In ... reasoning, ideas are tested against the empirical world:

Based on the question "In ... reasoning, ideas are tested against the empirical world", the missing word is likely "scientific". Therefore, the full sentence would be: "In scientific reasoning, ideas are tested against the empirical world."

Translation: В ... рассуждениях идеи проверяются на соответствие эмпирическому миру:

Answer: scientific

Translation of the answer: научный