《科學、哲學與幾何學的空間表達》第七章 觀念與形式之窮盡性 摘要
一、 愛因斯坦與 形上學 It is the fundamental emotion which stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed. It was the experience of mystery—even if mixed with fear—that engendered religion. A knowledge of the existence of something we cannot penetrate, our perceptions of the profoundest reason and the most radiant beauty, which only in their most primitive forms are accessible to our minds— it is this knowledge and this emotion that constitute true religiosity; in this sense, and in this alone, I am a deeply religious man. 為什麼史先生該書結語會引用愛因斯坦那段話? 比較簡單的解釋是 第四章 形上學本義 ( 第 37 頁 ) 有段話: 然而在另一方面,若以人存在中另一極端之科學知識而言,假如其方法或對其對象的瞭解,可達到徹底完善的地步,當然也就不再需要形上學的存在了。設若不能,那麼科學方法之窮盡處,其實就是和形上學最為接近的地方。 而這種情形,尤自現代數理學家 ,Cantor, Lobachtevsky, Russell, Hilbert, Lowenheim, Gödel 等人 , 發現了形式表達之「設定」、「不定」與「矛盾」性之後,更清楚地向我們展現出來。 換句話說,現代數學只要再進一步從形式表達窮盡般之「設定」、「...