basic assumption vs supposition

basic assumption and supposition both are nouns.

Word	Noun	Adjective	Verb	Adverb
basic assumption	Yes	No	No	No
supposition	Yes	No	No	No

As nouns, supposition is a hypernym of basic assumption; that is, supposition is a word with a broader meaning than basic assumption:

Other hypernyms of basic assumption include assumption, supposal.

basic assumption (noun)	supposition (noun)
an assumption that is basic to an argument	a hypothesis that is taken for granted
	the cognitive process of supposing
	a message expressing an opinion based on incomplete evidence