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🤔intro to philosophy review

key term - Reductio ad Absurdum

Citation:

Definition

Reductio ad absurdum is a logical argument that attempts to disprove a statement by showing that it leads to an absurd or contradictory conclusion. It is a philosophical method used to discover the truth by demonstrating the falsehood or logical inconsistency of an opposing position.

5 Must Know Facts For Your Next Test

  1. Reductio ad absurdum is a powerful tool for exposing logical flaws or inconsistencies in an opponent's argument or position.
  2. The method involves assuming the truth of the opponent's claim and then deriving a conclusion that is clearly false or absurd, thereby demonstrating the original claim must be false.
  3. Reductio ad absurdum can be used to disprove a statement by showing that it leads to a contradiction or an outcome that is clearly unacceptable or impossible.
  4. This technique is often employed in mathematical proofs to establish the validity of a theorem by demonstrating the absurdity of its negation.
  5. Reductio ad absurdum is a common philosophical method for discovering truth by systematically eliminating false or logically inconsistent propositions.

Review Questions

  • Explain how the reductio ad absurdum method is used to discover truth in philosophical inquiry.
    • The reductio ad absurdum method is a powerful tool for philosophical discovery because it allows philosophers to systematically eliminate false or logically inconsistent propositions. By assuming the truth of an opponent's claim and then deriving a conclusion that is clearly absurd or contradictory, the philosopher can demonstrate that the original claim must be false. This process of logical elimination helps to uncover the truth by ruling out untenable positions and narrowing down the field of viable arguments or beliefs.
  • Describe how reductio ad absurdum is commonly used in mathematical proofs.
    • In mathematics, reductio ad absurdum is frequently employed to establish the validity of a theorem. The mathematician will begin by assuming the negation of the theorem is true, and then logically derive a conclusion that is clearly false or absurd. This demonstrates that the original assumption, the negation of the theorem, must be false, and therefore the theorem itself must be true. By showing that the opposite of the theorem leads to a contradiction, the mathematician can indirectly prove the theorem through this process of reductio ad absurdum.
  • Analyze how the reductio ad absurdum method differs from other philosophical methods for discovering truth.
    • Unlike inductive or deductive reasoning, which rely on building up arguments from observations or logical premises, the reductio ad absurdum method works by systematically tearing down the opposing position. Rather than constructing a positive case for a claim, reductio ad absurdum focuses on demonstrating the falsehood or logical inconsistency of an alternative view. This indirect approach can be a powerful tool for philosophical discovery, as it allows philosophers to eliminate untenable propositions and narrow the field of viable arguments. However, the reductio ad absurdum method does not on its own establish the truth of a particular claim, but rather clears the way for other philosophical approaches to build a positive case for the truth.