[mmalone]

This. There are three (and arguably only three) common programming paradigms: imperative programming, functional programming, and logic programming with lineages back to Turing machines, lambda calculus, and formal logic / proof search, respectively. Languages can be broken down along other dimensions, but usually the term "paradigm" is reserved for the sort of irreducible foundation of a language, and these seem to be the three useful ones.

Edit: to put a slightly finer point on it, this irreducible foundation mostly has to do with how the language "computes." Imperative languages compute via statements that modify program state. Functional languages compute via proof reduction to normal form. Logic languages compute via proof search.

[adwn]

There's no reason why you couldn't integrate functional programming and imperative programming into a single language – for example, an imperative layer (for I/O) around a functional, lambda-calculus based core (for computations). Now what is the "irreducible foundation of [this] language"?