possible for mathematically literate people to read and understand Euclid’s Elements, a document written over 2000 years ago in a culture very different from their own. This means it is potentially a useful tool in generating coordinated, international action – a necessity for the overthrow of capitalism.
• Expression of a concept in mathematical language is sort of a prerequisite to expression in terms a computer can understand. If we can create models of capitalism, class society, certain communist systems of production, etc., that can be implemented on computers, then perhaps we can run simulations and experiments to help in the struggle against capitalism and the construction of communism. Of course this has dangers as well – we cannot get lost in navel-gazing on the computer and lose sight of the meatspace task of organizing the working class to challenge capitalism and build a new social order.
• Mathematical concepts and arguments can be made modular. We can make our arguments as reusable as possible by using as few assumptions as possible, and making this fact clear. For example, implicit in Capital Volume I are several models of capitalist society of different levels of generality. The simplest model (what I would call MCM') is very general and conclusions derived from this model are broadly applicable, but the text does not clearly demarcate which conclusions follow from this model and which from additional assumptions, so it is not immediately clear which conclusions can be applied in any given context.
• I am a mathematical person and writing down my understanding of concepts in mathematical terms helps me personally to understand it better. So, I probably would be doing this out of personal compulsion even if I didn’t think it wasn’t useful generally.

Downsides/caveats:

• Mathematical writing consists of simple models. They are provisional and do not perfectly represent reality. As a result, any conclusions drawn from them should be understood provisionally and we should remain open to revising our models. Math has a certain aura of objectivity that leads to some people taking it too seriously. It is, like all human expressions of thought, simplistic (compared to reality) and should not be treated with reverence.
• In the current moment, mathematical language is not very accessible, and to many it is alienating. Most people are not trained in math, and many are traumatized by their mathematical education and as a result have negative associations with math. This is not a historically necessary state of affairs, but it is the current state (at least in America. I don’t know about other countries.)
• Speaking mathematically means restricting one’s language to a subset of the full range. As a result, the meanings and associations present in ordinary language are not available when writing mathematically. As described above this has various pluses, but it also means that many things can be described more effectively using the full range of language than with the restricted subset of math.

Let me conclude by saying speaking mathematically is a spectrum. One can speak more or less mathematically (i.e., restrict one’s language to a smaller or larger subset.) Speaking completely mathematically means writing in a fully formal way comprehensible only to a computer. In practice, one incorporates aspects of mathematical language within a larger text that uses non-mathematical language as well. I am just attempting to use more than the 0% of mathematical language which is customary.