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A State-of-Affairs-Semantic Solution to the Problem of Extensionality in Free Logic
Journal of Philosophical Logic Pub Date : 2020-02-20 , DOI: 10.1007/s10992-020-09550-z
Hans-Peter Leeb

If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ‘extensionality’, so that it would not be the truth-value that had to be preserved under the substitution of co-extensional expressions, but the state of affairs that the sentence described. The question is whether or not elementary sentences containing empty singular terms, such as ‘Vulcan rotates’, are extensional in the substitutivity sense. Five conditions are specified under which extensionality in the substitutivity sense of such sentences can be secured. It is demonstrated that such sentences are state-of-affairs-as-extension-related extensional . This implies (in accordance with the basic idea of state-of-affairs semantics) that such sentences are also truth-value-related extensional in Quine’s sense, but not truth-value-as-extension-related extensional.

中文翻译:

自由逻辑中外延性问题的一种状态语义解决方案

如果人们认真对待科学语言必须是外延的这一观点,并接受奎因的与真值相关的外延性的概念,并承认科学语言必须允许不涉及现有对象的单数术语,那么就有问题,因为这种假设的组合一定是不一致的。我将讨论这个问题的一个特定解决方案,即改变“外延性”一词的含义,以便在共同外延表达式的替换下必须保留的不是真值,而是句子所描述的事态。问题是包含空单数术语的基本句子(例如“Vulcan rotations”)在替代性意义上是否是外延的。指定了五个条件,在这些条件下可以确保此类句子的替代性意义上的外延性。证明这些句子是 state-of-affairs-as-extension-related 外延。这意味着(根据事态语义的基本思想)这样的句子在奎因的意义上也是与真值相关的外延,但不是真值作为与外延相关的外延。
更新日期:2020-02-20
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