postulieren
to demand
To forcefully demand or call for something.
Die Opposition postulierte den sofortigen Rücktritt des Ministers.
The opposition demanded the minister's immediate resignation.

to postulate / demand
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to demand
To forcefully demand or call for something.
Die Opposition postulierte den sofortigen Rücktritt des Ministers.
The opposition demanded the minister's immediate resignation.

'Postulieren' (to postulate/demand) is a word of written language and is used mainly in formal, academic, or political contexts. In everyday colloquial speech, it sounds very elevated and unusual.
Der Autor postuliert in seinem neuen Buch eine gewagte These.
In his new book, the author postulates a bold thesis.
The verb 'postulieren' (to postulate/demand) is closely related to the noun 'das Postulat' (the postulate). A postulate is either a forceful demand or an unproven assumption that serves as the basis for a theory.
Ein zentrales Postulat seiner Philosophie ist die Freiheit des Individuums.
A central postulate of his philosophy is the freedom of the individual.
The verb 'postulieren' (to postulate/demand) is usually used with a direct object in the accusative. You always postulate or demand 'etwas' (something).
Die Wissenschaftler postulierten einen direkten Zusammenhang.
The scientists postulated a direct connection.
When 'postulieren' (to demand) has the meaning 'fordern' (to demand/call for), the subject is often a political or social group (e.g., a party, a union). The object is then a concrete political or social demand.
Die Bürgerinitiative postulierte mehr Transparenz bei politischen Entscheidungen.
The citizens' initiative demanded more transparency in political decisions.
In the scientific or philosophical meaning 'als wahr annehmen' (to assume to be true), the subject is often a researcher, an author, or a theory. The object is then a thesis, a principle, or the existence of something.
Einstein postulierte, dass die Lichtgeschwindigkeit eine universelle Konstante ist.
Einstein postulated that the speed of light is a universal constant.
to demand / challenge
'fordern' and 'postulieren' can both mean that someone clearly demands something. 'fordern' is the normal word in everyday life, politics, work, or arguments. 'postulieren' sounds much more elevated and is more often used in formal texts, speeches, or theoretical contexts. It often feels more abstract than 'fordern'. When a group demands more money, rights, or a change, people usually say 'fordern'. 'postulieren' is more appropriate when a demand is formulated in a very fundamental or programmatic way.

In seinem Vortrag postuliert er ein Recht auf freien Zugang zu Bildung.
In his lecture, he postulates a right to free access to education.
Die Mitarbeiter fordern mehr Zeit für die Vorbereitung.
The employees are demanding more time for preparation.