I am surprised that in this long thread, the word 'craft' did not appear more often.
Here is my pebble thrown into the lake:
The poet is concerned with the craft of poetry.
The critic and, often, the educator is concerned with the science of poetry.
The audience is concerned with the art of poetry.
Let me clarify that the audience is there because they love the form, not because it is required by school or society. The groups are not exclusive.
As for a definition of poetry, I am content to live in the indefinable. It is a place where I am continuously delighted by the conversation. Let me add two quotes from
Edith Franklin Wyatt's essay from Poetry Magazine, October 1912:
"[Poetry is] the infinite music of words meant to speak the little and the great tongues of the earth."
"It does not occur to them [educated people] simply to listen to the nightingale. But poetry, I believe, never speaks her beauty—certainly never her scope and variety, except on the condition that in her presence one sits down quietly with folded hands, and truly listens to her singing voice."