Expressive completeness in modal language
Expressive completeness in modal language
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情态语言的表达完整性
DOI：
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发表时间：
1976
影响因子：
1.5
通讯作者：
A. Hazen
中科院分区：
文献类型：
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作者：
A. Hazen
结论：模态运算符和量词的逻辑具有明显的相似性。类比是如此广泛，以至于当假设一类特殊的实体（可能世界）时，可以将自然和非任意的翻译过程从具有模态运算符的语言定义为纯量化的语言，在这种语言下，必然性和可能性运算符可以转换为全称和存在量词。鉴于此，我愿意将情态操作符归类为“伪装的”量词，我认为对情态语言的完全接受应该被认为是对可能世界的本体论承诺。作为描述同一主题的两种语言，情态语言和纯量词语言表现出有趣的差异。纯量化语言的算子变量赋予它们比模态语言更强大的功能，但至少由算子变量装置执行的一些功能也可以由模态语言中的现实算子以更原始和更少通用的方式执行。最后一点。奎因写了很多关于量词、同一性和存在概念的相互关系的文章。他认为，这些构成了一个紧密结合的概念系统，这个系统已经发展到一个完美的顶点，但可以想象，它还可能进一步改变他还暗示可能存在一个更简单、原始或有缺陷的系统版本，在这个版本中，量词没有以它们习惯的方式得到同一性概念的支持。他将由此产生的概念称为“前个体”的存在概念，或“没有身份的实体”的概念。"前个体存在的概念会是什么样的？奎因有时提出，一个人可能会在使用质量名词时体现出来，但身份概念既与事物有关，也与事物有关：“这是昨晚杯子里的同一杯咖啡吗？”我认为模态提供了一个更好的例子。鉴于情态语言的相对弱点，与被奎因视为规范的明确量化语言相比，在某种意义上，存在的概念体现在伪装的存在量词中，即可能性算子，是一个有缺陷的概念。正如我们所看到的，模态运算符和显式量词之间的区别之一是模态运算符不能像量词和操作符变量那样与单位谓词连接。当然，在某种意义上，与莱布尼茨或大卫·刘易斯的形而上学理论化相反，普通言语将可能世界视为没有同一性的实体。
ConclusionThe logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity.