I suppose I think more in terms of systems, although not strictly so:
When I encounter a system (such as logic as used in analytical statements) I ask myself:
“What are the constraints on this system?”
Once I identify the constraints on the system, I ask myself,
“What are the purposes of these constraints?”
In the case of the bachelor: As a poet (if I allowed myself, I’d write poetry all of the time but I almost never do), I can find many uses for the word bachelor. It’s not limited to strictly unmarried men to me.
But a constraint upon the system of, say, our conversation here, you have placed a constraint upon the term bachelor to have a singular meaning – for the purposes of this discussion. Or perhaps for the purposes of proving a point, which is often one of the purposes of logic.
Proving a point does not guarantee an absoluteness of truth, only a satisfaction of the purposes given the constraints of the system we’re working within.
That’s how my brain works anyway