Having a generic dictionary definition is nice and dandy. However, in the present context, the term 'homology' has a much more specific meaning: it pertains to the having (or not) of a common ancestor. Thus, it is a binary concept. (*)
But how do we establish phylogeny? - Based on simple similarity! (Structural/morphological in early days and largely on sequence identity today). It's clearly a circular logic: "Lets not use generic definition; instead, lets use a specialized definition; and lets not notice that the specialized definition wholly depends on a system that is built using the generic definition to begin with".
Plus, presumably all living things trace their ancestry to the primordial soup - so the presence or a lack of ancestry is just a matter of how deeply one is willing to look. In other words, it's nice and dandy to have theoretical binary concept but in practice it is just as fuzzy as anything else.
IMHO, the phylogenetic concept of homology in biology does not buy you much of anything useful. It seems to be just a leftover from pre-Darwinian days - redefined since but still lacking solid foundation.
Dima
