Corollary vs. correlation

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In modern English, a corollary is an obvious deduction, a natural consequence, or a proposition that follows with little or no proof from one already proven. The word usually takes the preposition to, though of and from also workA correlation is a complementary or parallel relationship between two things, not necessarily involving causation or a direct relationship. It usually takes the preposition between. So a corollary involves one thing springing from another, while a correlation involves two things that relate to each other in some reciprocal way.


In each of these examples, the corollary is an obvious result of or conclusion from something else:

He argues that the right of biological parents to keep and raise the child they produce is a corollary of a more general right, which is, to be allowed to finish what one has begun. [Metapsychology]

It’s ingrained in the culture; there is no shame or stigma attached to failure because it’s seen as the necessary corollary of risk-taking. [Irish Times]

As all written words consist of letters, it is an undeniable corollary from the preceding premises, that all written words are formed of the written signs of spoken sounds. [The Gentleman’s Magazine (1837)]

And in each of these examples, the correlation involves a reciprocal relationship between two things:

Despite traditional negative correlation, gold and USD has been moving in tandem since the outbreak of the anti-government unrest in Egypt. [International Business Times]

Never mind that there’s no correlation between state fiscal health and whether public employees can unionize. [Harvard Crimson]

Prepositions thus exhibit a wonderful correlation between the intellectual and physical worlds ; a correlation which shows that both worlds proceeded from the same Author. [English Grammar, William Chauncey Fowler (1850)]