What is the meaning of “reductio ad absurdum”?
“Reductio ad absurdum,” a term with its roots in Latin, translates literally to “reduction to absurdity.” This philosophical argumentative technique endeavors to disprove a statement by showing that its logical conclusion leads to an absurd or contradictory outcome. It’s a form of argument that proves the falsehood of a proposition by demonstrating that its logical extension leads to a nonsensical or impractical conclusion. This method has been a staple in mathematical proofs, philosophical discourse, and rhetorical strategies across various fields, from ancient times to modern debates.
Definition
At its core, reductio ad absurdum operates by taking a proposition to its logical extremes to highlight inconsistencies or contradictions that would arise if the proposition were true. If these extremes are shown to be impossible, illogical, or absurd, then the original proposition is undermined and thus can be concluded to be false.
Examples
Mathematical Proofs: A classic example is the proof that √2 is an irrational number. Assume, for contradiction, that √2 is rational, meaning it can be expressed as a fraction a/b, where a and b are integers that have no common factors other than 1, and b is not zero. Through a series of logical steps, this assumption leads to the conclusion that a and b must have a common factor, contradicting the initial assumption that they have no common factors other than 1. Therefore, the assumption that √2 is rational leads to an absurdity, and thus √2 must be irrational.
Philosophical Argument: In the realm of ethics, imagine arguing against the notion that “might makes right” by suggesting that if this were true, then any act of theft, violence, or tyranny could be considered morally acceptable if the perpetrator is strong enough to succeed. This leads to the absurd conclusion that moral values have no inherent worth, which contradicts basic ethical principles shared by most societies.
Legal Reasoning: Consider the argument against the infallibility of eyewitness testimony. If one were to argue that eyewitness testimony is always reliable, then in cases where two eyewitnesses provide mutually exclusive accounts of events, both would have to be considered infallibly correct, an absurdity since two contradictory accounts cannot both represent the truth simultaneously.
Political Discourse: An argument could be made against unrestricted free speech by suggesting that, if all speech were entirely without limits, it would be permissible to shout false alarms in crowded places, causing panic and potential harm. This scenario illustrates the absurdity of the original premise by highlighting dangerous or harmful outcomes, thereby supporting the idea that some restrictions on speech are necessary for public safety.
* * *
Reductio ad absurdum is a Latin phrase that translates to “reduction to absurdity” It refers to a specific type of argument in logic. Here’s how it works:
• You want to prove a statement (conclusion) is true.
• Instead of directly proving it, you assume the opposite (denial) is true.
• You then logically show that assuming the opposite leads to an absurdity or contradiction.
• Since the opposite leads to something nonsensical, the original statement must be true.
It’s basically a way of proving something by showing that the alternative is impossible.
