I recently delved into a discussion about a statement attributed to the renowned mathematician and philosopher, Benjamin Peirce. In this statement, he refers to mathematics as "the science that draws necessary conditions." This has piqued my curiosity about the linguistic origins and historical context of the term "necessary condition" in mathematics.

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Interpreting "$q$ is a necessary condition for $p$" seems to be a formal way to express that "$p$ implies $q$" ($p \Rightarrow q$). This realization has led me to several questions:

  • Main question: Who was the first person that introduced the term "necessary condition" in mathematical discourse?

  • second important related question: Was there a specific rationale or historical backdrop that necessitated the introduction of this term?

  • How has the understanding and utilization of this term evolved in the landscape of mathematical language over time?

I am genuinely interested in uncovering the historical nuances surrounding the inception and adoption of this phrase in the mathematical community.

  • $\begingroup$ Peirce says "conclusions", not "conditions". $\endgroup$ Sep 20 at 8:20
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    $\begingroup$ IMO you have to search in the Latin tradition, from Medieval logic to Port Royal and Leibniz. If you use Google book search, you implicitly restrict the search to "early modern" sources. $\endgroup$ Sep 20 at 10:06

1 Answer 1


Oxford English Dictionary, s.v. “'necessary condition' in necessary, adj., sense I.1.e”, July 2023. https://doi.org/10.1093/OED/1255631544

The Oxford English Dictionary (subscription required) shows earliest quotation for "necessary condition" in 1650, Hobbes, Leviathan

It shows "sufficient condition" only from 1914, but earlier uses of "sufficient cause" (1656) and "sufficient reason" (1717). They also mention the terminology of Leibniz, "raison déterminante" (1710) later changed to "raison suffisante" (1714).

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    $\begingroup$ Google Books shows several uses of 'necessary condition' in the first half of the 1600s before Hobbes, also in theological contexts. Such as the 1611 google.com/books/edition/… . $\endgroup$ Sep 18 at 16:56
  • $\begingroup$ @kimchilover, how to you search in Google books sorting by date? $\endgroup$ Sep 19 at 13:14
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    $\begingroup$ you can restrict the time range in google books search $\endgroup$ Sep 19 at 13:38

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