The term DECLARE WITH CONVICTION can be broken down into two crossword solutions: AVER (4 letters) and ASSERT (6 letters). AVER is a verb meaning to state as a fact, often with confidence. It is derived from the Latin verb 'averare' which means to make firm or confirm. ASSERT is also a verb meaning to state a fact or opinion confidently and forcefully. It is derived from the Latin verb 'assertare' which means to affirm or declare. Therefore, DECLARE WITH CONVICTION can be interpreted as confidently and forcefully stating a fact or opinion.