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In his article Methodological Character of Theoretical Concepts (Section II), he lists the requirements proposed for any language L to be meaningful. However, I don't understand what he means exactly when he talks about extensionality:

  1. Requirement of extensionality. The language contains only truth-functional connectives, no terms for logical or causal modalities (necessity, possibility, etc.).

I don't understand what it means for an observational language to be extensional without terms for logical or causal modalities. What does this imply?

Vanessa
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  • It means that singular terms in such languages are interpreted as objects and predicates as sets of objects, with truth values assigned to sentences compositionally. They have the property that truth values do not change when any expression is substituted by another with the same extension, i.e. all contexts are extensional. In contrast, modalities create *intensional* contexts, where such substitutions are invalid. E.g. in "necessarily, Obama is Obama" one cannot replace one "Obama" with "first black president", see [SEP](https://plato.stanford.edu/entries/carnap/semantics.html#InteSema). – Conifold Sep 02 '21 at 05:25
  • Interesting that Carnap does not explicitly include quantifiers in his notion of an extensional language, the more so as first-order quantifiers can be regarded as S5-modalities. – sequitur Sep 02 '21 at 23:25

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