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Reductio ad absurdum

THOUGHT_EXPERIMENT logic

In logic, reductio ad absurdum (Latin for 'reduction to absurdity'), also known as argumentum ad absurdum, (Latin for 'argument to absurdity') apagogical argument, or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs

Metadata

  • Slug: 00642-reductio-ad-absurdum
  • Type: THOUGHT_EXPERIMENT
  • Tags: logic
  • Sources: 1
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Axioms

  • Assume the rules of the domain apply uniformly.
  • Assume the observer’s criteria remain fixed.
  • Assume classification boundaries stay consistent.
  • Assume the model describes the real case.
  • Assume repeated steps do not change the outcome.
  • Assume no hidden variables are introduced midstream.

Contradictions

  • Two reasonable lines of inference yield opposite conclusions
  • A global rule conflicts with a local judgment
  • A stable resolution appears to violate a starting premise
  • Changing the framing reverses the outcome
  • Intuition and formalism diverge at the same step

Prompts

  • Which assumption is doing the most hidden work?
  • What changes if you relax the smallest constraint?
  • Does the paradox dissolve or relocate when reframed?
  • What is conserved, and what is sacrificed?

Notes

Sources

Overview

In logic, reductio ad absurdum (Latin for “reduction to absurdity”), also known as argumentum ad absurdum, (Latin for “argument to absurdity”) apagogical argument, or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs

Tension

  • Two reasonable lines of inference yield opposite conclusions.
  • A global rule conflicts with a local judgment.
  • A stable resolution appears to violate a starting premise.
  • Changing the framing reverses the outcome.
  • Intuition and formalism diverge at the same step.

Why It Matters

This entry tests how a stable rule-set can yield unstable conclusions under certain assumptions.

Prompts

  • Which assumption is doing the most hidden work?
  • What changes if you relax the smallest constraint?
  • Does the paradox dissolve or relocate when reframed?
  • What is conserved, and what is sacrificed?