Treeness

A tree may, for the imagination, present forcibly one of its qualities at a time; it may be a green dome of shade on a hot day, a ladder of retreat for a man from the attentions of a mad bull, a peg on which an apple hangs, a screen for an assassin, a choir for birds; and its own business of spreading out its million pores to the air and propagating its kind, which comes nearest to being its “treeness,” may be what occupies the artist least and bores him most.

Source: wiktionary

A word represents the entity but not THE entity itself. "tree" is not a tree, you can call it "ca^y" or whatever but the conceptual meaning of treeness stays the same.

Source: wiktionary

Let us say that the pigeons learned to recognize treeness, in the sense that they quickly enough learned to differentiate whatever exemplified treeness from whatever did not.

Source: wiktionary

If factors that contribute to a tree-like pattern of the variance–covariance matrix dominate the evolutionary picture over those that tend to destroy it, one can expect treeness to be reasonably high. Only if this is true, reconstruction of the evolutionary process by tree analysis and a tree representation for descriptive purposes can be useful.

Source: wiktionary