牟宗三先生《邏輯典範》對於羅素的批評

Mou Zongsan’s Criticism of Russell’s Logicism

本文反省牟宗三《邏輯典範》對於羅素的批評。首先，概述羅素如何藉由集合論而還原數學，並說明「存在公理」何以為羅素學說的公認致命傷。接著，回顧數學哲學的「唯實論」(realism) 與「唯名論」(nominalism) 二大傳統，以見羅素的特性與定位。最後，說明牟氏如何以「純理之自己展現」來看待邏輯與數學，並提出筆者的反思。牟氏觀點未必為羅素所能接受，但我們的結論仍肯定，《邏輯典範》對於牟氏思想的發展具有一拓荒與轉折的意義。

The present essay examines Mou Zongsan’s criticism in his Luoji dianfan of Russell’s logicism. First, the author gives a sketch of how Russell reduces mathematics to logic on the base of the set theory and why he has to assume the axiom of infinity and the multiplicative axiom. Second, Russell’s position is traced to nominalism, one of the two main traditions in the philosophy of mathematics. Finally, I present Mou’s doctrine that logic (and mathematics) is the displaying of pure reason itself and give my reflection on the doctrine. I conclude that in spite of Mou’s disagreement with Russell, Luoji dianfan did play an indispensable role in the development of his thought.