Instead of talking about ‘bachelor’ as an analytical concept, related to my ideas of how words work, I think what we need to concentrate instead is what is that in the world that ‘bachelor’ refers to.
And put in that way one answer is that ‘bachelor’ is related to phenomenon of bachelorhood, and that is what we are aware, which was baptized by the word, and which we think of when we use the word. But in analyzing the term ‘bachelor’, then we don’t need to put attention to some “concept” of bachelor which would be analytically reducible to some other terms, but instead to understand bachelorhood we need to look at the world in which this phenomenon (of which we are aware) appears.
And the phenomenon of there being bachelors is related to the wider social context. We might not be aware of the dependence of the phenomenon to this context, but it is there. For example bachelorhood depends on the social relations in which males of certain age are expected to be married. In the society in which the institution of marriage doesn’t exist, the phenomenon can’t exist. In same way, it is related to the social context in which we live, in which a male can be married just to one female. If it wasn’t so, again the phenomenon of bachelorhood wouldn’t be possible.
Thinking about ‘bachelor’ and what it refers to, and thinking about propositions which include bachelors is then thinking about phenomena in the world, and their inter-relatedness.
The questions then if the Pope is a bachelor, or if a Muslim with one wife is a bachelor, are then seen as problematic not because ‘bachelor’ doesn’t have precise meaning, but because its meaning is connected to a phenomenon that appears in certain conditions (context), although we might not be aware of this relation. In that way, the choice if we would name those other cases – bachelors, is not an issue which has an objective answer. It is that – a choice if we will use words that refer to concrete phenomenon that exists in concrete conditions, to different (but similar in something) cases which appear in different conditions.