Two distinctive features of Frege’s approach to compositionality are reconstructed in terms of the theory of extension and intension: (i) its bias in favour of extensional operations; and (ii) its resort to indirect senses in the face of iterated opacity. While (i) has been preserved in current formal semantics, it proves to be stronger than a straightforward extensionality requirement in terms of Logical Space, the difference turning on a subtle distinction between extensions at particular points and extensions per se. (ii) has traditionally been dismissed as redundant, and is shown to lead to a mere ‘baroque’ reformulation of ordinary compositionality. Nevertheless, whatever Frege’s motive, the very idea of having opaque denotations keep track of the depth of their embedding gives rise to a fresh view at certain scope paradoxes that had previously been argued to lie outside the reach of a binary distinction between extension and intension.
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