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Reductio Ad Absurdum Flowchart

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About This MicroSim

This interactive MicroSim helps students demonstrate the reductio ad absurdum technique by tracing the logical steps from assumption through contradiction to conclusion.. It supports the learning objectives in Chapter: Reasoning and Argumentation.

How to Use

Use the interactive controls below the drawing area to explore the visualization. Hover over elements for additional information and click to see detailed descriptions.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

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<iframe src="https://dmccreary.github.io/theory-of-knowledge/sims/reductio-flowchart/main.html"
        height="450px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

9-12 (High School / IB TOK)

Duration

15-20 minutes

Prerequisites

  • Basic understanding of logical reasoning and what constitutes a valid argument
  • Familiarity with the concept of proof in mathematics
  • Ability to follow an if-then chain of reasoning

Learning Objectives

  • Apply the reductio ad absurdum technique by stepping through structured proofs and identifying the contradiction that drives each conclusion

Activities

  1. Exploration (5 min): Step through the classic proof that the square root of 2 is irrational. Click through each stage of the flowchart, reading how the argument assumes the opposite of what it wants to prove, then follows logical steps until a contradiction appears. Identify which specific step produces the contradiction and write it down.
  2. Guided Practice (10 min): Now switch to the proof that there are infinitely many prime numbers. Step through the flowchart again, but this time pause at each node and predict what comes next before clicking. After completing the proof, compare the two proofs with a partner: What structural similarities do they share? At what point does each proof "break" the initial assumption?
  3. Assessment (5 min): Without using the sim, outline the general structure of a reductio ad absurdum argument in 3-4 steps. Then, given the claim "There is no smallest positive rational number," sketch how you would begin a reductio proof (state the assumption and identify what kind of contradiction you would look for).

Assessment

  • Correctly identifies the contradiction step in at least one of the sim's proofs
  • Accurately describes the general structure of reductio ad absurdum in their own words
  • Demonstrates ability to begin applying the technique to a new claim

Quiz

Test your understanding with this review question.

1. In a reductio ad absurdum proof, what is the first step?

  1. State the conclusion you want to prove and provide direct evidence for it.
  2. Assume the opposite of what you want to prove, then derive logical consequences.
  3. List all known facts related to the topic and find one that is false.
  4. Test multiple numerical examples until a pattern emerges.
Show Answer

The correct answer is B. Reductio ad absurdum works by assuming the negation of the desired conclusion, then showing through valid logical steps that this assumption leads to a contradiction. Since contradictions cannot be true, the original assumption must be false, and the desired conclusion must be true. This is an indirect proof technique, unlike the direct approaches described in options A, C, and D.

Concept Tested: Structure of reductio ad absurdum reasoning

References

  1. International Baccalaureate Organization. Theory of Knowledge Guide. Cardiff: IBO, 2022.
  2. Woolman, M. Ways of Knowing: An Introduction to Theory of Knowledge. IBID Press, 2006.