There are infinite isms

11 Jun, 2025

If not neocapitalism, then what?

Ok, let's see.

Let's define

be a countable or perhaps larger set of atomic features; yes/no statements such as:

• $f_1$: "private property is protected"
• $f_2$: "banks may lend at interest"
• $f_3$: "the state plans heavy industry"

So that each ideology can flip those switches on or off.

What is an ism?

The second version lets us say things like if $f_1$ and $f_2$ hold, then $f_4$ must hold.

If $|\mathcal{F}|={\aleph }_0$ (merely countably many features) then its powerset has cardinality

the size of the continuum. Even after we throw out logically inconsistent collections, we still get uncountably many consistent theories. Mathematically we are living in a Boolean algebra of subsets, or its Lindenbaum–Tarski algebra (all theories), whose points form a compact totally disconnected Stone space.

So the slogan it’s either capitalism or communism is like flattening a three-dimensional city map onto a single street.

Geometry of the ideology space

• Order; inclusion $I\subseteq J$ says J contains every principle of I.
• Distance; Hamming or Jaccard distances on $\{0,1{\}}^{|\mathcal{F}|}$ count how many switches differ.
• Lattice moves; intersection lets us find common ground; join (union + closure) fuses programs.

A toy example

Take just four features:

Then $2^{\mathcal{F}}$ has $2^4=16$ possible ideologies.

Already 14 of the 16 points are neither pure capitalism nor pure communism.

Takeaway

Because the space is a full-blown Boolean cube (and, with logic, a Stone space), there is (1) continuum of coherent isms, (2) natural neighbourhoods (market-friendly socialism), and (3) structured ways to travel with reform paths, compromises, hybrid programs.

Notes for a future post:

#social-science