This conversation reminds me of Bill Cosby's joke:

Philospher: "Why is there air?"
Jock:  "Everybody knows why there is air. There is air to blow up
basketballs and footballs."

I understand David's quest for a philosophical, notional explanation of
a sentence, but I would suggest that it ends up detracting from
teaching. Every speaker of English (and thus every student) intuitively
understands what a sentence is. They understand that "Bread" is not a
sentence, nor is "old bread," even though "old bread" contains a
"complete thought" -- "The bread is old." Attempts to get students to
come to terms with the philosophical implications of sentences will
simply take time away from the more important task of getting students
to understand how sentences work, and how complicated sentences are
complex embeddings of simpler sentences.
      Once again I suggest that ATEG is ignoring the important questions
-- which grammatical constructions are pedagogically important, how
should they be defined, and how (and when) should they be taught?
Ed V.