[axlprose]

> It's certainly easy to falsify my claim.

Without a proper definition of what you're looking to be "explained", or a reproducible quantitative metric that you're using to to measure a successful "explanation" vs an unsuccessful one, no it isn't falsifiable. If you provide a detailed framework with clear quantitative conditions, then it might be falsifiable, but as of now, it is purely subjective and it is disingenuous to suggest that's an objective test.

For example, why would an explanation of functional programming (which could include any of a huge number of topics), have to explain to you why it exists? Since it is literally an extension of a specific branch of math, there need not be much more of a reason than 'for exploratory purposes', because often that's the only thing that drives many mathematical innovations.

Secondly, it's important to point out the implicit assumption in that argument, that an explanation of a topic is the only possible source for learning and understanding that topic, which is easily proven false by observing the way humans learn to walk. Do babies usually need a complete and thorough explanation of how to walk before they can master it? No, they go through trial and error and learn largely on their own via experience, and even if they could understand language that early, you'll still likely find it very cumbersome to try and explain to somebody how/why to walk in the kind of detail you seen to be asking of fp articles. Therefore, why can't a discipline/activity like programming or mathematics, also require experience learning to fully grasp? Is there a reason why the assumption was made that it can only be learned/understood via thorough explanation?

And while being able to explain something well is a decent rule of thumb to show competence in an area, it's not universal, as demonstrated by the learning to walk example. Similarly, you can't have a fixed minimum requirement for what qualifies as a good explanation to rate against, because understanding changes and evolves with time. For example, a "good" explanation of how the solar system works circa 300BC, would not be a very good explanation now.

[logicallee]

You take a tone as though you disagree with me, but actually do agree with my conclusion, just not my argument. We have reached the same conclusion. So this is just a technical reply to your criticism of the argument I use to get there - you get there via a different argument, and you claim mine is wrong. But we don't disagree about my conclusion.

For how you get there: in your third paragraph you give a shining example that it is not necessary to be able to explain something in order to do it: though everyone (barring a specific hindrance which we would identify and name as a disability) "knows" how to walk, it is clear that if you asked a thousand people "explain how you walk" you would not have a thousand good explanations. So, you have actually produced another example that it is possible to know something without being able to explain it!

Walking is a bit different from a purely mental knowledge/skill/etc, of course, and yet we can probably generalize it without taking too many allowances.

Returning to your criticism in your first paragraph, I feel like given the fact that you introduced the word "disingenuous" I would say it is disingenuous of you to suggest that people cannot tell whether they have received an explanation that is good. Of course we can.

Compare these two explanations:

"Why is two the only even number that is prime?"

- http://math.stackexchange.com/questions/1003491/why-is-two-t...

Explanation 1:

"Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two. ... Because every even number other than 2 is obviously divisible by 2 and so by definition cannot be prime."

versus

Explanation 2:

"Pick a prime p. Call a number n p-divisible if p∣n. Then p is the only p-divisible prime, trivially. In particular, 2 is the only 2-divisible, or even, prime."

Can't you easily tell the subjective difference between the two explanations? One is easy to understand. One is hard to understand.

To be honest, I can't parse and follow the second example. I have to resort to what I actually KNOW it's saying! Rather than its misplaced formalism.

So as you can see this has nothing to do with the subject matter!!

It simply shows that KNOWLEDGE is not reflected in CLEAR EXPLANATION. The second explainer clearly has deep knowledge. But this does not translate to an explanation.

In essence I am saying the same thing. That yes, we can tell a good explanation when we see one (sorry, this is a subjective claim but I'm sticking with it) but that this in no way, shape, or form is a requisite (or even indication) of actual understanding!