1. Note that this question was not subjective. I was not asking about peope's personal idiosyncratic definitions of the terminology, nor about the difference between copyleft and permissive licencing, nor about which type of license was "better". (I did get a bunch of off topic responses answering those questions which I hadn't asked, but I edited the question to clarify, and there's been no trouble since.)
Actually you are asking us to verify or dispute your idiosyncratic definitions of the terminology, right here:
These definitions, although they derive from very different ideologies, are broadly compatible, and most Free Software is also Open Source Software and vice versa. I believe, however, that it is possible for this not to be the case: It is possible for software to be Open Source without being Free, or to be Free without being Open Source.
That's not a question, that's a confusing & confused opinion based on unreferenced claims.
2. Note that the question has an excellent, simple, accepted answer.
3. Note that, in general, good answers are voted up, and a bad answer is voted down.
Also note that there are four deleted answers, two of them up voted. You confused a lot of people with your question, 11 answers in total, all answering to a slightly different question. That, by definition, is not constructive.
4. Note that the question is nearly two years old, and has stood without trouble that long.
Sorry about that, we should have closed this one earlier.
So why was it suddenly and unilaterally closed as "Not Constructive"? What does this achieve? Who is helped by this closure?
It helps signal future readers that the question and its answers are problematic. You rushed in accepting an answer, and arrived at a possibly wrong conclusion:
And the answer, it seems, is that it's impossible to be Free without being Open, but possible to be Open without being Free. Thank you everyone who actually answered the question.
Examples of licences that are approved by the FSF but not by OSI:
In fact some of those where pointed to you in a later answer, at which point you dismissed OSI approved as a parameter, and moved on to your own definition of what an open source license is. That's unfair to the answerers, your question is build around the FSF and OSI definitions, and it's implied that one of the parameters of it is that the licences discussed should be approved by either the FSF or OSI, or both.
We are not here to discuss personal interpretations and ideologies, what is the actual practical problem you are trying to solve? Your question lacks well defined parameters, it's a very interesting discussion topic, but unfortunately discussions don't really work with the Q&A philosophy and format of the site.