Full Idea
While words are semantic atoms, sentences remain the primary semantic units, in the sense of the smallest bits of language by means of which it is possible to say anything.
Gist of Idea
Sentences are the primary semantic units, because they can say something
Source
Michael Dummett (Thought and Reality [1997], 3)
Book Reference
Dummett,Michael: 'Thought and Reality (Gifford Lectures)' [OUP 2006], p.40
A Reaction
Syncategorematic terms (look it up!) may need sentences, but most nouns and verbs can communicate quite a lot on their own. Whether words or sentences come first may not be a true/false issue.