please, stop assuming that you can NEVER prove a negative

Question

It's always possible to answer a closed-ended question in the negative. An obvious example would be "are you the Queen of England?" You can answer it in the negative unless you, of course... you get the point.

But, more broadly, a few of my questions are getting dismissive comments and attitudes because it is presumed that I am attempting to ask open-ended questions which cannot be answered in the negative (because completely-open-ended questions indeed cannot be proved to have a negative answer).

But the more narrow the scope of a question is, the easier it is to answer it in the negative.

Here's a few examples of open-ended questions:

• were there any days on which the temperature in the US dropped below -100 degrees F
• are there voters who always vote for the Republicans even though they are left-handed lapsed Catholic transsexual lawyers?

Contrast them with these examples of closed-ended questions:

• were there any days on which the temperature in the US dropped below -100 degrees F in 1995
• are there voters who always vote for the Republicans even though they are left-handed lapsed Catholic transsexual lawyers licensed to practice in Rhode Island?

The last one is a bit tricky. It's actually a closed-ended question which may seem like an open-ended question at 1st sight. If there is a public registry of lawyers who can practice in Rhode Island (a very small state), then it would not be that hard to know if any of them meet all of the other criteria.

The fact is that there is a Galois connection between how many criteria a category must meet and how large that category happens to be. The more criteria must be met, the more restrictions it has. The more restrictions it has, the less members are in the category.

If the category is small enough, then it is not difficult to make statements of the kind "no member of this category meets condition X" because it's trivial to show that each single member of it does not meet that condition.

I've asked questions about highly-restricted categories trying to figure out if it is known whether certain political facts are true about their members. These can be easily answered in the negative if the answer is indeed a no. Each of these categories probably had less than 20 members. These were not open-ended questions. Please, stop treating them like they were.

Answer 1

I think you're using "open-ended" and "close-ended" differently than my understanding of them.

I understand an open-ended question to be one where the answer may be invalidated at any time.

Were there any days on which the temperature in the US dropped below -100 degrees F? This, as you said, is open-ended, because even if it's never happened in the past, it may happen in the future. It's still answerable based on past-to-now data if it's available, but any answer may be changed by a sudden extreme cold snap.

On the other hand, a close-ended question is one where no new data can possibly be added.

Were there any days on which the temperature in the US dropped below -100 degrees F in 1995?

This is a good close-ended question, because there will never be more days in 1995, so one can never get so cold.

Are there voters who always vote for the Republicans even though they are left-handed lapsed Catholic transsexual lawyers?

This is an open-ended question. There may be more such voters at any time, even if there's none currently. Handedness doesn't change, but a current left-handed, Catholic, transsexual, Republican lawyer could decide not to practice Catholicism any more and become lapsed. Or a known example could die, and no longer qualify.

Are there voters who always vote for the Republicans even though they are left-handed lapsed Catholic transsexual lawyers licensed to practice in Rhode Island?

This is just as open-ended. Adding another condition reduces the number of people who could qualify, but it's still possible for the answer to change at any time.

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These last two, however, are not only open-ended, they're also unanswerable, which is entirely unrelated. The information to answer it just doesn't exist, and at best, someone can try to estimate the answer from what information does.

Even a closed-ended (or finite-scope) question can be unanswerable. "Were there voters who ... licensed to practice in Rhode Island, in the year 2010?" is closed, but likely just as unanswerable.

In theory, these questions can be answered. They do have a definite answer that could be determined by someone with perfect knowledge. Even without that, it's possible to go to every lawyer in the {country or state}, check them for handedness, and then ask them about their voting, sexual, and religious habits. But absent an exhaustive analysis of every possible value, or someone publicly declaring they fit the criteria, it's not possible to answer.

A simpler example to illustrate the point: "Were there any people named Sam living in my house last year?"

There's a definite answer. I happen to know it, as does everyone else who lives here. But no one here has any way to discover it, so unless I choose to share that information, the question is unanswerable.

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That still leaves the question of whether an "unanswerable" question should be left up on the SE network in hopes that someone will someday come forward to answer it. That's something which each community has to decide for themselves. Software Recs.SE leaves such questions open indefinitely, because something may change and the asked-for software may get written, or someone who knows an obscure utility may find the question and provide an answer. Skeptics.SE permits them, with some caveats, and often doesn't give them a conclusive answer. Stack Overflow.SE, on the other hand, will close any question that either doesn't provide enough information to be able to answer, or where the answer requires knowledge of something unknowable (what a language designer was thinking, for instance).

Politics.SE has a policy of downvoting such unanswerable answers and sometimes closing them. We can change this policy, and you're welcome to make a case to do so, but this particular question doesn't do that.

Answer 2

I'm not sure if your specific questions fit this or not, but some people may find a "is there?" type of question objectionable on other grounds. For example, the answer would be extremely irrelevant to big picture (the answer is an anecdote, which as we all know is not pluralized to "data"); YET, by its very existence, biases the discourse towards the side that the anecdote illustrates.

In pother words: Why does it matter if there's a single lawyer in Rhode Island fitting your criteria 1,2 and 3? That wouldn't matter in any way shape or form to politics, which is by definition about groups of people, not single anecdotes.

The dislike may come from either people who dislike anecdotes as a class, OR those who dislike YOUR specific request's implications as far as their own bias preferences.