The metatheoretic variation Cohen's forcing reveals is a pathology of first-order set-theoretic surrogates for second-order semantics, not evidence that second-order semantic content is itself indeterminate.
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Second-order semantics/Second-order logic(as the fuller, more complete system that first-order logic is being compared to)
A more powerful logic system that can quantify over properties and sets themselves, not just individual objects—it's more expressive but also more complicated.
forcing(set theory)
A technique in set theory for constructing new models in which certain statements hold or fail, used to prove independence results
metatheoretic(Used to characterize the role of logical semantics)
Providing a framework for theorizing about the relationship between symbols (used externally in language and internally in thought) and the world, rather than positing cognitive entities for computational manipulation
semantic content(Cappelen and Lepore's literalist/minimalist framework)
Propositions determined solely by conventions of meaning, precisification, disambiguation, and reference fixing — not by pragmatic inference.