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postulate (v.)

1530s, "nominate to a church office," from Medieval Latin postulatus, past participle of postulare "to ask, demand; claim; require," probably formed from past participle of Latin poscere "ask urgently, demand," from *posk-to-, Italic inchoative of PIE root *prek- "to ask questions." Use in logic dates from 1640s, borrowed from Medieval Latin.

postulate (n.)

1580s, "a request, demand," from Latin postulatum "demand, request," properly "that which is requested," noun use of neuter past participle of postulare (see postulate (v.)). The sense in logic of "self-evident proposition" is from 1640s. The earlier noun in English was postulation (c. 1400).

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Definitions of postulate from WordNet
1
postulate (v.)
maintain or assert;
Synonyms: contend
postulate (v.)
take as a given; assume as a postulate or axiom;
Synonyms: posit
postulate (v.)
require as useful, just, or proper;
This intervention does not postulate a patient's consent
Synonyms: necessitate / ask / need / require / take / involve / call for / demand
2
postulate (n.)
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning;
Synonyms: posit
From wordnet.princeton.edu