# Reductio Ad Absurdum

Pronunciation: /reˈduk.ti.oː æd æbˈsɝd.m̩/ Explain

Reductio ad absurdum is a logical argument that attempts to disprove a statement by showing that, if the argument is taken to its extremes, the result is absurd, or illogical. Reductio ad absurdum is also called argumentum ad absurdum and appeal to extremes. It is the original basis of the mathematical proof by contradiction.

### Example

Statement: There is a smallest positive real number. Contradiction: However, since any real number can be divided by two, and a number divided by two is smaller than the original number, there must be a real number smaller than any number. Conclusion: Therefore, there can be no smallest positive real number.

### History

The process of taking an argument to its logical extremes was used before the Greek philosopher Socrates. Socrates and Aristotle formalized and taught this method.

### References

1. reductio ad absurdum. www.merriam-webster.com. Merriam-Webster Online Dictionary. Merriam-Webster. Last Accessed 1/7/2019. https://www.merriam-webster.com/dictionary/reductio%20ad%20absurdum. Buy the book
2. Bobzien, Susanne. Ancient Logic. plato.stanford.edu. Stanford Encyclopedia of Philosophy. Stanford University. Winter 2016. Last Accessed 1/7/2019. https://plato.stanford.edu/entries/logic-ancient.
3. Ferguson, Thomas Macaulay and Priest, Graham. A Dictionary of Logic (Oxford Quick Reference Online). Kindle edition. Oxford Quick Reference Online. Oxford. June 16, 2016. Buy the book

• McAdams, David E.. Proof. allmathwords.org. All Math Words Encyclopedia. LIfe is a Story Problem LLC. 1/7/2019. https://www.allmathwords.org/en/p/proof.html.