Dan Everett has prompted a number of discussions on Facebook recently which touch on core issues in Peirce’s thought — but threads ravel on and fray so quickly in that medium one rarely gets a chance to fill out the warp. Not exactly at random, here’s a loose thread I think may be worth the candle.
Compositionality started out as a well‑defined concept, arising from the composition of mathematical functions, abstracted to the composition of arrows and functors in category theory, and generalized to the composition of binary, two-place, or dyadic relations. In terms of linguistic complexity it’s associated with properly context‑free languages. That all keeps compositionality on the dyadic side of the border in Peirce’s universe. More lately the term has been volatilized to encompass almost any sort of information fusion, which is all well and good so long as folks make it clear what they are talking about, for which use the term “information fusion” would probably be sufficiently vague.
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