irrational

Etymology

It is inherited from Middle English irracional,^[2][3] borrowed from Latin irratiōnālis (“without reason, not rational”),^{[4][5][3][6][7]} formed from in- (“not”), in its assimilated form ir-, and ratiōnālis (“of or belonging to reason, reasonable”),^[5][7][6] the source of rational.^[3][8] The Latin adjective has also the form inratiōnālis.^[5] In mathematics it was used to translate Ancient Greek ἄλογος (álogos) in Euclid, and the English mathematical sense comes from that use.^[5]

Earliest recorded meaning

Of quantities, that cannot be expressed in ordinary numbers or fractions: before 1398, in Trevisa's translation of Bartholomaeus Anglicus's De Proprietatibus Rerum, where it renders Latin irrationales.^[2][3] Etymonline likewise dates the mathematical sense to the late 14th century.^[5]

Semantic evolution

Apart from the mathematical term, the word first meant "not endowed with reason", said of animals and the like; the OED's first record is perhaps before 1500, in Henryson's translation of Aesop's fables, and Etymonline dates it to the late 15th century.^[4][5] The OED's first quotation for the mathematical sense is later, from Recorde's Pathway to Knowledg (1551).^[4] The sense "contrary to reason, absurd" is recorded from 1641.^[4][3][5] Johnson (1755) gave "void of reason; void of understanding" first, with Milton's Paradise Lost, and "absurd; contrary to reason" second.^[9] The noun followed in the 17th century: a being without reason from 1646, and an irrational number from before 1690.^[4][10] In the 19th century the word became a term of Greek prosody, first recorded in 1844.^[4]

Timeline

• a1398 – of a quantity, not expressible in ordinary numbers, in Trevisa.^[2][3]
• ?a1500 – not endowed with reason, in Henryson's fables.^[4]
• 1551 – mathematics, of a number or magnitude, in Recorde.^[4]
• 1641 – contrary to reason, illogical, absurd.^[4][3]
• 1646 – noun, a being without reason.^[4][10]
• a1690 – noun, an irrational number; a surd.^[4]
• 1755 – Johnson defines it as "void of reason" and "absurd".^[9]
• 1844 – Greek prosody, of a syllable or foot.^[4]

Meanings

Adjective

1. Not in keeping with reason or logic; unreasonable or absurd: an irrational dread of open water.^[11][10][4]
2. Not able to reason: irrational animals.^[11][10][4]
3. Lacking normal mental clarity, as after an illness or injury.^[10]
4. (mathematics) Of a number or quantity, not expressible as a ratio of two integers; not rational.^[11][4][10]
5. (prosody) In Greek or Latin verse, of a syllable whose metrical value does not match its actual length, usually a long syllable in place of a short one, or of a foot containing such a syllable.^[11][4][10]

Noun

1. (mathematics) An irrational number; a surd.^[11][10][4]
2. A being without reason, or one not guided by it.^[10][4]

Word family

• irrationally
• irrationalness
• irrationality
• irrationalism
• nonirrational
• irrationalize
• irrational number

Related words

• rational
• reason
• ratio

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c Kurath, Hans; Kuhn, Sherman M.; Lewis, Robert E., eds. (1952–2001), Middle English Dictionary, Ann Arbor: University of Michigan Press; online edition ed. Frances McSparran et al. (2000–2018)
3. ^ a b c d e f g Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
4. ^ a b c d e f g h i j k l m n o p q r Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
5. ^ a b c d e f g Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
6. ^ a b Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
7. ^ a b Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
8. ^ Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
9. ^ a b Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
10. ^ a b c d e f g h i Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
11. ^ a b c d e Collins English Dictionary (2023), Glasgow: HarperCollins