|Extensionality, philosophy: (also extensionality principle, extensionality thesis) an attempt to make the language distinct by taking complete sets of denoted objects as the meaning of the referring words. See also extensions, intensions, extensional language, ambiguity, propositional attitudes.|
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Extensionality/Homogeneity: a context is extensional if the possible world equivalent relation does not have to be divided more finely than the designation equivalent relation: (Problem: the equivalence of "Snow is white" and "Grass is green") - therefore, the relationship between designated inferences and inferetial role of freestanding sentences is not homogeneous - it is not sufficient to know whether the sentences are true inferences - (because sentences are no inferences at all) - therefore we need a different extensionality at the top level: a sentential context with embedded phrases is extensional in the sense of being part homogeneous iff the substitution of statements with the same inferential role never changes the inferential role of the contained sentence.
This is not always the case: E.g. the role of the expression "S claims that p" does not depend on the role p has for the speaker, but on the role he has for S.
Expressive Vernunft Frankfurt 2000
Begründen und Begreifen Frankfurt 2001