Does the mathematical notation you used mean anything?

ChatGPT said:

Yes — it’s drawn from standard welfare economics notation. The expression

$$W = \sum \mu_i U_i$$

represents a social welfare function, where:

• $W$ is total (aggregate) welfare,

• $U_i$ is the utility (or well-being) of individual i,

• $\mu_i$ is a weighting coefficient applied to each person’s utility.

In this model, individuals are treated as variables whose value contributes to the overall sum. The artwork’s critique is that when moral worth is modeled this way, individuals’ intrinsic dignity collapses into instrumental contributions to the equation — they become weighted terms rather than beings with irreducible moral standing.

Would you like me to explain how this equation evolved historically (e.g. from Bentham to modern welfare economics)?

You said:

yes

ChatGPT said:

Excellent — here’s the conceptual and historical arc behind that equation, which shows how it came to embody precisely the moral reduction your quote critiques.

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1. Bentham and the Utilitarian Foundation

Jeremy Bentham (1748–1832) proposed that morality could be mathematized:

“The greatest happiness of the greatest number.”

He assumed that pleasure and pain could be treated as measurable magnitudes, so that society’s moral aim was simply to maximize total utility.
Formally, this implied:

$$W = \sum_i U_i$$

where $U_i$ represents each individual’s pleasure or satisfaction.

This was revolutionary because it collapsed ethics into arithmetic—moral judgment became a matter of calculation, not deliberation or justice.

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2. Edgeworth, Pigou, and the Early Mathematical Turn

In the late 19th and early 20th centuries, economists like Francis Edgeworth and Arthur Pigou formalized this intuition into what became welfare economics.
They introduced weighting factors ($\mu_i$) to account for different circumstances, moral priorities, or diminishing marginal utility:

$$W = \sum_i \mu_i U_i$$

However, this did not restore individuality—it simply allowed for adjustments to how strongly each person’s utility counted.

Edgeworth dreamed of a “hedonometer,” a device to measure pleasure.
Pigou worried about fairness and introduced corrective taxation, but still assumed welfare could be aggregated.

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3. The Mid-Century Crisis: Ordinal Utility and Pareto Optimality

By the 1930s, economists realized you can’t actually measure utility across persons.
So the field shifted: utility was treated as ordinal, meaning we can only compare preferences within one person, not across individuals.

Thus emerged Pareto efficiency (Vilfredo Pareto):

A state is “better” only if at least one person is better off and no one is worse off.

This move avoided moral comparison entirely—but at a cost: it emptied welfare analysis of ethical content. The individual became a point in a preference space, and collective welfare became an abstract equilibrium, not a moral condition.

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4. Postwar Aggregation and the Return of the Equation

Economists like Bergson and Samuelson reintroduced the general welfare function ($W = f(U_1, U_2, \dots, U_n)$), sometimes returning to the additive form for simplicity.
Yet, they emphasized that this was not morally neutral: the choice of $f$ reflects society’s ethical stance.

Even so, in practice, policy analysts and utilitarians (e.g., in cost-benefit analysis) often defaulted back to additive aggregation, treating lives as weighted inputs to a maximization problem.

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5. Rawls, Sen, and the Moral Backlash

John Rawls rejected aggregation altogether, arguing that summing utilities violates the separateness of persons:

“Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override.”

Amartya Sen pushed further: what matters is not utility but capability—what a person is able to be and do. He called the purely utilitarian view “fetishistic,” because it reduces moral life to measurable outcomes.

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6. Today: From Welfare Equations to Metrics of Control

The equation still appears in policy, AI ethics, and global development metrics (e.g., DALYs, QALYs, GDP per capita).
But each time it is used, it risks converting moral standing into instrumental value—precisely the collapse your artwork depicts.
The human becomes a parameter, a token of value within a system’s optimization logic.

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Would you like me to sketch a philosophical counterformulation of that equation—something that preserves individuality while still being formally expressible?

You said:

Ok

ChatGPT said:

Good. Let’s construct a counterformulation — something that resists the logic of reduction while still retaining a formal structure.

We’ll start by naming the problem clearly:

In the classical welfare equation, the person appears only as a term contributing to an aggregate. The structure itself enforces the collapse of individuality into instrumentality.

So we need a new kind of formalism, one that makes individuality irreducible and relational, rather than summable.

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1. From Summation to Relation

Instead of

$$W = \sum_i \mu_i U_i$$

we posit

$$\mathcal{W} = \mathcal{R}(P_1, P_2, \dots, P_n)$$

where each $P_i$ is not a unit of welfare but a person-process — a situated being whose value emerges only in relation to others.
$\mathcal{R}$ is not additive but relational: it expresses how well the relations themselves sustain the dignity and agency of each participant.

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2. Introducing Incommensurability

Formally, we can define:

$$\forall i, j: P_i \not\equiv P_j$$

and therefore

$$\text{No total order } \exists \text{ over } \{P_i\}$$

That is, there is no meaningful way to rank or aggregate moral standing.
Each person retains an axiological singularity — a unique standing that resists substitution.
Any “welfare function” that presupposes commensurability thereby violates moral reality.

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3. A Process-Relational Form

We could define a processual moral function:

$$\Phi = \int_{\mathcal{T}} f(P_i(t), P_j(t), \dots) \, dt$$

This integrates over time the quality of mutual regard, rather than summing static welfare quantities.
What’s morally valuable here is the temporal unfolding of care, recognition, and non-domination among agents — not their outcomes.

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4. Ethical Constraint, Not Maximization

Where utilitarianism says maximize $W$,
our counterformulation imposes a moral constraint:

$$\text{For all } i, \quad \text{Preserve}(P_i)$$

subject to which other optimizations may be performed.
This encodes Rawls’s insight — that justice requires the protection of each person’s inviolability before any aggregate welfare is considered.

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5. Interpretation

In this alternative frame:

• The good is not a sum, but a field of sustained relations.

• Moral standing is non-aggregable and non-fungible.

• Social health is measured not by total utility but by relational integrity — the capacity of individuals to appear, act, and be recognized without being reduced to means.

This equation cannot be computed by standard means, because it refuses the arithmetic of substitution. Its ethical force lies precisely in its noncomputability.