In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers.
There is a criticism of the isomorphism-invariance criterion for logical terms that is expressed in several variations in the literature on logical terms. The criticism in most cases was aimed against the criterion of invariance under isomorphism, 1 but it can be seen as applying to criteria of invariance under other transformations 2 just as well. The gist of the objection is that invariance criteria pertain only to the extension of logical terms, and neglect the meaning, or the way the extension is fixed. A term, so claim the critics, can be invariant under isomorphisms and yet involve a contingent or a posteriori component in its meaning, thus compromising the necessity or apriority of logical truth and logical consequence.The criticism has been expressed in different variations by various authors. The first to present the criticism, to the extent of my knowledge, is McCarthy.
Contextualist theories of truth appeal to context to solve the liar paradox: different stages of reasoning occur in different contexts, and so the contradiction is dispelled. The word 'true' is relativized by the contextualists to contexts of use. This paper shows that contextualist approaches to the liar are committed to a form of semantic relativism: that the truth value of some sentences depends on the context of assessment, as well as the context of use. In particular, it is shown how Simmons's and Glanzberg's contextualist approaches entail relativism. In both cases, the liar sentence gets different semantic evaluations as uttered in a fixed context of use but assessed from different contexts. Shift in context of use alone cannot provide the full explanation of the liar. These contextualist approaches, as originally presented, were thus mischaracterised and they should be re-evaluated according to their full implications.
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