形式語言與自然語言的邏輯──談殷海光《邏輯新引》

Formal Language and Natural Language: On Yin Hai-Kuong's New Introduction to Logic

在本文中，我檢視了殷海光《邏輯新引》中，關於他稱之為「選取推論」的一段討論。在該段討論中，殷海光區分了選取語句的四種可能情形，並討論在這些情形下關於選取語句的有效與無效推論形式。除了標準的「相容之或」與「不相容之或」的區分外，殷海光亦試圖區分選取語句之「窮盡」與「不窮盡」的可能情況，並以此為基礎討論它們的有效推論。但這部分的討論，有些較難理解之處。本文猜想這主要是因為《邏輯新引》是以較日常的對話體裁書寫，談及的推論皆為自然語言中的推論。在沒有引進一套形式語言及其語意學的情況下，我們其實很難定義清楚有效推論是什麼。因此，本文主張，自然語言與形式語言的區分，對於進行邏輯研究而言，是十分重要而不可或缺的。

In this paper, I critically discuss a passage from Yin Hai-Kuong's New Introduction to Logic, which concerns what he calls 'disjunctive inferences'. Based on a four-fold classification of the formal conditions of disjunctive sentences, Yin investigates into the valid and invalid patters of inference involving disjunction. However, while the distinction between the 'inclusive or' and the 'exclusive or' is quite standard, Yin makes a parallel distinction between the 'exhaustive' and the 'non-exhaustive' conditions for disjunctive sentences and tries to draw some parallel conclusions about their validity. This part is somewhat difficult to follow. I suspect that this is due to the informal, dialectical style of New Introduction to Logic, which discusses validity and invalidity entirely for sentences in the natural language. Without introducing a formal language with a separable formal semantics, it is difficult to define validity in a crystal clear way that avoids all potential confusions. The contrast between the natural language and the formal languages is therefore very crucial for logical inquiries, or so I argue.