foundation has 18 distinct synonyms spread across 5 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the basis on which something is grounded
“there is little foundation for his objections”
an institution supported by an endowment
lowest support of a structure
“it was built on a base of solid rock”
the fundamental assumptions from which something is begun or developed or calculated or explained
“the whole argument rested on a basis of conjecture”
a woman's undergarment worn to give shape to the contours of the body
the act of starting something for the first time; introducing something new
“she looked forward to her initiation as an adult”
Synonyms, antonyms and the broader and narrower relations for foundation come from Princeton University’s WordNet. Full sources and licences.