The clue for the first blank is “are rejected by modern science in its attempts to find secular insights.” Otherworldly interpretations contrast the secular, and the best choice for the first blank is preternatural. There would be a paradox only if scientists could hold non-secular beliefs. Therefore, a good word for the second blank is prevent, and a good phrase for the last blank would be in agreement. Preclude is synonymous with prevent, and consonant is synonymous with in agreement, making these the correct answers.