Unfortunately, I'm unable to find any blogs that treat this from theology or philosophy so I'm simply pulling together some interesting pieces.

From Quora:

question said:

How do you know what you don't know you don't know?

As expressed so eloquently by the preeminent epistemologist of our time, "there are known knowns, known unknowns and unknown unknowns". Over time, I've observed that it's those unknown unknowns that end up being the achilles heel for most people/organizations.

The problem is, even once you become aware of this, you know there are certain things which you don't know you don't know but you don't know what they are. How then, can you know what you don't know you don't know?

answer by Venkatesh Rao said:

Let's call 'em UU's (unknown-unknowns). Here's a breakdown:

1. Continuous UUs: things you find if you get to the boundary of your current knowledge. A literal example is spatial knowledge. As you wander, UUs pop-up from beyond the horizon.

2. Disjoint-set UUs: space is continuous, but most knowledge domains actually are not. If you hop along the positive integers, you'll never reach a boundary or discover negative integers. You need to ask a frame-bustin' question like "what happens if I subtract 5 from 3?" to get there. Knowledge is kinda like that. If you just creep along pushing the boundary of what you know, you can never get to certain things. A clearer example is learning-by-meeting-others. Suppose you primarily learn new things by meeting new people, and you ONLY meet people via people you already know. You could easily inhabit a social network that doesn't get to other networks, and therefore never learn from disjoint networks.

3. Creative-Destructive UUs: Often to get to a new UU, you have to decide to disbelieve what you think you know, even if it seems silly. Einstein deciding that the velocity of light was constant for all observers seemed like a silly and obvious falsehood to anyone with a basic intuition about relative velocity. That was a jump to a UU. Non-Euclidean geometries arrived at by assuming that the self-evident parallel postulate was wrong, is another example.

4. Doubt: this is my favorite. You can sense UUs before you actually notice them. Your reaction is called doubt. "Something is wrong here, I am missing something..."

5. True UUs: By definition, you won't know it till it hits you, and then you'll be utterly surprised. They don't even creep up on you via doubt. In some ways this is the only true kind of UU. Everything else is an outlier variety of KUs (known unknowns).

answer by Flemming Funch said:

Explore boundaries. Question assumptions. What's at the edge of what you think you know? What came before, what does it lead to, what if it were true, what if it weren't?

Look for what doesn't fit. Any kind of incongruence or anomaly is a sign that there's something to discover.

Everything happens at many levels at the same time. If you're only looking at a couple of them, you can be misled and mistaken. The more levels you're conversant with, the fewer clues you will miss. Everything leaves traces.

Gather contrasting or conflicting viewpoints. Any datum that's too neat and finalized is suspect. Look for anybody who has a different idea about it.

To know more, you need to become comfortable with the unknown. If you spend all your time moving around the things you know, you'll miss the opportunity to discover something new from the much larger pool of stuff you don't know.

answer Jeff Wright said:

A pragmatic answer is reflection on pattern recognition failure. 

You bump into something that "appears" where you didn't expect it.  You try to figure out what went wrong with your "knowing".

This is backed up by extrapolating from ideals about what could be. 

You speculate about how recently-discovered known unknowns could have others "of their kind".  (Then you go and look.)   See Venkatesh Rao's answer for examples. 

Some examples, please.  I like philosophy too but let's stick with hard sciences.

There's a zone of space around the outside of the solar system called the Oort cloud, thought to contain billions of comet-like objects and who knows what else.  It's dark out there, and our instruments can't easily detect things in that space. But, a priori, there's no good reason to assume it is empty of signifiant objects.  In 2013, a large planet-like object was discovered.  Sedna was the first in that category of inner Oort cloud objects.  At that time, we didn't know if it was unique, but there was no reason to think so.  And then, recently, something new has been "discovered", another planet-like object.  (The article Solar system has a new most-distant member should actually say "new most-distant known member").  So now there are two knowns.  But that's not all.  There's something fishy about their orbits.  Astronomers speculate that there's a massive gas giant planet out there, disturbing the orbits of the known knowns, but we haven't actually spotted it yet.  And are there more of that class of planets in that area?  Unknown unknowns, but they are within the realm of possibility.

End of story?  Of course not.  Our extrapolating-from-ideals (in this case, gravity) tells us that outside the Inner Oort Cloud there is anothe zone (aptly named the Outer Oort Cloud) in which objects would have highly chaotic orbits due to the gravitational influence of nearby stars.  There's no reason to think the area is empty, but we can say that the unknown objects there are harder to know, both due to distance and because they have chaotic behavior.  Which is to say, there are degrees of knowability for the unknown unknowns.  Interesting to know that.

From "Knowing what we don't know (on the web)" by Tanya Gupta on People, Places, Deliberation:

In our last posting we talked about six techniques to make our questions more precise so as to get the best answers from the Web. In this blog, we look at the other side of the equation: how can we be reasonably confident that the answers we get from an online resource are correct? How can we know that the web has given us the right answer when we do not have the subject matter expertise ourselves?

Path to “Confucian” wisdom

How to know what you don’t know

The adage “True wisdom is knowing what you don't know” has been attributed to Confucius. While addressing this philosophical statement is beyond the scope of this blog, it is appropriate to title a pragmatic article borrowing from ancient wisdom. Knowing what you do not  know is the essential problem of learning in the modern era. Legacy learning depends on teachers and textbooks who you can rely on to be correct. However, for contemporary learning - how can you tell the correct from the incorrect if you don’t have sufficient knowledge of a domain?
 
We describe a four step process one can use to eliminate the really bad answers and get a decent idea of which ones are very good.
 
The process may not be able guarantee the answers we got are absolutely correct, but the level of accuracy of the answers we will get by following the process will be useful in most cases.

The process is as follows:

1. Filter out the really bad answers
2. Understand each answer, really understand
3. Confirm quality of the source
4. And, finally choose the best answer

Step 1: Filter out the really bad answers
Finding the right answer means knowing the wrong answers. While there is no foolproof way to weed out the incorrect answers, there are some giveaways we can look for:

• Is the answer changing the question you are asking? (bad)
• Is the answer concise and concrete? (good)
• Does the answer have data supporting it? (good)
• Is the answer an opinion rather than statement of facts? (bad)

Step 2: Understand each answer, really understand
So now, let’s say you filtered the potential answers from 10 to 4. How do we eliminate the rest? Read the answer carefully, and if you run into critical words you do not understand, search the web for their meaning. If it is a definition that you are looking for, there are specific rules you can follow to find what you want, On Google for example, if you are looking for the definition of a word, use the following “define:term” where term is the term you are looking up. Take the following question:
“How can a you make a profit on the stock market?
 
Let’s say one answer found is:
 
“By going short an overpriced security, while concurrently going long the portfolio the Arbitrage Pricing Theory calculations were based on, the arbitrageur is in a position to make a theoretically risk-free profit”.  
 
A careful reading of the answer would mean understanding the terms: portfolio, the Arbitrage Pricing Theory, going short, and security.
 
Let’s say you are able to google the terms and are able to find out what each term means. How much time should you spend in your search before you conclude it is too much? A useful rule of thumb could be what we can term as the 5-2 rule. If there are more than 5 words you don’t understand, the resource is probably in a source you are not ready to use yet. If the words are less than 5, but for each word you have to do more than 2 searches, then the resource is probably not your best bet. If there are terms you are unable to locate or a logic is described that you do not understand, it could be that the answerer is making non transparent assumptions. In such cases, without making the assumptions explicit, it will be difficult for you to understand the answer and such answers should be discarded despite the fact that they may be correct.
 
Step 3: Confirm quality of the source
Let us say you have narrowed down the potential answers from 4 to just 2. Are there any metrics you can use to confirm the quality of the responder and the source ? Many question and answer tools allow users to upvote or like an answer. Keeping timeframes in mind (very popular answers from a while ago may be obsolete in the present), lots of upvotes are good, downvotes are bad. The source quality of the site should also be assessed. At this point, you may want to develop and use your own metrics, and ways to verify quality.
 
Take this question:



One of the answers to this question, offering a workaround as a solution has 164 votes - quite a high number, suggesting the quality of the answer is likely to be high.

 
 
 
Step 4: And, finally choose the best answer
Now, use any additional metrics you might want to apply and choose the right answer.
 
We should note that the guiding principles we to used develop the process are the same ones we used to come up with the techniques to form precise queries in our last blog. To ask the right question and to choose the right answer requires proficiency in the terms used in the domain where you have a question. Developing the vocabulary, understanding the assumptions that the responder may be making, getting a sense of the quantification needed, and familiarity with reputable sources, require a well defined process such as the one we have described above. After a while, the set of informal rules transform into a “gut-feeling” or an intuition for that domain.

And final from Mixor Limited:

How to know what you don’t know – infographic

Foresight
A thorny problem for those looking into the future is the issue Unknown Unknowns.  The abbreviation – ‘unk-unks’ – has even entered the Oxford English Dictionary.
We would all like to know what lies ahead of us, but the fact is that most predictions are rather inaccurate.
I’ll be completely open with you; there is no sure fire way to predict the future.  However I have come to realise that there is a way to peer between the folds of the fabric of time and look ahead.
The starting point came from my good friend Chris Bentley, who writes an excellent blog on strategy. www.thestrategyexchange.co.uk.  He pointed me in the direction of William Gibson who made the famous quote that ‘the future is already here, it’s just not evenly distributed’.
The key thing I’ve realised is that there is a lot of knowledge out there already. People don’t realise the importance of this hidden knowledge.  They can unwittingly hoard things that can be a revelation to others.
“So what have you done” I hear you say.  Well, one of my key skills is getting people to talk to one another in a structured way. I’m a facilitator.
So I bring together groups of informed people to share what they know and access their secret knowledge.  These people are CEO’s and International consultants connected by a curiosity about the future and a desire to do something with this knowledge.  It is one of the more valuable things I choose to do with my time.
I’ll share some of this knowledge with you in future posts.  In the meantime here is an infographic that gives some of the thinking behind our approach.
Feel free to share with others.