Hierarchy of Thought

Drew Crawford had an interesting article recently on different kinds of knowledge. He makes some interesting points, and while his article has a good deal of breadth, I feel like it lacks depth – specifically, that it wasn’t followed through to its end. Which is fine, because I think he was answering different questions than I have. So, I thought I should share my thoughts at least as a supplement to his article. A warning first though: Thinking about thinking is an inherently complicated thing. I’ll try to make this as clear as possible, but please post a comment if you don’t understand something.

Being a good mathematician, we need a few definitions. So, for the purposes of this discussion:

  • Self is used as a more personal form of an individual. Who “you” “are” is a different and equally tricky discussion, but for the purposes of this discussion, let self be the real you that you know better than anyone else.
  • Real is an abstract concept invoking ideas of some standard against which life can be judged. Certainly, this exists for the self, though some debate its applicability toward others. But once again, a different discussion.
  • Authority is defined by the self. If something is authoritative it is because the self has accepted it as such, even though the thought may not be real in some universal sense.
  • Truth is defined as something that is real and authoritative for the self.

And now the 4 stages of knowledge:

Doubt
The thought has been expressed, but is not fully conceived or contained. These things are not authoritative.
Example: Most people doubt the size of the universe.

Knowledge
Knowledge is a thought fully conceived and contained. Knowledge may be authoritative, but it’s not that common.
Example: Most people know that the sky is blue.

Understanding
Understanding is knowledge fully expressable by the self. This is when the self becomes able to explain the thought to another, or at least to fully appreciate the difficulty in doing so. Often, understanding is a result of experience. Understanding is often authoritative, though sometimes we conciously decieve ourselves.
Example: Some people know music and can play it while others understand music and can rearrange and improvise with it.
Example: Some people understand why the sky is blue and can explain it.

Belief
Belief is the unquestioning, automatic understanding of a thought. Beliefs are often perceived and manifested without the conscious awareness of the self. Beliefs are authoritative, and beliefs are truth. You can’t conciously decieve yourself about a belief.
Example: Prejudices.

Whenever people interact, beliefs are always involved; all that are applicable. Only after beliefs have responded can doubt enter in. Further consideration and questioning can produce knowledge, and knowledge applied can lead to understanding. If understanding is true (that is, if it is consistent with and agreeable to all other beliefs), it can become a belief and truth. Truth is a bi-state system (that is, a thought is either true or it is not). Therefore, I don’t think beliefs can ever be removed, because if the idea is no longer true, then there must be some contradicting idea that refuted the original belief; So beliefs can only be replaced. I don’t think anyone likes losing something they’ve believed, and it’s even more jarring to have to immediately accept a different belief, which is why beliefs are so hard to change. But, I don’t think people mind adding new beliefs that don’t conflict with anything. It explains some things about childhood development effecting who you are long term and perhaps even about teenage angst out of questioning their beliefs. But that’s a different, though interesting discussion if you can still remember what it was like to be a kid.

Anyway, all that to say ideas are complicated, but I think understanding them can help us understand who we are and how we got here.

About Bion

I'm a software developer at Modo Payments, a mobile payment provider. When I'm not hacking away the office, you I'm usually at home hacking on something else. Or practicing Aikido. Anyway, I just post things here that Google couldn't help me with, so maybe it'll help you in the future. Since you're reading this, I guess it worked :)
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4 Responses to Hierarchy of Thought

  1. Drew says:

    > “Understanding is knowledge fully expressable by the self.”

    Consider the integers. Do you understand them? (Hopefully, at this point in your math education.) Can you express them? Not by exhaustion. Perhaps you can express them by definition? Or by application? Neither of these seem like good candidates to talk about “understanding.”

    Consider P =? NP. By any common meaning of “understand”, we do not “understand” this problem. But it’s very well-defined, and we have a lot of applications. What is true about the integers but not true about P =? NP?

    I would prefer to appeal to computability–consider a function f(x). I “understand” f if for every x in the domain of f I can compute f(x). This gets around the problem of “understanding” infinite things, like the set of integers. For some definition of computability.

    • Bion says:

      I think Synk makes a valid point that we’re talking about different kinds of knowledge here. Computability might be a more “useful” term for whatever you happen to be working on, but for my purposes, I am wholly content to let definition suffice as understanding if that is the fullest expression I can have in my mind. This is part of why I included the qualifier “or at least to fully appreciate the difficulty in [explaining]”.

      Part of the problem with me responding to your p=np argument is that I’ve never understood the problem. I KNOW about the problem, and I’ve even tried to explain it people before, but I’ve never really understood it (I think this is largely because I’ve never understood the canonical example of the halting problem). But I know you understand it, because I’ve heard you explain it. Does that make sense?

  2. SynK says:

    I think that the article by Drew and the article you wrote are inherently about two different types of knowledge. It seems that this is more about knowledge that is directly applicable to life. Things like personal philosophy, theology, etc. fall into this category. Drew’s article seems to talk about technical knowledge. For the difference, consider a simple mathematical concept: the derivative. No matter how well I know the derivative, it will never influence how I think about the world in general. However, I can reach Drew’s “6th Level” of knowledge for derivatives. I think that we need a construct (call it a “knowledge tree” or “thought heap” or something programmer-y to fit in with the blog) to describe these differences in knowledge.

  3. While this issue can be very vexing for most people, my thought is that there has to be a middle or common ground that we all can find. I do value that you’ve added pertinent and sound commentary here though. Thank you!

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