Thursday, April 2, 2026

Concentration among exploiters (more rigorous)

Nice, yes, please make a more rigorous theorem-proof version.

Absolutely. Here is a more theorem-proof version.

I will state a minimal model, then prove four claims:

exploitation rents are dissipated under free entry into coercive appropriation;
exclusive jurisdiction is therefore necessary for positive exploitation profit;
exploitative organizations have a structural tendency toward concentration;
conditional on growth, each exploitative organization has a structural tendency toward internal centralization.

0. Environment

There is a unit mass of subjects spread over a unit territory. A firm can obtain revenue only by noncontractual transfer, not by production. So all revenue is a coercively appropriated transfer from subjects.

Let $s\in[0,1]$ denote the measure of territory-population under a firm’s control.

Assume that under exclusive jurisdiction over size $s$, a firm obtains gross transfer revenue

\[
R(s)=as,\qquad a>0.
\]

To maintain coercive control over size $s$, it incurs operating cost

\[
C(s)=F+cs^\eta,\qquad F>0,\ c>0,\ 0<\eta<1.
\]

Hence operating profit under exclusive control is

\[
\pi(s)=R(s)-C(s)=as-F-cs^\eta.
\]

The assumption $0<\eta<1$ is the scale-economy assumption: coercive cost rises with size, but less than proportionally.

1. Competition for a given territory dissipates rents

Fix one territory of size $s$, with prize

\[
V=R(s)=as.
\]

There are $m\ge 2$ potential exploiters. If they contest the territory, each chooses coercive effort $e_i\ge 0$, and the probability that firm $i$ wins exclusive jurisdiction is

\[
p_i(e)=\frac{e_i}{\sum_{k=1}^m e_k},
\]

with payoff

\[
u_i(e)=p_i(e)V-e_i.
\]

This is a pure transfer contest: effort does not create output, it only affects who gets to seize it.

Theorem 1 (contest rent dissipation)

For fixed $m$, the contest has a unique symmetric Nash equilibrium with

\[
e_i^*=\frac{m-1}{m^2}V
\]

for every $i$. Equilibrium expected profit is

\[
u_i^*=\frac{V}{m^2},
\]

and aggregate dissipation is

\[
\sum_{i=1}^m e_i^*=\frac{m-1}{m}V.
\]

Hence as $m\to\infty$,

\[
u_i^*\to 0
\quad\text{and}\quad
\sum_i e_i^*\to V.
\]

Proof

In a symmetric profile $e_i=e$ for all $i$, player $i$'s payoff from deviation $x$ is

\[
u_i(x;e)=\frac{x}{x+(m-1)e}V-x.
\]

FOC:

\[
\frac{(m-1)e}{(x+(m-1)e)^2}V-1=0.
\]

At a symmetric equilibrium, set $x=e$. Then

\[
\frac{(m-1)e}{(me)^2}V=1
\quad\Longrightarrow\quad
e=\frac{m-1}{m^2}V.
\]

Second derivative is negative, so this is optimal. Then

\[
u_i^*=\frac{1}{m}V-\frac{m-1}{m^2}V=\frac{V}{m^2}.
\]

And

\[
\sum_i e_i^*=m\frac{m-1}{m^2}V=\frac{m-1}{m}V.
\]

Taking $m\to\infty$ gives the limit. ∎

Corollary 1 (free entry eliminates net exploitation rents)

Suppose entry into the contest requires cost $k>0$, and entrants choose whether to enter before the contest. Then free entry implies the equilibrium number of entrants $m^*(k)$ satisfies

\[
\frac{V}{(m^*(k))^2}\approx k.
\]

So as $k\downarrow 0$, $m^*(k)\to\infty$, and expected net profit converges to $0$.

Proof

By Theorem 1, post-contest gross expected profit per entrant is $V/m^2$. Under free entry, entry continues until $V/m^2\le k$, with equality up to integer rounding. As $k\to 0$, the implied $m$ diverges and net profit vanishes. ∎

Interpretation

This formalizes the claim that exploitation as a profitable activity requires restricted entry into coercive appropriation. If coercive appropriation itself is competitively open, the prize is dissipated in the struggle over who gets it.

So the relevant “market structure” of exploitation is not competitive supply of transfers, but exclusionary monopoly over a territory and population.

2. Concentration across exploiters

Now consider an industry of exploiters dividing total controlled size $S\le 1$. Suppose this size is partitioned among $n$ firms as $s_1,\dots,s_n$, with

\[
\sum_{i=1}^n s_i=S.
\]

Theorem 2 (superadditivity of exploitative profit)

For any nontrivial partition $s_1,\dots,s_n$ of $S$,

\[
\pi(S)>\sum_{i=1}^n \pi(s_i)
\qquad\text{whenever }n\ge 2.
\]

Hence a single exploiter controlling all $S$ is strictly more profitable than any fragmentation of that same total territory-population.

Proof

Compute

\[
\pi(S)-\sum_{i=1}^n \pi(s_i) = \big(aS-F-cS^\eta\big)-\sum_{i=1}^n \big(as_i-F-cs_i^\eta\big).
\]

Using $\sum_i s_i=S$,

\[
\pi(S)-\sum_i \pi(s_i) = (n-1)F + c\left(\sum_{i=1}^n s_i^\eta - S^\eta\right).
\]

Since $0<\eta<1$, the map $x\mapsto x^\eta$ is strictly concave, so for any nontrivial partition,

\[
\sum_{i=1}^n s_i^\eta > \left(\sum_{i=1}^n s_i\right)^\eta = S^\eta.
\]

Also $(n-1)F>0$. Hence the difference is strictly positive. ∎

Corollary 2

Merger, conquest, annexation, cartelization under one command, or any other elimination of separate exploitative apparatuses is privately profitable for exploiters.

This gives a formal concentration logic: the total exploiter surplus is maximized by unification, not fragmentation.

3. A dynamic law of concentration

To move from comparative statics to dynamics, define per-unit fitness

\[
w(s)=\frac{\pi(s)}{s}=a-\frac{F}{s}-cs^{\eta-1}.
\]

Lemma 1

$w'(s)>0$ for all $s>0$.

Proof

Differentiate:

\[
w'(s)=\frac{F}{s^2}+c(1-\eta)s^{\eta-2}>0.
\]

Since $F>0$, $c>0$, and $0<\eta<1$, both terms are strictly positive. ∎

Thus larger exploiters have strictly higher per-unit net return.

Now let exploiters’ shares evolve by a replicator law:

\[
\dot s_i=s_i\big(w(s_i)-\bar w\big),
\qquad
\bar w=\sum_{k} s_k w(s_k).
\]

This says firms with above-average per-unit exploitation return grow at the expense of those with below-average return.

Define concentration by the Herfindahl index

\[
H(s)=\sum_i s_i^2.
\]

Theorem 3 (concentration rises along the dynamic)

Along the replicator dynamic,

\[
\dot H = 2\sum_i s_i^2\big(w(s_i)-\bar w\big)
= 2,\mathrm{Cov}_s(s_i,w(s_i)).
\]

Because $w$ is strictly increasing, $\dot H\ge 0$, with strict inequality whenever at least two active firms have different sizes.

Proof

Differentiate:

\[
\dot H = 2\sum_i s_i \dot s_i
= 2\sum_i s_i^2\big(w(s_i)-\bar w\big).
\]

Since $\sum_i s_i=1$, this is exactly the covariance of $s_i$ and $w(s_i)$ under the share weights $s_i$. Because $w$ is strictly increasing in $s$, larger shares are paired with larger fitness. Therefore the covariance is nonnegative, and is strictly positive unless all positive-share firms have equal size. ∎

Theorem 4 (fragmented equal-share states are unstable; monopoly is stable)

Any rest point with $k\ge 2$ active firms of equal size $1/k$ is unstable. Each monopoly state $s=(1,0,\dots,0)$ is locally asymptotically stable.

Proof

A $k$-firm equal-share state is a rest point because all active firms have the same fitness. To show instability, perturb two firms:

\[
s_1=\frac1k+\varepsilon,\qquad s_2=\frac1k-\varepsilon,
\]

with $\varepsilon>0$ small, leaving others unchanged. Since $w$ is strictly increasing,

\[
w(s_1)>w(s_2).
\]

Hence the larger firm has a higher growth rate than the smaller, so the perturbation expands rather than contracts. Therefore the equal-share state is unstable.

For a monopoly state, say $s_1=1$, $s_j=0$ for $j\ge 2$, consider a nearby state with $s_j>0$ small. Then for each small rival $j$,

\[
\dot s_j=s_j\big(w(s_j)-\bar w\big).
\]

Since $w(s)$ is increasing and $s_j\ll 1$, one has $w(s_j)<w(1)$, and $\bar w$ is close to $w(1)$. Hence $\dot s_j<0$. Small rivals shrink, so the monopoly state is locally asymptotically stable. ∎

Interpretation

The theorems show not merely that concentration is profitable, but that under a simple evolutionary law it is dynamically selected. Competition among exploiters is eliminative because larger coercive units are fitter than smaller ones.

4. Centralization within each exploitative firm

Now take one exploiter of size $s$. It must rule through subordinate coercive agents. Those agents can skim transfers, retain local control, or secede. Let $z\ge 0$ denote the intensity of centralization: surveillance, standardization, command concentration, monopoly of force inside the organization, audit capacity, and suppression of local autonomy.

Write the firm’s problem as

\[
\max_{z\ge 0}\ \Pi(s,z)=\pi(s)-L(s,z)-K(z),
\]

where:

$L(s,z)$ is internal leakage/loss;
$K(z)$ is the resource cost of centralization.

Assume:

$K'(z)>0,\ K''(z)\ge 0$;
$L_s(s,z)>0$: larger domain creates more internal leakage risk;
$L_z(s,z)<0$: more centralization reduces leakage;
$L_{zz}(s,z)>0$: diminishing returns to centralization;
$L_{sz}(s,z)<0$: the marginal benefit of centralization is larger in larger organizations.

Condition 5 is the key “centralization tendency” assumption.

Theorem 5 (monotone comparative statics of centralization)

Under assumptions 1–5, the optimal centralization choice $z^*(s)$ is nondecreasing in $s$. If the optimum is interior and $L_{sz}<0$ strictly, then $z^*(s)$ is strictly increasing in $s$.

Proof

The objective is

\[
\Pi(s,z)=\pi(s)-L(s,z)-K(z).
\]

Its cross-partial is

\[
\Pi_{sz}(s,z)=-L_{sz}(s,z)>0.
\]

So $\Pi$ has increasing differences in $(s,z)$. By monotone comparative statics, the argmax correspondence $z^*(s)$ is nondecreasing in $s$. If the optimum is interior and the inequality is strict, then the first-order condition

\[
-K'(z)-L_z(s,z)=0
\]

implies that a rise in $s$ raises the marginal benefit of $z$, so the optimal $z$ rises strictly. ∎

Parametric corollary

Take

\[
L(s,z)=\lambda \frac{s^\beta}{z},\qquad \beta>1,\ \lambda>0,
\qquad
K(z)=\kappa z,\qquad \kappa>0.
\]

Then

\[
\Pi(s,z)=as-F-cs^\eta-\lambda \frac{s^\beta}{z}-\kappa z.
\]

Corollary 3

The optimal centralization level is

\[
z^*(s)=\sqrt{\frac{\lambda}{\kappa}}, s^{\beta/2},
\]

so $z^*(s)$ is strictly increasing in firm size.

Proof

FOC:

\[
\frac{\partial \Pi}{\partial z} = \lambda \frac{s^\beta}{z^2}-\kappa=0.
\]

Hence

\[
z^*(s)=\sqrt{\frac{\lambda}{\kappa}}, s^{\beta/2}.
\]

Since $\beta>1$, this is strictly increasing in $s$. ∎

Interpretation

Internal centralization is not an arbitrary managerial taste. It is the endogenous response to the fact that a large exploitative firm must itself govern subordinate exploiters.

So the same organization that eliminates external rivals also suppresses internal rivals.

5. Main synthesis theorem

We can now combine the pieces.

Theorem 6 (tendency toward concentration and centralization)

Suppose:

coercive appropriation over any given territory is contestable as in Theorem 1;
net operating profit under exclusive jurisdiction is $\pi(s)=as-F-cs^\eta$ with $0<\eta<1$;
firm shares evolve by the replicator dynamic;
internal centralization is chosen optimally as in Theorem 5.

Then:

profitable exploitation requires exclusion of rival exploiters from each territory-population;
the exploiter industry has a structural tendency toward concentration;
along any path of concentration, each surviving exploiter has a structural tendency toward higher internal centralization.

Proof

(1) follows from Corollary 1: under free entry into coercive appropriation, exploitation rents are dissipated.

(2) follows from Theorems 2–4: unified coercive organizations are more profitable than fragmented ones, and the dynamic raises concentration over time.

(3) follows from Theorem 5: as each surviving exploiter grows in size, its optimal centralization rises. ∎

6. What has been formally shown

In theorem-proof terms, the argument is:

Exploitation is a pure transfer prize.
Free entry into contesting that prize dissipates the prize.
Therefore positive exploitation profit requires monopoly jurisdiction.
Given monopoly jurisdiction, coercive profit is superadditive in scale, so fragmentation is privately dominated by concentration.
Under a simple growth law, larger exploiters outgrow smaller ones, so concentration is dynamically selected.
As firms grow, the marginal value of central control rises, so internal centralization also increases.

That gives a clean formal statement of your original conception:
competition among exploiters is eliminative externally and centralizing internally.

The next natural step would be one of these two:

a state-formation version, where firms are interpreted as proto-states and annexation is literal war;
a general equilibrium version, where subjects reduce output when predation rises, so excessive exploitation can shrink the future tax base.

I can write either one in the same theorem-proof style.

Concentration among exploiters

The prompt is based on a paragraph from Marxist and Austrian Class Analysis by Hans-Hermann Hoppe.

Exploitation, defined as nonproductive and noncontractual property acquisitions (e.g. theft, extortion), is only possible as long as there is anything that can be appropriated. Yet if there were free competition in the business of exploitation, there would be nothing left to expropriate. Thus, exploitation requires monopoly over some given territory and population; and the competition between exploiters is by its very nature eliminative and must bring about a tendency toward relative concentration of exploitative firms as well as a tendency toward centralization within each exploitative firm. Attempt to make a formal model of exploitation and its tendency toward concentration and centralization that clarifies these conceptions.

Here is one minimal formalization that captures the logic you want. It is not the only possible model, but it makes each claim explicit and shows where the tendency toward concentration and centralization comes from.

1. Exploitation as a contest over an appropriable surplus

Take a territory $j$ with population $n_j$. The territory yields an appropriable surplus $V_j>0$ per period. This is not newly produced by the exploiter; it is a transfer extracted from the population.

Suppose $m$ exploiters try to seize the right to exploit that territory. Let exploiter $i$ choose coercive effort $e_i\ge 0$. A simple contest payoff is

\[ u_i(e_i\;e_{-i}) = \frac{e_i}{\sum_{k=1}^m e_k}V_j - e_i \]

This says the prize is the right to expropriate $V_j$, and coercive effort is pure dissipation.

In the symmetric Nash equilibrium of this Tullock contest,

\[
e_i^*=\frac{m-1}{m^2}V_j,\qquad
u_i^*=\frac{V_j}{m^2},\qquad
\sum_{i=1}^m e_i^*=\frac{m-1}{m}V_j.
\]

So as $m\to\infty$,

\[
u_i^*\to 0,\qquad \sum_i e_i^*\to V_j.
\]

That is the clean formal version of your first point: under free entry into the business of exploitation, the exploitable surplus is dissipated in the struggle over who gets to seize it. There may still be a gross surplus $V_j$, but there is no net exploitation rent left. Positive exploitation profit therefore requires exclusion of rivals, which is to say: monopoly jurisdiction over a territory and population.

So monopoly is not accidental here. It is a condition for exploitation to be a positive-return activity.

2. Why rivalry among exploiters is eliminative

Now suppose the total territory/population is normalized to 1, and exploiter $i$ controls share $s_i$, with $\sum_i s_i=1$.

Let the net rent from exclusive control of share $s$ be

\[
\pi(s)=\alpha s - F - c s^\eta,
\qquad 0<\eta<1,\ \alpha,F,c>0.
\]

Interpretation:

$\alpha s$: gross expropriable flow from the controlled population.
$F$: fixed cost of maintaining a coercive apparatus.
$c s^\eta$ with $0<\eta<1$: variable coercion/administration cost with economies of scale.

Because $\eta<1$, coercive control is cheaper per unit at larger scale.

Now compare two exploiters controlling $a$ and $b$ separately with one exploiter controlling $a+b$. The gain from combination is

\[
\Delta(a,b)=\pi(a+b)-\pi(a)-\pi(b)
=F+c\big(a^\eta+b^\eta-(a+b)^\eta\big).
\]

Since $0<\eta<1$, $x^\eta$ is concave, so

\[
a^\eta+b^\eta>(a+b)^\eta,
\]

hence

\[
\Delta(a,b)>0.
\]

So one larger exploitative firm is more profitable than two smaller ones controlling the same total population. This is already a concentration result: conquest, annexation, cartelization, or merger is privately profitable because it removes duplicate coercive fixed costs and exploits scale economies in domination.

That is why competition among exploiters is eliminative rather than price-competitive. The rival is not someone to undercut; he is an obstacle to be absorbed or destroyed.

3. A dynamic concentration law

To make the tendency explicit, define per-unit fitness as

\[
w(s)=\frac{\pi(s)}{s}
=\alpha-\frac{F}{s}-c s^{\eta-1}.
\]

Then let shares evolve by a replicator-style law:

\[ \dot s_i = s_i\left[w(s_i)-\bar w\right],\qquad \bar w = \sum_k s_k w(s_k) \]

This says exploiters with above-average net rent expand at the expense of below-average ones.

Now

\[
w'(s)=\frac{F}{s^2}+c(1-\eta)s^{\eta-2}>0.
\]

So larger exploiters have higher fitness. Once an exploiter becomes larger, he has lower average coercion cost and therefore grows faster still. That is the formal engine of concentration.

A compact way to see concentration rise is through the Herfindahl index

\[
H=\sum_i s_i^2.
\]

Differentiating,

\[
\dot H
=2\sum_i s_i^2\big(w(s_i)-\bar w\big)
=2,\mathrm{Cov}_s\big(s_i,w(s_i)\big).
\]

Because $w(s)$ is increasing in $s$, that covariance is positive whenever sizes differ. Hence

\[
\dot H>0
\]

except at knife-edge equal-size configurations. So concentration rises endogenously.

Under these assumptions, fragmentation is unstable and monopoly or near-monopoly is the stable endpoint.

4. Why each exploitative firm tends toward internal centralization

Now treat each exploitative firm itself as a small political order. A firm of size $s$ cannot directly coerce everyone; it must delegate power to local agents. But those agents are themselves potential exploiters. If left autonomous, they skim, withhold remittances, or break away.

Let $z\ge 0$ measure centralization: surveillance, bureaucracy, monopoly of arms inside the organization, standardization of commands, suppression of local autonomy.

Let internal leakage be

\[
L(s,z)=\lambda \frac{s^2}{z},
\qquad \lambda>0,
\]

and let the cost of centralization be

\[
K(z)=\kappa z,
\qquad \kappa>0.
\]

Then firm net rent is

\[
\Pi(s,z)=\alpha s - F - c s^\eta - \lambda \frac{s^2}{z} - \kappa z.
\]

The firm chooses $z$ to maximize $\Pi$. The first-order condition is

\[
\frac{\partial \Pi}{\partial z}
=\lambda \frac{s^2}{z^2}-\kappa=0,
\]

so the optimal degree of centralization is

\[
z^*(s)=s\sqrt{\frac{\lambda}{\kappa}}.
\]

Therefore

\[
\frac{dz^*}{ds}>0.
\]

This is the centralization result: as the exploitative firm grows, it becomes optimal to concentrate command more tightly at the center, because the danger posed by semi-autonomous sub-exploiters rises with scale.

So concentration across firms and centralization within firms come from the same logic. External rivals must be excluded to preserve net rents; internal rivals must be subordinated to preserve remittances.

5. What the model shows, in plain terms

Under these assumptions:

Exploitation requires exclusive jurisdiction.
Free entry into coercive appropriation dissipates the exploitation rent.
Competition among exploiters is eliminative.
Since larger coercive units are more profitable than smaller ones, rivals are to be annexed, not merely competed with.
There is a built-in tendency toward concentration.
Fixed costs and scale economies in coercion make larger exploiters fitter, so concentration rises over time.
There is a built-in tendency toward centralization.
Delegated coercers become internal threats, so growing exploitative firms centralize command.

6. The shortest possible summary

A compact formal statement is this:

External problem: exploiters contest monopoly rights over a transferable surplus; free entry dissipates the rent.
Size effect: once monopoly exists, coercive profit is superadditive in size.
Dynamic result: larger exploiters grow faster than smaller ones.
Internal problem: delegation creates secondary exploiters inside the organization; growth raises the value of central command.

That yields exactly the structure you described: monopoly as a condition of exploitation, elimination as the form of competition among exploiters, concentration across firms, and centralization within each firm.

I can also turn this into a more rigorous theorem-proof version, or into a continuous-time war-state model with explicit conquest probabilities.

I took it up on the first offer here.

Grammar cases ontologized (GPT-5-Thinking version)

Armstrongian states of affairs are thought to be composed unmereologically. Develop a formal philosophical theory of states of affairs that composes them mereologically by postulating abstract cases. For instance, the real Romeo has “cased counterparts” nominative-Romeo, accusative-Romeo, genitive-Romeo, etc. Then the state of affairs “Romeo loves Juliet” is the mereological sum of nominative-Romeo with the relation of love and accusative-Juliet, while “Juliet loves Romeo” is a state of affairs composed of the relation of love, accusative-Romeo, and nominative-Juliet. This solves the asymmetry problem. The relation between an object and its cased counterparts naturally cannot be identity or parthood, and we may call it the relation of reference. Develop formal features of this theory as well as how it might be motivated and challenged and how it might answer challenges.

Here’s a compact but fully-worked theory that does exactly what you asked: it treats states of affairs (SoAs) as mereological fusions whose parts include a relation and “cased counterparts” of the relata. I’ll call it Case-Mereological Truthmaking (CMT).

1) Ontological palette

We posit four basic categories:

Objects: $O$.
Relations/Properties (Universals): $U=\bigcup_{n\ge 1}U_n$ where $U_n$ are $n$-adic universals.
Case types: a fixed finite set $K$ (e.g., $\mathrm{Nom},\mathrm{Acc},\mathrm{Gen},\ldots$). These are abstract cases (argument-roles), not linguistic artifacts.
Cased counterparts: $C = O\times K$. Intuitively, $\langle o,k\rangle$ is “$k$-Romeo”, “$k$-Juliet”, etc.

There is a single extensional mereology $\langle E,\leq\rangle$ (parthood $\leq$; fusion/sum “$\bigsqcup$”) whose domain $E\supseteq O\cup U\cup C\cup S$ contains all entities we need, including the set $S$ of states of affairs (defined below).

2) Case machinery and reference

Case formation: for each $k\in K$, a total function $c_k:O\to C$ with $c_k(o)=(o,k)$.
Decasing: $\mathrm{dec}:C\to O$ with $\mathrm{dec}(o,k)=o$.
Case-type: $\mathrm{case}:C\to K$ with $\mathrm{case}(o,k)=k$.
Reference (primitive binary relation): $\mathrm{Ref}(c,o)$. Axioms:
1. $\forall c,\exists!o,\mathrm{Ref}(c,o)$.
2. $\forall o,k,\mathrm{Ref}(c_k(o),o)$.
3. Non-identity: $\forall o,k;c_k(o)\neq o$.
4. No cross-category parthood: $\neg(c\leq o)$ and $\neg(o\leq c)$ whenever $\mathrm{Ref}(c,o)$.

(We could identify $\mathrm{Ref}(c,o)$ with $\mathrm{dec}(c)=o$. Keeping it relational makes room for variants where counterparts depend on times or contexts.)

3) Relational signatures (case profiles)

Each $n$-adic relation $R\in U_n$ carries a case profile $\sigma(R)=\langle k_1,\ldots,k_n\rangle\in K^n$. Think of $\sigma$ as the abstract argument-role typing for that universal.

Example: $\sigma(\mathrm{Love})=\langle \mathrm{Nom},\mathrm{Acc}\rangle$.
For symmetric relations like Adjacent, we still pick two distinct role-types $k_1,k_2$ (even if the relation is symmetric in extension). The symmetry shows up in truth conditions, not in identity of parts.

4) States of affairs as mereological fusions

An atomic SoA is any fusion of the form
\[
\mathbf{s} = \bigsqcup {,R,; c_{k_1}(o_1),\ldots,c_{k_n}(o_n),}
\]
where $R\in U_n$ and $\sigma(R)=\langle k_1,\ldots,k_n\rangle$.

Identity for SoAs: Extensionality—SoAs are identical iff they have exactly the same parts. So order is not encoded; role information is carried by case-types on the parts.
Category disjointness: No cased counterpart is a universal, and vice versa; neither is identical to a state.

Examples

“Romeo loves Juliet”: $\mathbf{s}_{RJ}=\bigsqcup{,\mathrm{Love},; c_{\mathrm{Nom}}(\mathrm{Romeo}),; c_{\mathrm{Acc}}(\mathrm{Juliet}),}$.
“Juliet loves Romeo”: $\mathbf{s}_{JR}=\bigsqcup{,\mathrm{Love},; c_{\mathrm{Nom}}(\mathrm{Juliet}),; c_{\mathrm{Acc}}(\mathrm{Romeo}),}$.

By extensionality and the different case-typed parts, $\mathbf{s}_{RJ}\neq \mathbf{s}_{JR}$. That is the asymmetry solution.

5) Truth conditions and truthmaking

Let $W$ be a set of worlds. Each $R\in U_n$ has a world-relative extension $||R||_w\subseteq O^n$.

Obtention: An atomic SoA $\mathbf{s}$ obtains at (w) iff
\[
\exists \langle o_1,\ldots,o_n\rangle\bigg(\bigwedge_{i=1}^n \mathrm{Ref}(c_{k_i}(o_i),o_i);\land; \langle o_1,\ldots,o_n\rangle \in ||R||_w \bigg).
\]
Truthmaking: $\mathbf{s}$ is a truthmaker for the proposition $R(o_1,\ldots,o_n)$ (with roles given by $\sigma(R)$). Truthmaking is hyperintensional: if $R$ and $R'$ are necessarily coextensive but distinct universals, then the SoAs that use $R$ vs $R'$ are distinct because the relation part differs.

6) Mereological background (ECM)

Adopt classical extensional mereology:

Reflexive, antisymmetric, transitive parthood.
Fusion: For any nonempty $X\subseteq E$, there exists the unique $y$ such that $\forall z,(z) overlaps (y \leftrightarrow \exists x\in X, z) overlaps (x)$. Write $y=\bigsqcup X$.

SoAs are special fusions constrained by §4.

7) Formal properties and theorems

T1 (Asymmetry)
If $\sigma(R)=\langle k_1,\ldots,k_n\rangle$ and $i\neq j$, then, for fixed objects $o_1,\ldots,o_n$, swapping $o_i,o_j$ while keeping case-types fixed yields a different SoA unless $o_i=o_j$ and $k_i=k_j$.
Reason: the cased parts differ (e.g., $c_{k_i}(o_i)$ vs $c_{k_i}(o_j)$), hence the fusion differs.

T2 (Role-invariance of the sum)
The order of mereological summation is irrelevant. Case-types encode the argument mapping; no appeal to sequences is needed for identity.

T3 (No Bradley regress)
We do not need a further “nexus of exemplification” as a constituent: the role-typing $\sigma(R)$ and the case-marks on counterparts determine the predication structure. No additional tie gives rise to a regress.

T4 (Hyperintensionality)
If $R\neq R'$, then for any tuple $\bar{o}$,
$\bigsqcup{R, c_{k_1}(o_1),\dots}\neq \bigsqcup{R', c_{k'_1}(o_1),\dots}$, even if $||R||_w=||R'||_w$ at all worlds.

8) Quantification and “gappy” frames

To handle quantification and predicates with open argument places, introduce frame-SoAs (templates):

For $R\in U_n$ and a subset $I\subseteq{1,\ldots,n}$, a frame is a fusion of $R$ with cased counterparts $c_{k_j}(o_j)$ for $j\notin I$, leaving “gaps” at positions in $I$.
A λ-case abstraction builds a property from a frame:
$\lambda x_{k_i},., [R;\ldots,\_,\ldots]$ is the property had by an object $o$ iff the completed SoA (fusing $c_{k_i}(o)$ into the gap) obtains.

Then:

“Someone loves Juliet” is true at $w$ iff $\exists o,$ the frame $\bigsqcup{ \mathrm{Love}, c_{\mathrm{Acc}}(\mathrm{Juliet})}$ can be completed with $c_{\mathrm{Nom}}(o)$ to an obtaining SoA at $w$.

9) Monadic and higher adicity

For monadic $F\in U_1$ set $\sigma(F)=\langle \mathrm{Nom}\rangle$.
“Romeo is mortal”: $\bigsqcup{F, c_{\mathrm{Nom}}(\mathrm{Romeo})}$.
For adverbials, events, etc., either:
- treat them as relational modifiers (new universals with enriched signatures), or
- add distinct adjunct cases (e.g., $\mathrm{Manner},\mathrm{Instrument}$).

10) Symmetric and plural relations

If $R$ is symmetric, $\sigma(R)=\langle k_1,k_2\rangle$ with $k_1\neq k_2$. Then distinct SoAs can both obtain for $\langle a,b\rangle$ and $\langle b,a\rangle$. This is compatible with truthmaker pluralism.
For plurals and mass terms, let $O$ include pluralities (closed under fusion). Then $c_k$ applies to pluralities; distributive/collective readings can be encoded by distinct universals (e.g., Lift_collective vs Lift_distributive) with their own case profiles.

11) Motivations

Solves order/asymmetry: Unlike Armstrong’s unmereological “exemplification” tie or bundles lacking order, CMT encodes argument-structure via case-typed parts. “Romeo loves Juliet” vs “Juliet loves Romeo” differ mereologically.
Truthmaker-friendly: SoAs are concrete truthmakers (in the ontological sense) with clear identity conditions; no extra nexus entity.
Hyperintensional granularity: Coextensive universals still yield distinct SoAs when the relation part differs—useful for attitude reports and fine-grained propositions.
Simplicity of composition: All structure is delivered by standard extensional mereology plus a modest role apparatus (cases and signatures).
Category discipline: The reference relation prevents collapsing objects and their role-bearers (no identity or parthood between $o$ and $c_k(o)$).

12) Anticipated challenges and replies

C1. “Aren’t cases just linguistic?”
Challenge: If cases are grammatical, the ontology looks language-dependent.
Reply: Cases here are abstract roles (akin to thematic or argument positions). Linguistic case is evidence, not identity. Formally, $\sigma$ assigns role-types that need not mirror any particular language.

C2. “Explosion of entities (too many counterparts)!”
Challenge: For each $o$ and $k$ there is $c_k(o)$.
Reply: (i) These are lightweight abstracta—ordered pairs $(o,k)$ in the simplest model. (ii) They are indispensable bookkeeping devices replacing a primitive nexus. (iii) They are dependent on $o$: add an existence-dependence axiom if desired: $\exists c_k(o)\Rightarrow \exists o$.

C3. “Why isn’t reference identity or parthood?”
Challenge: If $c_k(o)$ is not identical with or part of $o$, what ties them together?
Reply: Exactly reference does: a sui generis, functional relation implementing decasing. It prevents category mistakes (no object is a role-marked proxy) and blocks trivialization in mereology (no $o$ contains all its roles as parts).

C4. “Bradley regress lurking?”
Challenge: Doesn’t the relation need a further tie to its relata?
Reply: The tie is encoded by (a) the presence of the relation universal itself as a part, plus (b) the case profile $\sigma(R)$ and the cased counterparts as distinct parts. No additional item is required to ‘unify’ them; fusion does that.

C5. “Permutation invariance vs identity of indiscernibles.”
Challenge: In mereology, unordered sums collapse structure.
Reply: We re-introduce structure via typed parts. Two fusions that differ only by swapping $\mathrm{Nom}$- vs $\mathrm{Acc}$-parts are numerically distinct (T1).

C6. “Passivization and alternations.”
Challenge: “Juliet is loved by Romeo” uses different surface roles.
Reply: Keep $\sigma(\mathrm{Love})=\langle \mathrm{Nom},\mathrm{Acc}\rangle$ as the deep case profile; passive morphology concerns sentence form, not the SoA. The same obtaining SoA makes both active and passive sentences true.

C7. “Empty names and negative existentials.”
Options:
(i) Actualist: counterparts exist only for existing objects; negative existentials are made true by lack of obtaining SoAs.
(ii) Meinong-friendly: allow non-existents in $O$ with a separate existence predicate $E!$. The truth-conditions then quantify over $O$ with $E!$ filters. The core CMT is neutral; pick your favorite.

C8. “Symmetric relations double-count truthmakers.”
Reply: Accept truthmaker pluralism: two distinct obtaining SoAs can both make “$a$ is adjacent to $b$” true. If you dislike that, stipulate $\sigma(R)$ uses a single multiset case so that ${c_k(a),c_k(b)}$ fuses into a unique multiset-typed part; CMT is flexible.

C9. “Are SoAs too fine-grained?”
Reply: Fine granularity is a feature: we often want $\mathrm{Loves}(r,j)$ and $\mathrm{Loves}(j,r)$ distinct in attitude and causal explanations. Coarser individuation can be recovered by quotienting over case-permutations if desired.

13) Variants and extensions

Temporalized counterparts: let $C=O\times K\times T$ for times $t$; $\mathrm{Ref}((o,k,t),o)$. Then SoAs are fusions including time-slices.
Event semantics: add an event universal $e$ as a part, with $\sigma(\mathrm{Agent})=\langle \mathrm{Ag}\rangle$, $\sigma(\mathrm{Theme})=\langle \mathrm{Th}\rangle$, etc.; adverbs/locations become further case-typed parts.
Category-theoretic gloss: view SoAs as labeled hyperedges in a typed hypergraph; mereological sum corresponds to edge union; case labels ensure role sensitivity.

14) Worked examples

Romeo loves Juliet
Parts: ${\mathrm{Love}, c_{\mathrm{Nom}}(\mathrm{Romeo}), c_{\mathrm{Acc}}(\mathrm{Juliet})}$.
Obtains at $w$ iff $(\mathrm{Romeo},\mathrm{Juliet})\in ||\mathrm{Love}||_w$.
Juliet loves Romeo
Parts: ${\mathrm{Love}, c_{\mathrm{Nom}}(\mathrm{Juliet}), c_{\mathrm{Acc}}(\mathrm{Romeo})}$.
Distinct from the first; obtains iff $(\mathrm{Juliet},\mathrm{Romeo})\in ||\mathrm{Love}||_w$.
Juliet is admired by Romeo (passive surface form)
Same SoA as “Romeo admires Juliet” given $\sigma(\mathrm{Admire})=\langle \mathrm{Nom},\mathrm{Acc}\rangle$.

15) Compact axiom list (for reference)

Mereology: Classical extensional mereology over $E$.
Sorts: $O,U,C,S\subseteq E); (C=O\times K$.
Reference: (unique-reference, coverage for all $c_k(o)$, non-identity, no cross-category parthood).
Signatures: $\sigma:U_n\to K^n$.
SoA formation: If $R\in U_n$ and $o_i\in O$, the fusion $\bigsqcup{R,c_{k_1}(o_1),\ldots,c_{k_n}(o_n)}\in S$.
SoA identity: extensionality of parts.
Obtention: as in §5.
Hyperintensionality: Distinct universals yield distinct SoAs (no collapsing by necessary equivalence).

Bottom line. CMT gives you a rigorously mereological construction of states of affairs that cleanly handles argument order—asymmetry is captured by case-typed counterparts—while preserving truthmaking, avoiding a regress, and remaining flexible about linguistic surface forms. It’s ontologically modest (adding only lightweight case-proxies) yet hyperintensional enough to support fine-grained theorizing. If you’d like, I can also sketch a natural deduction system or a proof theory for λ-case abstraction over these frames.

Heidegger among the Nazis

Contextualize Heidegger’s politics among the range of competing interpretations of National Socialism in the German intellectual scene

National Socialism did not present itself to German intellectuals as one settled doctrine. In the late Weimar and early Nazi years, it was variously interpreted as a sovereign state revolution, a national-spiritual rebirth, a racial myth, or—by its opponents—a manufactured political mythology and a form of fascist mass manipulation.

Decisionist-statist reading. Carl Schmitt is the clearest case here: his Weimar works attacked parliamentary liberalism, grounded politics in the friend/enemy distinction, and sought a strong executive capable of decisive action in a state of crisis. In that register, National Socialism could appear as the force that ended liberal indecision and restored political unity. (Stanford Encyclopedia of Philosophy)

Conservative-revolutionary / national-rebirth reading. A broader right-wing milieu—Moeller van den Bruck, Jünger, Freyer, and others—framed Germany’s crisis as one of Kultur versus liberal-commercial “civilization,” rejected both the capitalist West and the communist East, and imagined a specifically German “third way.” Herf’s reconstruction of this milieu shows how it fused anti-Enlightenment politics with enthusiasm for discipline, technology, mobilization, and sacrifice; Jünger is emblematic as the “ardent militarist” whose wartime and postwar writing made struggle and mobilization spiritually meaningful.

Racial-mythic / völkisch reading. Alfred Rosenberg represents a different pole: Nazism as an explicit doctrine of Nordic racial purity, anti-Semitism, and eastward expansion. In this version, the regime’s essence lay in racial hierarchy and mythic ethnonational destiny, not just anti-liberal revolt or constitutional decisionism. (Encyclopedia Britannica)

Liberal-humanist counter-reading. For Cassirer and, in a different way, Jaspers, Nazism was not a national rescue but a collapse of reasoned politics into myth and domination. Cassirer’s Myth of the State treats modern political myths as manufactured products amplified by mass communication and substituting for rational principles; Jaspers, after the break with Heidegger and his own persecution under the regime, defended the university as a free community of truth-seeking rather than an instrument of political alignment. (Routledge Encyclopedia of Philosophy)

Marxist / critical-theory counter-reading. Walter Benjamin’s formula is the sharpest: fascism gives the masses expression without rights, preserves property relations, aestheticizes politics, and culminates in war. That critique directly targeted the kind of redemptive militarism and “total mobilization” celebrated on the Weimar right.

Within that spectrum, Heidegger belongs closest to the conservative-revolutionary interpretation, with some proximity to Schmitt’s anti-liberalism, but he is not best understood either as a Schmittian jurist or as a Rosenbergian racial ideologue. The basic facts matter: Heidegger became rector of Freiburg in April 1933, joined the Nazi Party on May 1, and as rector took part in the university’s Gleichschaltung with Nazi aims. Yet the long-running dispute over his case—opportunist, naïf, would-be reformer of the movement, or committed believer—exists precisely because his Nazism was articulated less as party doctrine than as an attempt to endow 1933 with philosophical-historical significance. (Stanford Encyclopedia of Philosophy)

So Heidegger’s politics are best contextualized as a metapolitical Nazism: he read the movement primarily as an event of historical destiny, collective resolve, and spiritual renewal of a people, rather than chiefly as a constitutional order (Schmitt) or a racial program in Rosenberg’s blunt style. That places him nearer the Jünger/Freyer side of the scene: anti-liberal, anti-parliamentary, hostile to bourgeois normality, attracted to sacrifice and collective mobilization, and receptive to the idea of a German “mission” beyond both liberal capitalism and Marxism.

At the same time, it would be too soft to describe this merely as a “higher” or more refined version of conservatism. The post-2014 debate over the Black Notebooks matters because those notebooks contain anti-Semitic passages, often invoking “World-Jewry,” even after Heidegger’s disenchantment with aspects of actually existing Nazism; scholars describe that anti-Semitism not as a stray prejudice but as something woven into the language of his thought. So the distance from Rosenberg is a difference of idiom and philosophical level, not innocence. (MIT Press)

The cleanest one-line placement is this: Heidegger was the philosopher of National Socialism’s conservative-revolutionary self-understanding—its claim to be not merely a party program or a race doctrine, but a world-historical rupture that would overcome liberal modernity and re-found German existence. That is exactly why Cassirer, Jaspers, and Benjamin matter as foils: they saw, each in a different vocabulary, that this “spiritualization” of politics was not an antidote to Nazism but one of the ways it could be intellectually dignified. (Routledge Encyclopedia of Philosophy)

I can turn this into a compact comparison of Heidegger with Schmitt, Jünger, and Rosenberg specifically.

Against the Law of Concentration of Capital

it seems that many factors favor bigger companies over smaller ones: bigger companies can buy inputs cheaper in bulk, can sell more cheaply for longer, have more reserves, can survive low profits or temporary losses, have better access to credit, and are burdened less by fixed costs proportionally. what prevents all the small companies being put out of business?

Because the advantages of size are real, but they are not unlimited and they are not universal.

Big firms usually do have lower unit costs in some areas. But as firms grow, they also pick up countervailing disadvantages: more layers of management, slower decisions, harder monitoring, internal politics, weaker incentives, and more difficulty adapting to local conditions. Economists call that diseconomies of scale. Past some point, “bigger” stops meaning “more efficient.”

Also, a lot of markets are not won by being the absolute lowest-cost producer. Small firms survive by competing on things large firms are worse at: specialization, speed, customization, local reputation, personal service, niche products, and willingness to serve small or odd segments that are not worth a giant firm’s attention.

Some industries simply do not reward huge scale very much. A barber shop, plumbing business, law office, restaurant, design studio, or specialty manufacturer often has a limited efficient size. Once you have enough scale to cover fixed costs, getting much larger may add complexity faster than it adds savings.

There is also the problem of coordination. A big company can buy in bulk, but it cannot perfectly manage every worker, location, product line, and customer relationship. Small firms often have sharper owner incentives and less waste because the owner directly bears the gains and losses.

Entry matters too. Even if large firms drive down profits, that does not always kill small firms permanently. New small firms keep entering when they see unmet demand, new technology, or ways to operate more cleverly. Small firms are often the source of innovation precisely because they are less bureaucratic and can take focused bets.

And large firms do not always want to fight every small rival to the death. Keeping prices very low for a long time is costly for them too. In many markets it is more profitable to leave niches alone than to crush every tiny competitor.

Finally, policy and market structure matter. Antitrust law, limits on predatory conduct, bankruptcy rules, labor mobility, open capital markets, and platforms that reduce startup costs all make it easier for smaller firms to exist.

So the general answer is: size gives advantages, but not a one-way advantage. Small firms survive because large firms face their own limits, and because many customers value things other than lowest price.

A useful rule is:

In industries with very strong economies of scale, you tend to get a few big firms.
In industries where customization, trust, locality, or flexibility matter, small firms persist.

So your intuition is right, but only half the story: markets reward size up to a point, and beyond that they often start rewarding agility instead.

Monday, March 30, 2026

Double-lives mathematical model

In the way where a man who has parallel families leads a “double life”, we could say you have as many lives as there are groups of people you know where you intentionally avoid telling anyone in one group about anyone in any of the others. For instance, if you don’t tell your drug dealer about your therapist and you don’t tell your therapist about your drug dealer, then that’s a minimum setup for you to live a double life. Or if you don’t tell your far-right activist friends about your gay lover, and you don’t tell your gay lover about your far-right activist friends, that’s another double life.

I think it doesn’t count if you tell group A about group B but don’t tell group B about group A, since then it’s clear that your “real life” is more with group A. Call your life with group B a “fake life” in this case; call it “integration” when you have only one real life (with indefinitely many fakes) and “strong integration” when you have one real life and zero fakes.

I suppose you can have overlapping double lives. For example:

you don’t tell your drug dealer about your therapist
you don’t tell your therapist about your drug dealer
you don’t tell your Jewish lover about your Nazi friends
you don’t tell your Nazi friends about your Jewish lover

In the example scenario, it’s possible that you tell your Nazi friends and Jewish lover about both your drug dealer and your therapist, and you tell both your drug dealer and your therapist about both your Nazi friends and your Jewish lover. So it’s not like you have four lives – it seems cleaner to say you have four lives if you have four groups where none of the four knows about the other three. But you have overlapping double lives in different respects.

Please think of the cleanest and most natural way to set up a mathematical model of these ideas.

The cleanest model is:

the primitive thing is a directed “disclosure graph,” not a single number of lives.

A single scalar like “how many lives?” throws away too much structure. Your examples really involve two different phenomena:

mutual compartmentalization (“these two worlds are kept apart”), and
one-way incorporation (“this world is part of a more real world, but not vice versa”).

A directed graph captures both at once.

1. Primitive data: a directed graph of disclosure

Let $G$ be the set of your social compartments.
A compartment can be a literal group of people, or just a “social world”/role/context. It is better to think of vertices this way, because real groups can overlap.

For $x,y\in G$, write

\[
x \to y
\]

to mean:

people in compartment $x$ are intentionally told about compartment $y$.

Assume $x\to x$ for all $x$: each compartment “knows itself.”

So the whole social setup is a directed graph $D=(G,\to)$.

2. The three basic pairwise relations

For distinct $x,y$, exactly one of these can happen:

Mutual disclosure

\[
x\leftrightarrow y
\]
meaning $x\to y$ and $y\to x$.

This is the pairwise form of integration.

One-way disclosure

\[
x \Rightarrow y
\]
meaning $x\to y$ but $y\nrightarrow x$.

Then $y$ is a fake life relative to $x$.

Mutual concealment

\[
x \parallel y
\]
meaning $x\nrightarrow y$ and $y\nrightarrow x$.

This is the pairwise form of a double life seam.

So the intuitive English is already sitting in the edge-types.

3. “Real life” and “fake life” from knowledge-sets

For each compartment $x$, define its visible world
\[
K(x)={y\in G: x\to y}.
\]

This is the set of compartments that $x$ is allowed to know about.

Now compare compartments by how much of your overall life they see:

\[
x \succeq y \quad \text{iff} \quad K(x)\supseteq K(y).
\]

Interpretation: $x$ is at least as “real” or “integrated” a life as $y$, because $x$ sees everything $y$ sees, and maybe more.

Then:

$x$ is a real life if it is maximal under $\succeq$
(no other compartment sees strictly more than it does).
$y$ is a fake life if it is not maximal
(some other compartment strictly contains it).

This matches your intuition that if $A$ knows about $B$ but not conversely, then $A$ is the more real life and $B$ is fake.

4. Integration and strong integration

With that setup:

Integration

You have integration if there is exactly one maximal visible world.

In other words, there is one “top-level” life that contains all the others informationally, and everything else is subordinate/fake relative to it.

Strong integration

You have strong integration if every compartment has the same visible world:

\[
K(x)=G \quad \text{for all } x\in G.
\]

Equivalently: for every pair $x,y$, both $x\to y$ and $y\to x$.

So strong integration is just the complete bidirected graph.

5. Double lives and “how many lives?”

Now define the incompatibility graph $I$ on the same vertex set $G$, where

\[
{x,y}\in E(I) \quad \text{iff} \quad x\parallel y.
\]

So $I$ forgets one-way fake-life relations and remembers only mutual concealment.

This gives a very natural meaning of “$n$ lives” in your strict sense:

you have at least $n$ lives iff $I$ contains a clique of size $n$.

That is, there are $n$ compartments such that no one in any of them is told about any of the others.

So the strict “number of lives” is

\[
\omega(I),
\]

the clique number of the incompatibility graph.

That is exactly the quantity you seemed to want when you said it feels clean to say “four lives” only when there are four groups none of which knows about the other three.

6. Your overlapping example

Let the compartments be

$D$: drug dealer
$T$: therapist
$J$: Jewish lover
$N$: Nazi friends

and suppose:

$D\parallel T$
$J\parallel N$

but all cross-pair disclosures happen both ways:

$D\leftrightarrow J$, $D\leftrightarrow N$
$T\leftrightarrow J$, $T\leftrightarrow N$

Then the incompatibility graph $I$ has exactly two edges:

$D\!-\!T$
$J\!-\!N$

and no others.

So:

you definitely have double lives, because $I$ has edges;
these are overlapping double lives, because there is more than one edge-pattern of mutual concealment;
but you do not have four lives in the strict sense, because $I$ has no 4-clique;
in fact $\omega(I)=2$, so the strict life-count is only 2.

That seems to line up with your intuition almost perfectly.

7. Why this is the right model

It separates the things that should be separated:

Mutual concealment is modeled by missing edges both ways.
Fake life / real life is modeled by one-way visibility and inclusion of knowledge-sets.
Integration is not “no secrecy at all,” but “one top-level world.”
Strong integration is full mutual openness.
Overlapping double lives are just nontrivial structure in the incompatibility graph, without forcing a misleading scalar count.

So the best answer is:

Model the situation by a directed disclosure graph.
From it derive

a preorder by visible-world inclusion $K(x)\supseteq K(y)$ for real/fake/integration, and

an incompatibility graph for double-life structure and strict life-count.

That gives you one clean object and two natural derived notions, instead of trying to force everything into one number.

If you want, I can turn this into a compact definition/proposition style writeup, as if for a paper or notebook.

Friday, March 6, 2026

Scope of Misesian economic calculation problem

This was asked in a conversational context, omitted here, that contained the entire contents of Economic Calculation in the Socialist Commonwealth, by Ludwig von Mises.

Try formalizing the argument in abstract terms to make the scope of the problem very precise, e.g., it seems that there is an economic calculation problem along these same lines with individual state-owned firms, as well as nonprofits, so I would like the common abstract description that is shared by Misesian economic calculation problem situations.

Yes. A useful way to sharpen Mises’s point is to strip away the historical socialism-vs-capitalism framing and state a more general organizational decision problem.

The common structure is not “state ownership” by itself. It is this:

An agent or organization must choose among many technically feasible, intertemporally linked uses of scarce, heterogeneous resources, but lacks a nonarbitrary way to impute the opportunity cost of those resources across competing uses.

That is the abstract Misesian calculation problem.

A compact formalization

Let:

$R = {r_1,\dots,r_n}$ be scarce resources or productive assets.
$A$ be the set of feasible production plans.
Each plan $a \in A$ specifies:
- inputs used over time: $x(a) \in \mathbb{R}^n_+$,
- outputs/outcomes over time: $y(a)$,
- timing, complementarities, and irreversibilities.
The planner or manager must choose $a^* \in A$.

To choose rationally, the decision-maker needs some way to rank feasible plans. In a market setting this is typically done by a value functional like

$$
\Pi(a) = \text{value of outputs} - \text{value of inputs}
$$

or, intertemporally,

$$
NPV(a)=\sum_t \frac{R_t(a)-C_t(a)}{(1+i)^t}.
$$

The key issue is not the formula. It is whether the terms in it are economically meaningful.

For them to be meaningful, the organization needs a mapping

$$
V: \text{resource uses and outcomes} \to \mathbb{R}
$$

that assigns comparable values to different input combinations and output streams in a way that tracks opportunity cost.

Mises’s claim can be generalized like this:

A Misesian calculation problem exists when an organization must choose among alternative plans $A$, but lacks a reliable value-imputation rule $V$ for some crucial inputs, outputs, or time-structured combinations of them.

Without such a $V$, it can know engineering facts and physical quantities, but not whether plan $a$ is economically preferable to plan $b$.

What makes the problem specifically “Misesian”

The distinctive feature is not mere uncertainty, ignorance, or bad management. It is the absence of a way to reduce alternative resource uses to a common denominator that reflects their forgone alternatives.

So the problem appears when all of the following are present:

Heterogeneous resources
The organization uses different kinds of labor, land, machines, buildings, materials, and time.
Multiple feasible uses
Those resources can be recombined in many possible ways.
Complementarity and substitutability
Inputs matter not only individually but in combinations, and one input’s value depends on what else is available.
Intertemporal structure
Decisions today affect future options, often through long production chains.
No market-generated opportunity-cost signals for some key margins
At least some relevant assets, outputs, or constraints are not priced by competitive exchange.
No residual-claimant test strong enough to correct error
Decision-makers are not tightly disciplined by profit and loss tied to alienable ownership stakes.

That package is the common core.

The abstract mechanism

The mechanism can be stated very precisely.

A market with exchange in relevant assets does two things:

it generates relative prices that compress dispersed tradeoffs into a usable metric;
it subjects proposed plans to profit-and-loss tests, which compare ex ante appraisals to ex post realities.

The Misesian problem arises when an organization has to decide but lacks one or both of these:

price formation for the relevant means of action, and
a feedback mechanism that nonarbitrarily reveals whether the plan used resources well.

Then the organization can still act, but cannot know whether it has economized.

Why this is broader than “full socialism”

This is where your instinct is right.

Full socialism is just the limiting case where the missing valuation problem becomes system-wide, because nearly all higher-order goods are removed from exchange. But the same structure can appear at smaller scales.

The important distinction is between:

global calculation failure, where the whole economy lacks prices for capital goods, and
local calculation failure, where a particular organization lacks meaningful prices or meaningful output valuation at some decision margins.

Both are instances of the same abstract problem.

A general definition

Here is a concise abstract definition.

Misesian Economic Calculation Problem (MECP):
An agent faces a Misesian calculation problem when it must choose among alternative, resource-using, time-structured plans, but the institutional setting fails to generate a sufficiently informative and decision-relevant scalar ordering of those plans grounded in actual opportunity costs.

That scalar ordering need not literally be market profit in every case, but if it is not market-grounded, it tends to become arbitrary, politically assigned, donor-imposed, bureaucratically fixed, or otherwise detached from forgone alternatives.

State-owned firms

A state-owned firm can have the problem in stronger or weaker form depending on context.

Weak form: partial escape from the problem

A state-owned firm operating inside a broader market economy can often borrow market prices for many things:

wage rates,
fuel,
steel,
outside contractors,
comparable products,
interest rates.

So it is not in the same position as a fully socialist economy. It can often calculate using prices formed elsewhere.

That is why Mises emphasized that nationalized firms inside a market order can “parasitically” use the surrounding price system.

Stronger form: where the problem bites

The state-owned firm has a local Misesian problem when one or more of the following are true:

its capital is not bought and sold on markets;
its cost of capital is politically set or subsidized;
losses are covered by a soft budget constraint;
it has multiple noncommensurable goals;
output prices are regulated or politically fixed;
key inputs are internally allocated rather than competitively acquired;
there is no transferable residual claimant.

Then apparent “costs” and “returns” stop reflecting opportunity cost.

So the common abstract point is:

A state firm’s problem is not just bad incentives; it is that some of the terms needed for genuine economic calculation are inherited administratively rather than discovered competitively.

Nonprofits

Nonprofits fit the same schema, but in a different place.

A nonprofit usually buys many inputs on markets, so it often has meaningful input prices. Its distinctive difficulty is usually on the output side.

If a charity feeds people, counsels families, preserves habitat, funds art, or advocates for policy change, the outputs are often not sold at market prices. Then the nonprofit can know:

dollars spent,
people served,
measurable outcomes,

but not necessarily the opportunity-cost-ranked value of one program relative to another in the way a for-profit firm can compare revenues and profits.

So the nonprofit’s calculation problem is typically:

input prices exist,
output valuation is weak or plural,
mission tradeoffs are not fully commensurable.

That still fits the same abstract structure: choice among rival plans without a decisive value-imputation rule.

But it is usually less severe than under socialism because the nonprofit still benefits from market prices for most inputs, and donor behavior can reveal some valuation signals.

A useful typology

It helps to distinguish four cases.

1. Full market calculation

Prices exist for most relevant inputs and outputs, and managers face hard profit-and-loss discipline.

Example: competitive for-profit firm.

2. Partial calculation with borrowed prices

The organization can use market prices formed elsewhere, but some key margins are insulated.

Example: state-owned airline in a market economy.

3. Input-side calculation only

Inputs are market-priced, but outputs are mission-based or nonmarket.

Example: nonprofit hospital, museum, foundation.

4. Systemic calculation failure

No genuine market for means of production, so the entire capital structure lacks meaningful prices.

Example: comprehensive socialism.

These are not different species of problem. They are degrees and locations of the same problem.

What is essential and what is not

A lot of discussion muddies this by mixing the calculation problem with incentive problems or knowledge problems.

Not essential

These can worsen the problem, but are not the core:

corruption,
bureaucracy,
laziness,
ignorance,
lack of computational power,
absence of altruism,
weak managerial talent.

Essential

These are the core:

no genuine opportunity-cost prices for relevant assets or outputs,
no robust market test for alternative plans,
no strong residual claimant structure to force correction.

That is why the problem can persist even with honest, brilliant, public-spirited managers.

Another way to state it

Here is a more stripped-down version:

A Misesian calculation problem exists whenever control rights over resources are separated from a process that competitively imputes those resources’ alternative-use value.

That gives you the common abstraction across socialism, state enterprise, nonprofits, and even some internal divisions of large private firms.

Internal divisions of private firms

This is worth noting because it shows how general the idea is.

Inside a large corporation, many transfers are internal, not market transactions. Headquarters must assign transfer prices, overhead allocations, internal hurdle rates, and shadow values. Those can be arbitrary.

Why does this not immediately collapse into full Misesian chaos?

Because the private firm is still nested inside external markets:

capital markets value the firm,
product markets price outputs,
labor and supplier markets price many inputs,
ownership is transferable,
ultimate profit and loss discipline the whole structure.

So internal calculation problems are real, but bounded by the surrounding market order.

That is exactly the pattern Mises would predict.

The scope condition

The “scope” of the problem becomes precise if you say:

The severity of the calculation problem increases with the share of decision-relevant margins for which opportunity costs are not market-generated and not corrigible by profit-and-loss discipline.

That gives you a continuum rather than a binary.

At one end: full market firm.
At the other end: comprehensive socialism.
In between: regulated monopolies, public agencies, nonprofits, state-owned firms, internally bureaucratized corporations.

A clean formal criterion

A neat criterion would be:

Let $M \subseteq R$ be the set of decision-relevant resources and outputs for which the organization has market-grounded valuation signals.

Let $K \subseteq R$ be the set of decision-relevant resources and outputs for which valuation must be assigned administratively.

The organization faces a Misesian calculation problem to the extent that:

$K$ is large relative to $M$, and
choices in $A$ are highly sensitive to how $K$ is valued.

In words:

The problem becomes serious when many of the margins that matter most are precisely the ones that are not genuinely priced.

Final formulation

Here is the shortest common abstract description.

The shared structure in Misesian calculation-problem cases is this: an organization must allocate heterogeneous, multi-use, time-structured resources across rival plans, but lacks a nonarbitrary, institutionally grounded way to impute opportunity costs to those resources and outcomes. Where that happens, “rational planning” can at best be technical or administrative, not economic.

And the most important qualification is:

Full socialism is the universal case of this problem; state firms, nonprofits, and bureaucratic subunits exhibit local or partial cases of the same structure.

If you want, I can turn this into a more formal theorem-style statement with assumptions, propositions, and corollaries.

Thursday, March 5, 2026

Comtean Positivist World Order

This was in a conversational context containing the entire SEP article on Auguste Comte, which I have omitted.

Write an alternate history narrative where Auguste Comte’s proposed new world order was achieved, with a positivist “spiritual power” ruling over the European “republic of the west”, etc.

The first banners went up quietly.

Not in Paris—Paris was always too loud—but in Lyon, on a gray morning in 1858, when the river mist still clung to the quays and a procession of workers in clean aprons crossed the bridge behind a brass band that didn’t play a hymn so much as a march that remembered a hymn. They carried no crucifixes, no tricolor cockades. Their poles bore round plaques of polished wood: a woman’s profile in relief, serene and severe, above a single word burned into the grain:

HUMANITÉ.

A priest of the old kind watched from the doorway of Saint-Nizier with the baffled squint of a man who had been told that winter had been repealed.

No one called it a revolution. The Positivists disliked the word. Revolutions were critical, corrosive, metaphysical. This was a reorganization. This was a return to order as if order had been there all along and mankind had merely been too distracted to see it.

On September 5 of the previous year, Auguste Comte had died. On September 5 of this year, his followers began the work of proving him immortal.

I. The Second Concordat

History books in our world say Comte’s “Religion of Humanity” never took. In this world, it took because the old religions broke their teeth on the same problem at the same time: the gods had become plausible in the countryside and impossible in the cities. The factories swallowed the calendar. The rail lines turned holy days into scheduling headaches. The newspapers made miracles feel small.

Comte’s friends—once derided as a salon of cranks—had become, by 1860, the only group with a plan that spoke in the language of engineers and in the language of grief.

They understood what the liberals did not: people did not only ask to be free. They asked to belong.

The breakthrough was not philosophical. It was administrative.

Napoleon III, whose instinct for symbols was sharper than his instinct for justice, had always been willing to borrow costumes. He had borrowed Rome, he had borrowed Revolution, he had borrowed Empire. In 1861, after another season of strikes and barricade whispers, he borrowed the Positivists.

The deal was known later as the Second Concordat, though no pope signed it.

In exchange for public endorsement of the regime—order as basis—the Positivist Society was granted legal recognition as a national institution. Not a church; the word stank of ancient quarrels. They were chartered instead as the Council of Spiritual Power, tasked with “moral education, scientific coordination, and the harmonization of social life.”

The Emperor kept the police and the army. The Positivists got the schools, the civil registries, and the calendar.

When the first Positivist Calendar was printed in state presses, the day names were no longer saints or kings. They were the dead: Aristotle, Gutenberg, Shakespeare, Newton—women too, scandalously, like Hypatia and Joan. In every town hall, the old crucifix was replaced by a simple plaque: Vivre pour autrui—live for others.

And then the strangest thing happened: violence went down.

Not because people became better overnight, but because an invisible machinery of meaning slid into place. The Positivists did not promise salvation. They promised continuity: you were not a speck; you were a link. Your work went somewhere. Your suffering joined a ledger, not a void.

Even the skeptics admitted—grudgingly, of course—that Comte’s new priests had found the one thing modern Europe lacked: a way to say “we.”

II. The West Discovers Itself

Comte had always written as if “Europe” were an unfinished word. The Continent was too much geography, too little history. Nations were too much pride, too little purpose. The answer, he said, was not a continent at all but a tradition: the West, an “Occidentality” bound by a shared sequence of intellectual stages and a shared task—to lead Humanity out of metaphysics into positive maturity.

At first this sounded like a Frenchman polishing his own reflection.

Then came 1870.

In our world, France’s humiliation at Sedan and the birth of the German Empire solidified a violent new Europe. In this world, Sedan still happened—but its consequence was inverted by a single decision made in panic, in a room thick with cigar smoke and fear.

The Emperor fled, yes. The Paris streets boiled, yes. But the men who stepped into the vacuum were not the Commune’s improvisers and not the old monarchists clawing their way back. They were the Positivists, who had spent a decade building lists, schedules, curricula, and networks of local “intendants” across the provinces.

They did what engineers do when a bridge collapses: they stabilized the remaining structure before arguing about architecture.

A provisional government called itself, without irony, the Directory of Reorganization. It immediately did two things:

It invited the German states—not Bismarck’s empire, which had not yet fully congealed—to a congress “for the scientific settlement of European relations,” hosted in neutral Geneva.
It declared the French army temporarily under the “moral supervision” of the Council of Spiritual Power.

Germany, exhausted by its own victories and wary of endless occupation, came to Geneva expecting bargaining. It found something closer to an audit.

The Positivists did not appeal to honor. They appealed to arithmetic.

How many sons would this rivalry consume in the next fifty years? How much coal would be burned in military trains rather than factories? How many bridges would be built with the iron not melted into cannon?

They spread maps on tables like surgeons. They spoke of “division of labor between nations.” They offered a new model: not empires, not alliances, but a Republic of the West—a confederation of European temporal governments under a single spiritual authority responsible for education, science policy, and moral consensus.

Bismarck laughed—until he saw that the alternative was not French revenge, but French collapse, and that collapse would spill refugees and radicals across borders like acid.

He did not join. Not yet. But he agreed to a truce, to mutual recognition, and, most crucially, to a shared Western Commission on Industry and Public Health—the first permanent body in which the Positivist spiritual power sat as chair while kings and ministers sat as “temporal delegates.”

In later years, historians would point to Geneva as the moment “Europe” died and “the West” was born.

III. The Separation That Changed Everything

The Council of Spiritual Power, in Comte’s scheme, was supposed to have no soldiers, no prisons, no taxes. It would rule by education, ceremony, and the slow pressure of consensus. Temporal power would remain local, practical, coercive when needed—like a hand that could grip—but spiritual power would be planetary in aspiration, like a mind that could not be fenced.

This distinction was mocked as naïve.

Then it worked.

The Positivists never tried to replace parliaments with pulpits. They replaced arguments about ultimate values with a standardized civic formation that made most values feel settled by adulthood.

Schoolchildren learned the encyclopedic scale of sciences as naturally as prayers. They learned that social life had laws. They learned that freedom without cohesion dissolved into noise. They learned to commemorate. They learned to sing. They learned that “Humanity” was not a crowd but a continuity of the dead acting through the living.

Every year, on the Day of Gutenberg, apprentices in printing houses read aloud a list of books published in their district. On the Day of Pasteur (added after 1878), nurses and doctors processed together, as if medicine were a sacrament—which, in this world, it almost became.

The most controversial reform was the civic registry.

Birth, marriage, death—events once recorded by churches—were now registered by the Positivist clergy. Not clergy, they insisted. Functionaries of continuity.

To die in the Republic of the West was to be entered into Humanity’s ledger by name, occupation, and contribution. And once you were in the ledger, you could be invoked—not as a saint, but as an ancestor in the human project.

This did not make people immortal.

It made them count.

The Church protested, then negotiated, then retreated into the private sphere, still powerful in pockets, still beloved by millions, but no longer sovereign over the rhythms of public life. In Britain, where the monarch was head of an established church, the transition was bloodless precisely because the Positivists presented it not as an attack on belief but as a necessary separation of spatial scales: the Church, if it wished to be universal, could not be tied to one crown. The Anglican compromise became a model. Spiritual authority was no longer a throne’s ornament.

It was an institution of its own.

IV. The Nineteen Intendances

Comte’s critics had always said he was a centralizer at heart, a Frenchman addicted to Paris.

His followers proved the opposite with a pen stroke.

In 1882, the French Republic—now explicitly “a Western Republic in France”—divided itself into nineteen intendances, each designed to be large enough for economic coherence and small enough for human attachment. The move startled everyone because it seemed, at first glance, like decentralization.

And it was—temporally.

But spiritually, the curriculum, the calendar, the civic rites were identical across all intendances. You could travel from Marseille to Lille and find the same commemorations, the same hymns, the same lectures in workers’ halls on Sunday evenings replacing sermons. The mind had no boundaries.

Local governments handled roads, policing, trade disputes. The spiritual authority handled meaning.

A new European joke spread: “In the West, the mayor fixes your sewer; the priest fixes your soul—without mentioning God.”

It was a good joke. It was also almost true.

V. The Great Men and the Great Silence

Not everyone loved the new order.

There were riots in 1889 when the Council issued a “Moral Circular” discouraging nationalist rallies as “metaphysical agitation.” There were whispered pamphlets, in backrooms, mocking the Positivist liturgy as “Catholicism without Christ.”

And there were tragedies.

The most famous was the Great Silence of 1893, when a charismatic young mathematician—Emile Renaud, whose name is still spoken with a mixture of reverence and fear—refused to accept the Council’s condemnation of a new “metaphysical” philosophy spreading from Vienna.

Renaud argued that the Council had become exactly what it claimed to prevent: dogmatic, allergic to doubt, hostile to the ferment that produced science.

His public lecture in Paris ended with a sentence that shocked the city into stillness:

“Humanity is a god that bleeds.”

He was not arrested. The Council did not have prisons.

He was excommunicated—not from salvation, but from civic recognition. His name was removed from the registry of commemorations. His students were barred from teaching posts. It was the gentlest punishment imaginable and, therefore, the most terrifying.

The scandal forced a reform.

In 1895, after weeks of bitter internal debate, the Council issued the Charter of Critical Positivity, declaring that “the positive spirit includes systematic doubt as method, while excluding metaphysical doubt as aim.” It established “Free Academies” within the spiritual system—spaces where hypotheses could be proposed without moral censure, as long as they did not incite political fragmentation.

The West had learned something it had forgotten in its hunger for order: minds need oxygen.

Renaud’s name was restored to the calendar, though his day was placed in the “Controversy” week at the year’s end, a time set aside for public disputation. The Council called it “a hygiene of the intellect.”

People called it “the week we’re allowed to breathe.”

VI. The West and the Rest

The Republic of the West was not, as its enemies predicted, a militarized monolith. Its spiritual power distrusted conquest. Comte himself had condemned colonial brutality as a betrayal of Europe’s supposed mission.

So the West’s expansion was less flag and more syllabus.

In North Africa, in Indochina, in India, Positivist envoys—often English—argued against “civilizing missions” carried out with guns. They proposed instead a gradual withdrawal of temporal control paired with the offer of spiritual affiliation: independent states could join the “Western moral federation” through shared education, scientific institutions, and participation in the commemorative calendar.

Some called this merely imperialism in softer clothing.

Others—especially reformers trapped between tradition and invasion—found in positivism a third option: secularism without nihilism, modernity without the humiliation of mimicry.

The Ottoman intellectuals were among the earliest adopters. By 1908, when the old empire convulsed, the Young Turks in this world did not reach for ethnic nationalism first. They reached for the Positivist separation: local temporal reforms under a universal spiritual framework that could unify a multiethnic population without forcing it into one language of worship.

The slogan painted on the walls of Istanbul that year was neither “God” nor “Nation,” but:

Love as principle. Order as basis. Progress as end.

Even critics admitted it was a better prophecy than most.

VII. The War That Didn’t Happen

The greatest advertisement for Comte’s world order was a ghost: the First World War, which in our world burned Europe into the twentieth century.

In this world, the ingredients still existed: rivalries, arms manufacturers, assassins, pride. There was still an Archduke shot in 1914 in a city with too many histories.

But there was also, by then, a continental machinery built precisely to absorb shocks.

When the news reached Paris, Vienna, Berlin, London—by telegraph, crackling like a panic attack—temporal ministers demanded mobilization. The Council demanded a conference.

Not a conference of diplomats, but of sociologists.

This was the Positivist innovation that conservatives had once sneered at: when society was threatened, the West consulted the science of society.

Within seventy-two hours, the Western Commission convened in Geneva again. The assassination was treated not as insult but as symptom. The Council’s report—still studied today—began with a sentence that enraged patriots:

“A murder is not a cause; it is an occasion.”

They mapped the chain of alliances like a disease’s transmission. They identified points of escalation. And then they did something no nineteenth-century power would have dared: they publicly published the costs of full mobilization—projected dead, projected debt, projected political collapse—before a single train moved.

The report circulated faster than orders.

Workers in Germany refused to load artillery. French railwaymen slowed troop transports “for maintenance.” British dock unions held a “Day of Humanity” strike. The temporal powers, confronted not only with moral pressure but with the practical breakdown of compliance, backed down.

Austria demanded vengeance. The Council offered something new: a ritual.

A public trial, international, followed by a continental day of commemoration for “victims of political fanaticism,” with lectures in every city about the dangers of metaphysical nationalism.

Vengeance became pedagogy.

No war. A decade of tension, yes. But no continent-wide slaughter.

Later generations would argue about whether positivism saved Europe or merely postponed its reckoning. But everyone agreed on one point: the West had discovered a way to make bloodshed feel, not glorious, but unscientific.

And that was enough to change behavior.

VIII. A Walk Through Paris, 1937

You can still walk through Paris in this world and feel the difference in your bones.

The churches still stand. Cathedrals are too beautiful to demolish. But their bells ring less often, and when they do, they sound like a language spoken by grandparents.

On the Île de la Cité, Notre-Dame has been converted into what the Council calls a Temple of Continuity—not because it worships the building, but because it worships what the building represents: the dead laboring for the living. Inside, under the high vaults, there is a simple wall of names: masons, carpenters, anonymous donors. The famous are there too, but smaller. The point is not greatness. The point is linkage.

On the first floor of the old Hôtel de Ville, a lecture hall is full. Tonight’s topic: “Astronomical Conditions and Human Destiny.” Not astrology—Comte would have spit—but a sober meditation on the planet’s fragility, the atmosphere’s thinness, the dependence of life on cosmic steadiness. Children fidget. Adults take notes. Someone coughs. The mood is not holy, exactly. It is attentive.

Across the street, a café is loud with arguments about whether the Council’s new guidelines on “artistic education” are too prescriptive. A poet is calling the Positivists tyrants. An engineer is calling the poet childish. A woman at the bar says both are missing the point and orders another drink.

Outside, on the walls, posters announce the coming festival week:

WEEK OF DESCARTES
Public debates permitted under Charter of Critical Positivity
Topics: Free Will, Determinism, the Limits of Sociology
Attendance encouraged, violence prohibited

It is, oddly, a city that has institutionalized disagreement.

At the end of the boulevard, a statue stands in a small square. Not of Comte. The Council has always been careful to avoid idolizing the founder too openly. The statue is of a woman in a simple dress holding a ledger and extending her other hand.

The plaque reads:

À L’HUMANITÉ
Les vivants sont gouvernés par les morts.

The living are governed by the dead.

A tourist from America, where positivism has grown into a parallel spiritual authority rather than a ruling one, stares at the inscription and shivers. It sounds authoritarian, like a threat.

A Parisian beside him smiles, almost kindly.

“No,” she says. “It’s a comfort. It means you’re not alone. Even when you fail, you fail inside a story that continues.”

The tourist looks up at the woman’s stone face.

“And who governs the governors?” he asks.

The Parisian shrugs.

“Reality,” she says. “And the children. Eventually.”

IX. The Cost of Harmony

The West, by 1950, had achieved what Comte predicted in outline: a layered world order with temporal governments managing local life and a unified spiritual power coordinating education, science, and moral consensus across Europe and beyond.

The result was stability. Prosperity. A slower, steadier modernization without the jagged trauma of total war.

But every harmony has its price.

The Positivist spiritual power, lacking police, learned to rule through exclusion. It could not imprison you, but it could make you socially weightless. It could refuse you teaching licenses, deny you ceremonial recognition, cut you from the rituals that made life feel meaningful.

For many, that was worse than a fine.

The Council’s defenders argued that all societies enforce norms; the Positivists simply did so openly and, they claimed, rationally.

Their critics argued that a spiritual monopoly, even without guns, could become a velvet dictatorship over thought.

In the late twentieth century, a new movement rose within the West itself: Plural Positivism, insisting that the spiritual function could be fulfilled by multiple competing institutions, as long as they shared a commitment to the positive method and the social coordination of knowledge.

The Council resisted, then compromised—again, as it always had when it wished to survive.

By 2000, the Republic of the West had become less like a church and more like a federation of civic philosophies. The calendar remained, but people celebrated some days and ignored others. The temples remained, but they hosted concerts as often as ceremonies. The Council still issued moral circulars, but now they were debated in public, sometimes laughed at, sometimes obeyed.

Comte would have been horrified.

Comte would have been pleased.

He had wanted order. He had wanted progress. Above all, he had wanted a future shaped by deliberate thought rather than drifting tradition.

And perhaps the truest sign that his world order had achieved itself was this: it had become ordinary enough to argue with.

Epilogue: The Motto

In a school courtyard in Recife—yes, Brazil still took Comte seriously enough that the West’s spiritual authority became a global partner, though never a master—a child recites the old motto during a ceremony honoring the “Week of Great Women.”

She says it carefully, as if each clause must fit into place like a gear.

“Love as principle,” she begins.

Her classmates repeat it.

“Order as basis.”

They repeat it.

“Progress as end.”

They repeat it again, and the sound echoes off the walls painted with murals of scientists and nurses and farmers and poets, all woven into one long, continuous figure labeled, in bright letters:

HUMANITY.

The teacher watches with the tired affection of someone who knows that rituals are imperfect tools but still tools.

In the back row, one boy whispers to another, “Do we really have to say it every year?”

The other boy grins.

“Probably,” he whispers back. “Until we invent something better.”

And that, in the Republic of the West, is considered a perfectly positive hope.

In a separate conversation, I also generated this image based on the story above.

ChatGPT-generated image.

Wednesday, March 4, 2026

Activist movement model and strategy

A thread by eigenrobot had outlined a model of activist movements and their capture by their least sympathetic elements. This post cleans up that model and tries to use the result to answer strategic questions that were raised by Maya. It is stated in abstract terms, and applies variably to immigration, trans issues, etc. As with some of my other posts, the only custom instruction is “User language: English”.

I think Rothbard’s memorandum on activist movement strategy (and other Leninist writings on strategy) is also relevant to the problem in some way, but I did not try to incorporate anything from it.

Eigenrobot’s model, improved

1) Baseline primitives (yours, slightly normalized)
2) The missing structural assumption: inclusion is not separable
3) Who becomes “the face” of the group: a simple collective-action/attention stage

Stage 0: outside options
Stage 1: activism as a public good with type-dependent cost
Stage 2: visibility / representation

4) Equilibrium logic: why the high-friction subgroup dominates visibility
5) Bringing your “surplus transfer” intuition into the model
6) What this model explains (and what it predicts)

Explains
Predictions (useful if you want to push toward an empirically testable story)

7) One-line version of the refined intuition

Strategic implications

1) Keep “no carve-outs” credible without letting “worst examples” define the brand
2) Convert “high-friction types” into “high-friction states”
3) Subsidize moderate participation (raise $e_l$ without asking them to be saints)
4) Separate “mobilization engine” from “public face” via roles and institutions
5) Make internal representation robust to “activist capture”
6) Bundle demands in a sequence that avoids internal betrayal
7) Treat “appeasement” as a scarce resource; use it where it buys real votes

A compact strategic slogan (model-faithful)

Eigenrobot’s model, improved

Try to clean up and develop the model described below.

The following is a tentative rational agent explanation for why the public perception of identitarian activist groups tends to be dominated by the least sympathetic members of whatever community they purport to represent. The key intuition here is that it’s an act of self-defense for the high-friction group.

Imagine some excluded group A with measure α < 0.5 and an excluding majority B with measure (1-α). To become “included,” at least 0.5 of the population must agree to inclusion. inclusion imposes a cost C(Ai) borne by B, but produces a benefit Y accruing to included members of A. But A is not homogeneous: some fraction γ∈[0, 1] of A imposes a cost Ch on B when included; fraction (1-γ) imposes a cost Cl on B when included. Here, Ch > Cl.

To interpret these ideas, A is some minority group. If they were accepted by wider society, which currently shuns them, they would benefit; but it would moderately irritate the majority. The amount of irritation increases with the number of A-members accepted and varies by type. Some A-members are low-friction A-members. They’re already well integrated with the majority in some ways and basically chill. However, the high-friction A-members? They’re—say—crazy criminals who sacrifice dogs in their backyards.

Crucially, let’s stipulate that Ch > Y > Cl. That is: the benefit accruing to an included low-friction A-member is greater than the cost imposed on the majority by his inclusion. This means he can in theory bargain with the majority to gain his own inclusion in a Pareto improvement. This isn’t possible for a high-friction A-member because whatever he gets from inclusion is insufficient to compensate the majority for the inconveniences his dog sacrifice ceremonies are causing them.

In this base model, individual low-friction A-members each compensate the majority from some fraction of their inclusion returns, and high-friction A-members are left out in the cold. Obviously this doesn’t explain our phenomenon; we need an story for why the high-friction A-members are in charge. A richer model driving the observed equilibrium might include cost sensitivity heterogeneity in the majority group leading to some kind of coalition politics in the minority, or a structure in the game that requires a representative role for a subset of the minority group.

Regardless of what form a solution actually looks like, the intuition this is groping toward is that the high-cost subpopulation is motivated to dominate activism by the possibility that they’ll be shut out of the integration process and left in the cold by a majority-compatible subgroup.

Narrative variants: the high-cost subgroup has lower opportunity costs to activism (eg, no career or whatever) and pay that cost to control group bargaining position, using it to trade surplus accruing to the low cost subgroup in the base model in for their own inclusion; some kind of strategic lock into a coalition with superior bargaining power—maybe their benefit from inclusion is lower?; possession of some lever for extorting the majority. Regardless, the usual result is transfer of surplus from the low cost group to the high cost group.

Here’s a cleaner “workhorse” model that captures your intuition with a minimal set of added ingredients. I’ll keep your primitives, but I’ll (i) make the policy non-separable, and (ii) explicitly model who becomes visible / representative as an equilibrium selection outcome.

1) Baseline primitives (yours, slightly normalized)

Population mass 1. Minority group $A$ has mass $\alpha<1/2$; majority $B$ has mass $1-\alpha$.

Types in $A$:

Low-friction type $l$ has mass $\alpha(1-\gamma)$ and imposes per-capita cost $C_l$ on $B$ if included.
High-friction type $h$ has mass $\alpha\gamma$ and imposes per-capita cost $C_h$ on $B$ if included, with $C_h>C_l$.

Each included $A$-member gets benefit $Y$. Your key inequality: $$C_h > Y > C_l.$$ So (in a separable world) including $l$ is potentially Pareto-improvable; including $h$ is not.

2) The missing structural assumption: inclusion is not separable

To get “high-friction dominates the bargaining/branding,” you need a reason the world can’t just include $l$ and exclude $h$.

A crisp way to do that:

Non-separability / imperfect screening: the political/organizational decision is a single binary policy $I \in {0,1}$ (“include the group”), and if $I=1$ then all who can claim membership get included. Formally, the majority cannot condition inclusion on type: $$ I=1 \Rightarrow \text{all } A\text{-types included.} $$

This can represent: legal non-discrimination constraints, unverifiable “type,” administratively costly screening, or a norm that “inclusion must be group-wide.”

Then the majority’s cost of inclusion is $$ \text{Cost to }B = \alpha\left[(1-\gamma)C_l+\gamma C_h\right]. $$ Even if $l$ is “efficient,” the presence of $h$ can make the group’s inclusion unattractive in aggregate, which sets up a real conflict inside $A$: $l$ would like a carve-out; $h$ needs bundling.

3) Who becomes “the face” of the group: a simple collective-action/attention stage

Add a standard Olson-style activism stage with heterogeneous opportunity costs.

Stage 0: outside options

Let $u_t^0$ be the outside option for an $A$-member of type $t\in{l,h}$ if the policy fails ($I=0$). A natural asymmetry: $$ u_l^0 > u_h^0, $$ meaning low-friction members can partially “self-include” via assimilation, private markets, passing, norm-conforming behavior, etc., while high-friction members can’t.

So the incremental value of policy success is $$ \Delta_t := (Y - u_t^0), $$ with $\Delta_h > \Delta_l$.

Stage 1: activism as a public good with type-dependent cost

Each $A$-member chooses activism effort $e_i \ge 0$. Total effort $E=\sum e_i$ increases the probability of inclusion $p(E)$ where $p'>0, p''<0$.

Effort cost depends on type: $$ \text{cost}(e\mid t)=\frac{k_t}{2}e^2, $$ and crucially $k_h < k_l$ (lower opportunity cost / fewer career penalties / fewer foregone alternatives).

Each member solves $$ \max_{e_i\ge 0} ; p(E)\Delta_t ;-;\frac{k_t}{2}e_i^2. $$

Stage 2: visibility / representation

Public perception is shaped disproportionately by the most active/visible members. Model that as:

media/attention weight $w_i = \frac{e_i}{E}$ (share of attention proportional to effort), or
“the spokesperson” is the highest-effort individual (a tournament).

Either way: higher $e$ ⇒ more likely to be seen as representative.

4) Equilibrium logic: why the high-friction subgroup dominates visibility

In the standard public-good-with-heterogeneous-costs setup:

Those with lower marginal costs ($k$ small) and higher marginal benefits ($\Delta$ large) supply more effort.
Those with high $k$ (high opportunity cost) and low $\Delta$ free-ride.

Concretely, in any interior equilibrium, a type’s first-order condition is approximately $$ p'(E)\Delta_t \approx k_t e_t. $$ So effort scales like $$ e_t \propto \frac{\Delta_t}{k_t}. $$ Thus $e_h > e_l$ when $$ \frac{\Delta_h}{k_h} > \frac{\Delta_l}{k_l}. $$

Given $\Delta_h>\Delta_l$ and $k_h<k_l$, this inequality is very easy to satisfy. Then:

High-friction members supply most activism effort (they’re the “marginal activists”).
Attention/representation concentrates on them via $w_i$ or the tournament.
Public perception becomes dominated by the least sympathetic members even if they’re a minority within $A$.

This is already enough to generate your phenomenon without assuming “high-friction is in charge” as a primitive. They become in charge because equilibrium activism supply selects them.

5) Bringing your “surplus transfer” intuition into the model

Now add an internal bargaining constraint that’s especially natural under non-separability.

If inclusion is group-wide, then low-friction members may want “moderation” to maximize acceptance probability by $B$. High-friction members may prefer aggressive tactics that (i) increase mobilization and internal solidarity, or (ii) impose costs on $B$ to force bargaining.

A clean way to formalize “transfer from $l$ to $h$” is:

There is a group organization that chooses a “line” (demands/tactics) $a$ and funds activism.
Low-friction members can pay dues/transfers $T$ to influence $a$ toward moderation.
High-friction members have a credible “spoiler” action (they can produce damaging visibility or disruption) unless $a$ and/or $T$ meet their participation constraint.

Participation/spoiler constraint for $h$: $$ \text{If } (a,T) \text{ not acceptable, }h\text{ exerts independent effort }e_h^{\text{spoiler}} \text{ that captures attention.} $$

Then equilibrium often has the structure you described:

$l$ would like a “separable bargain” (include $l$, exclude $h$) but can’t get it.
$h$ uses (low-cost, high-visibility) activism as leverage to keep the coalition bundled.
$l$ pays (resources, rhetorical compliance, reputational cover) to reduce the damage of $h$’s dominance, which is a transfer of surplus from $l$ to $h$.

6) What this model explains (and what it predicts)

Explains

Why visibility skews toward “worst” or least sympathetic members: they have the biggest stakes and lowest opportunity costs, so they out-supply activism and capture attention.
Why moderates often appear passive: it’s rational free-riding + higher reputational/career costs.
Why internal rhetoric can look “hostage-like”: under non-separability, $h$ has a credible veto/spoiler, so coalition policy shifts toward $h$’s constraints, financed by $l$.

Predictions (useful if you want to push toward an empirically testable story)

When outside options for moderates improve ($u_l^0\uparrow$), activism and representation skew more extreme (because $\Delta_l\downarrow$).
When opportunity costs of public activism fall for everyone (e.g., anonymized online activism), you should see more “moderate supply,” potentially reducing the skew—unless anonymity benefits $h$ disproportionately.
When screening becomes feasible (separable inclusion), the extreme subgroup’s leverage collapses and “moderate representation” becomes easier to sustain.

7) One-line version of the refined intuition

If (i) inclusion is effectively group-wide and (ii) activism/visibility is supplied by those with the lowest opportunity costs and highest marginal benefits, then the subgroup that is hardest to integrate rationally becomes the most active and most visible—so public perception of the whole group gets anchored to them, and coalition bargaining shifts surplus away from the easy-to-integrate members.

If you want to take this one notch more “game-theory formal,” the next step is to explicitly model $B$’s decision as a voting game with heterogeneous tolerance (or moral payoffs) and make “tactics” affect both $p(E)$ and perceived expected cost. But the core mechanism above is already doing the main explanatory work with clean comparative statics.

Strategic implications

For a movement that ultimately wishes for inclusion of all A-members, it is better to have low-friction A-members as its public-facing identity, but incentives are against it, as we just modeled. Low-friction A-members also have the incentive to try to distinguish themselves and try to appease the B-members, but this is bad for the high-friction A-members. Think of how political movement strategy should account for this.

In your model, the movement is playing a two-level game:

External bargain (with B): you want B to believe “including A won’t be too costly / we can manage the costs.”
Internal bargain (within A): you need high-friction members not to veto/sabotage moderation, and low-friction members not to peel off into “separate-but-included” deals.

So “movement strategy” is mostly about engineering incentives and institutions so that (a) low-friction members reliably occupy the front stage (where persuasion matters), while (b) high-friction members still get credible inclusion and real voice (so they don’t rationally seize the mic).

Here are the main levers.

1) Keep “no carve-outs” credible without letting “worst examples” define the brand

Low-friction members distinguishing themselves (“I’m not like those people”) is locally rational but coalition-poisoning: it increases the perceived $\gamma$ and salience of $C_h$, and it tells high-friction members they’re about to be sold out.

A stable line is: “No carve-outs on personhood; lots of carve-outs on behavior.”

Don’t publicly split the identity into “good A” vs “bad A.”
Do publicly split conduct into “okay in civil society” vs “not okay,” and make that symmetrical (rules apply to everyone, not just A).
This lets the movement reassure B that costs are bounded without creating a permanent underclass inside A.

In your terms: you’re trying to reduce perceived $C_h$ (and perceived $\gamma$) without redefining $h$ out of A.

2) Convert “high-friction types” into “high-friction states”

Your model treats $h$ as a type. Movements do better if they treat much of it as a state that can be improved.

Strategically: invest movement resources in lowering $C_h$ rather than only arguing about it.

Examples (abstractly):

internal norms and accountability that prevent the most visibly costly behaviors
services/mutual aid that reduce dysfunction, instability, or antisocial spillovers
training/mentorship that increases members’ capacity to navigate mainstream institutions

If you can make $C_h$ move toward $Y$, you weaken the core “can’t be Pareto-improved” barrier that makes $h$ desperate to control bargaining.

3) Subsidize moderate participation (raise $e_l$ without asking them to be saints)

Your earlier equilibrium is driven by $\Delta_h/k_h > \Delta_l/k_l$: high-friction members have higher stakes and lower opportunity costs, so they out-supply activism and become “the movement.”

If you want low-friction members to front the movement, you must change those ratios:

Lower $k_l$: protect moderates from career/reputational costs (anonymity options, legal defense funds, employer shielding, professionalized comms that reduces personal exposure).
Raise $\Delta_l$: make movement success matter to them (status, leadership pipelines, selective benefits like networks, professional opportunities, real voice).

This sounds cynical, but it’s just mechanism design: if the movement needs “ambassadors,” it has to pay the opportunity costs of ambassadorship.

4) Separate “mobilization engine” from “public face” via roles and institutions

A common failure mode is pretending the same people can optimally do:

base mobilization (high arousal, high conflict)
elite persuasion (low arousal, high trust)
mass-image management (low variance, high discipline)

You can explicitly adopt a frontstage/backstage structure:

Frontstage: disciplined spokespeople; message coherence; high empathy; low variance; optimized for B’s median.
Backstage: broader internal deliberation; higher tolerance for anger/heterodoxy; optimized for keeping $h$ included and heard.

This only works if backstage has real power (agenda-setting, vetoes, budget shares), otherwise $h$ correctly treats it as a trick and fights for frontstage control.

5) Make internal representation robust to “activist capture”

If attention is proportional to effort, “whoever can shout all day becomes the movement.” Counter that with governance that weights membership more than activism hours:

leadership selection by election with high-turnout mechanisms, not whoever shows up to meetings
rotation/term limits for spokesperson roles
transparent decision rights: who sets demands, who chooses tactics, who speaks externally
formal “communication discipline” rules: not censoring beliefs, but controlling who represents the org publicly

The key is to decouple “time available” from “formal authority.”

6) Bundle demands in a sequence that avoids internal betrayal

Movements that want inclusion of all A-members usually need staging—but staging can look like betrayal to $h$.

A workable framing is:

Sequence policies, not people.
Start with policies that expand inclusion broadly while imposing minimal perceived costs on B.
Pair every early win with movement-visible investments that benefit $h$ (so $h$ sees progress, not abandonment).

So the coalition story becomes: “We win step 1 for everyone, then step 2 for everyone,” not “we win for the good ones first.”

7) Treat “appeasement” as a scarce resource; use it where it buys real votes

Low-friction members trying to appease B can backfire if it:

legitimizes B’s worst stereotypes
teaches B that outrage yields concessions
signals to $h$ that the coalition is conditional

So appeasement should be replaced with targeted reassurance:

acknowledge concrete concerns B has
offer universal safeguards (behavioral standards, enforcement symmetry, institutions that limit externalities)
keep moral posture consistent: “you don’t get to exclude people, but we do take costs seriously.”

A compact strategic slogan (model-faithful)

Keep identity inclusive, keep behavior governable, pay for moderation, and institutionalize who speaks.

If you want, I can sketch a simple formal extension where the movement chooses (i) a spokesperson-selection rule, (ii) an internal transfer $T$ to subsidize $e_l$, and (iii) a “cost-reduction investment” that lowers $C_h$, and then show the comparative statics for when “low-friction face, high-friction included” is an equilibrium.