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." The meaning in logic, "lay down as something which has to be assumed although it cannot be proved" dates from 1640s, from a sense in Medieval Latin.
1580s, "a request, demand, petition," from Latin postulātum "demand, request," properly "that which is requested," noun use of neuter past participle of postulare "to ask, demand; claim; require" (see postulate (v.)).
The sense in logic, "proposition proposed for acceptance without proof, something taken for granted," is from 1640s, from a sense in Medieval Latin. The meaning "self-evident practical proposition" is by 1751. The earlier noun in English was postulation "a petition, request" (c. 1400). Middle English also had postulate (adj.) "nominated to a bishopric or archbishopric" (mid-15c.).