INVARIANCE CRITERIA AS META-CONSTRAINTS

Gil Sagi
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Abstract

Abstract Invariance criteria are widely accepted as a means to demarcate the logical vocabulary of a language. In previous work, I proposed a framework of “semantic constraints” for model-theoretic consequence which does not rely on a strict distinction between logical and nonlogical terms, but rather on a range of constraints on models restricting the interpretations of terms in the language in different ways. In this paper I show how invariance criteria can be generalized so as to apply to semantic constraints on models. Some obviously unpalatable semantic constraints turn out to be invariant under isomorphisms. I shall connect the discussion to known counter-examples to invariance criteria for logical terms, and so the generalization will also shed light on the current existing debate on logicality. I analyse the failure of invariance to fulfil its role as a criterion for logicality, and argue that invariance conditions should best be thought of as merely methodological meta-constraints restricting the ways the model-theoretic apparatus should be used.
作为元约束的不变性标准
摘要不变性标准作为一种划分语言逻辑词汇的方法被广泛接受。在之前的工作中,我提出了一个模型理论结果的“语义约束”框架,它不依赖于逻辑和非逻辑术语之间的严格区分,而是依赖于以不同方式限制语言中术语解释的模型的一系列约束。在本文中,我展示了如何推广不变性准则,以便应用于模型上的语义约束。一些明显令人不快的语义约束在同构下是不变的。我将把讨论与已知的反例联系起来,以说明逻辑项的不变性标准,因此概括也将阐明当前存在的关于逻辑性的辩论。我分析了不变性在履行其作为逻辑性标准的角色方面的失败,并认为不变性条件最好被认为仅仅是限制模型理论设备使用方式的方法论元约束。
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