➘ #36 Source Article

◉ A plain English walkthrough of the Master Proof above.

1. Establishing the Logical Groundwork

The framework begins by defining clear, measurable relationships between actions and their consequences.
An offense can be finite or infinite in magnitude, and a punishment can also vary in magnitude—by duration, severity, or both.
A punishment is called “just” only when it is proportionate to the offense that caused it.
These predicates give precision to ideas that are often vague, such as “justice” or “proportion,” by grounding them in quantifiable relationships.

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2. Foundational Principles

Four core axioms define how proportional justice operates:

1. A punishment is just if and only if it is proportionate to the offense.
2. When something is proportionate, there exists a consistent function that maps the size of the offense to the size of the punishment.
3. If an offense is finite, its magnitude is finite.
4. That mapping function cannot take a finite value and produce an infinite result.

Together, these axioms capture a simple structural truth: proportionality preserves scale. A finite cause cannot generate an infinite effect without violating the definition of proportionality itself.

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3. Logical Consequence of the Axioms

From these axioms, one can deduce that if an offense is finite and the assigned punishment is both just and proportionate, then the punishment must also be finite.
This follows directly from the properties of the mapping: if the input (the offense) is finite, the output (the punishment) must also be finite.
Hence, any claim that a finite act warrants an infinite consequence contradicts the very concept of proportional justice.

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4. Independence from Measurement Scale

This conclusion doesn’t depend on how one measures punishment.
Whether punishment is measured in years, intensity, or some combined index of suffering, the proportional relationship holds.
The logic applies universally across all valid metrics.

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5. The Collapse of Infinite Scaling

A separate line of reasoning shows what happens when someone tries to justify infinite consequences by appealing to the infinite worth of the being offended.
If one assumes that “infinite worth” automatically translates to “infinite offense magnitude,” then every offense—small or large—becomes equally infinite.
The system loses all ability to distinguish between trivial and grave acts, collapsing into absurdity where all actions have the same penalty.
This demonstrates that invoking “infinity” as a scaling factor destroys proportional differentiation altogether.

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6. The Failure of Definition by Decree

Another principle examines what happens if justice is defined merely as “whatever is declared to be just.”
Under that rule, justice no longer describes a measurable relationship between acts and consequences—it becomes empty.
If “justice” simply means “declared right,” then the term carries no logical or normative content.
Proportionality and fairness vanish because the system’s definitions are circular.

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7. Inconsistency in Substitutional Logic

A further argument explores the contradiction that arises when one claims a punishment of infinite duration was fully borne by someone whose suffering was not infinite in duration.
If a penalty truly requires infinite duration, then by definition it cannot be completed.
To claim both “the infinite penalty was borne” and “the bearer’s suffering ended” produces a direct contradiction.
Finite experience cannot exhaust an infinite requirement.

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8. Limits of Restoration and Patience

The reasoning extends beyond individual cases:

• If a punishment has no end, there can be no restoration, no patience, and no meaningful hope of change.
• An infinite, irreversible state of punishment excludes growth and reconciliation by its very structure.
• A system that claims to embody love or patience cannot also include infinite, unending retribution.

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9. Unified Logical Outcome

Bringing all of these principles together yields a single conclusion:

• A finite offense cannot produce an infinite punishment under any coherent concept of justice.
• Any system that claims otherwise must either discard the idea of proportionality, redefine justice as mere decree, or accept logical incoherence.

In short, infinity cannot emerge from finitude without breaking the rules of scale preservation, rational consistency, and relational fairness that underlie the very notion of justice.

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Summary Insight

This proof works like a formal safety check on justice.
If justice is defined as proportionality (A1), and proportionality preserves scale through a bounded mapping (A2–A4), then it is impossible for any finite input—any finite wrongdoing—to yield an infinite output such as eternal punishment.
The logic of proportionality itself forbids it.
Thus, the idea of an “eternal penalty for finite offenses” violates the very structure of what it means for punishment to be just.

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◉ Narrative Summary

The logical system unfolds around one central idea: proportional relationships preserve scale. If an act is finite, the consequence attached to it must also be finite. To claim otherwise is to confuse magnitude itself — it’s like saying a short spark could yield an everlasting flame under the same physical law.

The argument begins with definitions that turn vague moral talk into measurable terms. Offenses and punishments each have magnitudes, and a punishment is “just” only when its magnitude corresponds to that of the offense. From this, four axioms structure the reasoning. Justice equals proportionality; proportionality follows a consistent mapping from cause to effect; finite causes have finite magnitudes; and the mapping cannot turn something bounded into something unbounded.

Once these foundations are set, the outcome is inevitable. A finite offense mapped proportionally can never yield an infinite punishment. Any claim that it can violates the very logic of proportionality, just as a function that multiplies two finite numbers cannot suddenly yield infinity. This conclusion holds no matter how the punishment is measured — whether in years, intensity, or accumulated suffering.

Attempts to escape this logic fail under scrutiny. When people claim that the offense is infinite because it is committed against a being of infinite worth, the scale collapses. Every offense becomes equally infinite, and distinctions between small and great wrongs disappear. When others insist that justice is whatever is declared by authority, justice loses meaning altogether — it becomes mere decree, stripped of any rational connection between action and consequence.

Even theological appeals to substitutional suffering fail within the same logical framework. If a punishment is infinite in duration, it cannot be said to have been fully borne by one whose suffering was finite. The claim refutes itself. And if punishment is truly infinite, it forecloses all possibilities of restoration, reconciliation, or growth; infinity allows for no change.

The reasoning, taken as a whole, leads to a categorical conclusion: proportional systems cannot produce infinity from finitude. To assert that finite offenses deserve infinite punishment is to abandon the logic of justice itself. Such a system can preserve proportionality, or it can preserve infinity — but never both.

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An Exhaustive (354-page) Treatment of this Issue:

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