to believe (something) before there is proof

believe, take for granted

to feel sure of the truth of (something, that a person is honest etc)

trust, rely on

of lay

put, place

to claim, suggest (something) as necessary, especially as a basis for reasoning

suppose, figure

a statement on which an opinion, argument, reason etc is based

hypothesis, argument

to suppose (something) to be true

make assumption; believe

something which seems likely although there is no proof; arrogance (the usual word)

belief, hypothesis

to thing of (something) as likely; to take (something) as a fact

assume, guess

the act of supposing something to be true but without proof; a guess

guess, belief

a long, detailed piece of writing explaining, supporting or criticizing something, especially as part of an academic course

belief, assumption to be tested