您好,以下是個人的淺見,請供您參考
這裡 "當時的自然科學處於分門別類地蒐集材料的經驗階段" ===> The science had been in a state that to collect and harvest the materials (experience, pieces of researching) then sorted them into different categories.
當時的自然科學處於分門別類地階段, The science had been in a state that was doing a sorting, categorizing (and to make it more in detail, what kind of sorting or categorizing the science was doing during the period of time.) ===> 一個蒐集材料的階段 甚麼樣的材料===>經驗
蒐集材料的經驗階段===> 經驗 是 "蒐集材料"的定語
''蒐集材料的經驗階段'' 可視為 ''當時的自然科學處於分門別類地'' 的 補語