古典对当方阵和广义量词

古典对当方阵可同溯到亚里士多德逻辑，并且自此后就一直被广泛地讨论，特别是在中世纪和现代。它刻画了所有、没有、并非所有和某些这四个量词之间的特定逻辑关系，即对当关系。亚里十多德和传统逻辑学家，以及人多数当代语言学家，都把“所有”看作具有存在预设，也即“所有A是B”可以推山“存在A”，而现代逻辑则放弃了这一假定。用现代逻辑对“所有”的解释来代替亚里十多德的解释（对“并非所有”也可以作类似处理），就产生了现代版本的对当方阵。近年来有许多争论，探讨这两个方阵中哪一个是正确的。本文中我的主要观点是，这个问题不是，或者不应该主要是关于存在预设的，毋宁说它是关于否定的模式的。我认为现代方阵表述了自然语言中否定的一般模式，而传统方阵则没有做到这一点。明乎此，不仅需要把对当方阵应用于四个亚里士多德量词，还需要把它应用到这一类型的广义量词上。现代方阵上的任一量词所展示的否定的模式，常常不是在传统方阵中发现的对当关系。本文提供了一些技术性结果和工具，阐述了解释各种英语限定词的量词方阵的若干例子。本文最后一个例子引入了否定的第二模式。它伴随特定复杂量词出现，也能够在方阵中被表达。

The Traditional Square of Opposition and Generalized Quantifiers

The traditional square of opposition dates back to Aristotle＇s logic and has been intensely discussed ever since, both in medieval and modern times. It presents certain logical relations, or oppositions, that hold between the four quantifiers all, no, not all, and some. Aristotle and traditional logicians, as well as most linguists today, took all to have existential import, so that ＂All As are B＂ entails that there are As, whereas modern logic drops this as- sumption. Replacing Aristotle＇s account of all with the modern one （and similarly for not all） results in the modem version of the square, and there has been much recent debate about which of these two squares is the ＇right＇ one. My main point in the present paper is that this question is not, or should not primarily be, about existential import, but rather about pattens of negation. I argue that the modern square, but not the traditional one, presents a general patten of negation one finds in natural language. To see this clearly, one needs to apply the square not just to the four Aristotelian quantifiers, but to other generalized quantifiers of that type. Any such quantifier spans a modern square, which exhibits that patten of negation but, very often, not the oppositions found in the traditional square. I provide some technical results and tools, and illustrate with several examples of squares based on quantifiers interpreting various English determiners. The final example introduces a second patten of negation, which occurs with certain complex quantifiers, and which also is representable in a square.