Perhaps, but I saw this as being similar to a logic problem. In my experience, the simplest answer to a problem is usually the best - in this case defining single. Otherwise, overthinking an issue can cause it to become overcomplicated, and a proper solution is never found. Similar to how the Gospel is a stumbling block to many due to it's simplicity.
Single can mean different things to different people, but the definition at it's core doesn't change. Some people may see being single as only not being currently married, not married or in a relationship, not married or divorced, etc. In another case, it could also mean not being in a group (the person is by themselves). In many cases, being single and available are also used interchangeably, even though they don't mean the same thing.
Singleness has it's subjective perceptions, but there is an objective definition for it which doesn't change: a person or object is by itself, based on the context by which the definition is being referred.
