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5. Theory of Logic / K. Features of Logics / 9. Expressibility

[limits of what can be said in a logical language]

2 ideas
Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P]
     Full Idea: Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system.
     From: Peter Smith (Intro to Gödel's Theorems [2007], 04.7)
A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro]
     Full Idea: A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings.
     From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)