Review of Symbolic Logic 11 (1):133-159 (2018)

Gil Sagi
University of Haifa
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.
Keywords logical constants  Löwenheim numbers  invariance criteria  model theory  meaning
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DOI 10.1017/S1755020317000247
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References found in this work BETA

The Concept of Logical Consequence.John Etchemendy - 1990 - Harvard University Press.
What Are Logical Notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
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Citations of this work BETA

The Simple Argument for Subclassical Logic.Jc Beall - 2018 - Philosophical Issues 28 (1):30-54.
Invariance and Logicality in Perspective.Gila Sher - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning. Cambridge, Britain: Cambridge University Press. pp. 13-34.
On Williamson's New Quinean Argument Against Nonclassical Logic.Jc Beall - 2019 - Australasian Journal of Logic 16 (7):202.
Invariance Criteria as Meta-Constraints.Gil Sagi - 2022 - Bulletin of Symbolic Logic 28 (1):104-132.

View all 7 citations / Add more citations

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