This couldn't really be stated any more clearly[1]; well put. I'll only add that this is true for any variety of abstraction, natural language included. Abstractions encode the biases of their creators[2]. The 'power' of an abstraction comes from the set of things that are easily and concisely expressible; its primitives. However, this is balanced by the truths that are no longer easily expressible, because the encoding doesn't allow for it. There's a certain intuition that semantics and abstraction are tied tightly in this sense; you don't can't really convey what something means unless it's concisely expressible in the abstraction you're using. Slang, idioms, calculus, etc.

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[1] and yet, I guess I'll just babble on adding more words anyway...

[2] be they mathematical concepts, programming paradigms, or cultural norms and quirks.

I learned this in designing the D programming language. The original syntax for lambdas seemed natural from a compiler point of view, but from a user point of view it was awkward and pretty much unusable. Changing the syntax was a complete transformation in its usage.