Glad I can finally get to replying to your post! First, there is a lot to cover, so I'll post a few answers at a time.
Sorites paradox: When does a heap become a heap?
What we have to understand here is that the word 'heap' is a purely cultural word. It was not invented with any particular amount of grains of sand in mind, only a 'feeling'. As long as two people share that feeling when looking at a pile of sand, they'll both agree its a 'heap'. If one person doesn't feel its a heap, there will be disagreement. The disagreement cannot be boiled down to explicit grains of sand however, but the personal applied feeling of the observed mass.
The problem here is attributing more to the identity than it ever had to begin with. So there is no paradox. Its just a word that is based on a cultural agreement of emotion. Not all distinctive knowledge is precise. We just can't expect precise application out of them.
Hume's problem
If you're referring to the problem of induction, the reasoning which leads to the inductive hierarchy takes care of that.
Karl Poppers Falsification This theory of knowledge is consistent with the idea of falsification. For something to be applied, there must be a scenario that we can imagine if it is misapplied.
Falsification is often misunderstood. It does not mean that, "X is false" or "Its possible that X is false." Its "There is a reasonable imagined possibility where X is false, and we can test it." Lets use an example of a unicorn that is falsifiable, vs one that is not falsifiable.
Non-falsifiable Unicorn - This unicorn has magical powers that hide itself from all detection. They will never let themselves be detected by humans, and will always use their magic to hide themselves from any detectable means.
As you can see, we cannot imagine a scenario to test in which this could be false. No matter our detection results, it will always be an affirmation of the unicorn's existence. There is no imagined scenario that we can test in which the unicorns' existence can be false. As I note in the paper, this would be an inapplicable plausibility, which is just one step above an irrational induction in the hierarchy.
Falsifiable Unicorn - This unicorn has magical powers that make it invisible. However, it cannot hide anything else. You can still hear it, it leaves footprints, etc.
As you can see, we can imagine a testable scenario in which this is false. Can we find horse-like footprints that lead to discovering an invisible creature? If we can't, then the claim is false. This is an applicable plausibility, which is essentially a testable hypothesis.
Thomas Kuhn's paradigms To easily sum his point: Science has a paradigm that remains constant before going through a paradigm shift when current theories can’t explain some phenomenon, and someone proposes a new theory.
This is completely consistent with the knowledge theory proposed here. As we create distinctive knowledge and applicably test it, we are constantly looking to see if the application is contradicted by reality. If it is not, then we assume it to be applicable knowledge, and we can build upon it. For example, lets say we applicably know that the Sun rotates around the Earth. After all, its obvious if we look up at the sky. We build a system of astronomy based on this.
One day, a person discovers that the Earth actually rotates around the Sun! This mind blowing discovery upends everything that was built upon the idea that the Sun rotated around the Earth. We have to go back to this new applicable base, and build from here. It doesn't mean that our previous applicable knowledge wasn't knowledge. For at the time, there was no other reasonable conclusion that could be made. But a reasonable conclusion of today may not be a reasonable conclusion of tomorrow. What we applicably know is a tool that could be invalidated with new information, but it does not invalidate the process of creating and applying distinctive knowledge applicably to reality.
Ship of Theseus Theseus buys a ship, and overtime replaces every piece of the ship due to repairs. At this point, is it still Theseus' ship? Ah, a great example! I have written about this before, it was just had to be cut out to make the original post more manageable.
This thought experiment is not so much one of application, but of how we define the ship. If we define his ship purely by its physical makeup, how detailed should that be? Is it based on the atomic makeup? Because that changes as soon as he buys the ship. So it can't be that detailed, even if we do base it purely on the physical makeup. Is it based on the replacement of one plank? Most would say no. So what is it based on?
Cultural ownership. We agree that there are certain identifiers that indicate ownership. Maybe there's a serial number. A great modern day analogy to this are software licenses. When you purchase software, you are copying from a base software implementation. But it doesn't have to remain a copy. As you save or make alterations to it, its still your program because you have a stable identifier, the license key.
The point though, is because it is cultural, there is no hard and fast rule. We can extend the initial Theseus ship example further. Over the years, Theseus replaces all of his parts, but keeps the old parts in a pile. Someone else comes along and uses all of his original parts to build the ship again. Is the ship of the old parts Theseus ship too? Again, this depends on the culture. Are abandoned old parts owned? Is ownership of something based on who builds it? It is how society that defines it that determines the answer.
Plato's allegory of the cave People in a cave look at the shadows on the wall based on a fire they behind them that they cannot see, and believe the shadows are reality. Looking behind reveals a different truth.
I believe this is covered by my remarks on Kuhn's paradigms. If you need me to go further into it, I will.
Brain in a vat Everything you experience seems real, but in reality its all in your head. The reality is you are a brain in a vat and no nothing of reality outside of your thoughts.
As you can start to glean by now, this is also answered by the theory. Applicable knowledge is what cannot be contradicted. The theory that we are brains in a vat is an inapplicable plausibility. It is impossible to apply, therefore an induction very low on the hierarchy. As such, while it is fun to think about, it is no better than an inapplicably plausible unicorn.
I'm not too familiar with the biblical reference, so I'll pass for now. I think we have enough for now to tackle your other points.
And you also seem to 'misunderstand' me to such a degree, that I wonder if you are able to see me as someone who actually does something very similar to you, in a very rigorous manner, but through a process I might call Indiscrete experience/Inferring. — Caerulea-Lawrence
We are two people with different outlooks in the world. Hopefully through discussion we'll reach a common understanding. Please don't take my disagreement or my viewpoint as looking down or disrespecting yours. You are obviously an intelligent person trying to communicate a world view you see very clearly. Most people think it is simple to convey this experience to others until you have to write it down in a cohesive way. Its much more difficult then we expect!
One interesting thing about Jesus and Platon's cave is 'why would they try to change people's minds?' However, when we look at the interactions, at least between Jesus and the Pharisees, it doesn't look like he understood that they didn't 'get it'. If one person went out of the cave, and had their life changed, why 'wouldn't' the second one do it once told about it? But it seems neither of them were aware of the Typical Mind Fallacy
To me, this is more of a question of inferring, than deduction or induction. It is of course possible to induct in these instances, but you need some kind of 'weighing' process. — Caerulea-Lawrence
This is a question that I have addressed in the past, but never tackled in depth because most people never had the understanding of the base discussion to get this far. This is more theory then, "I have the answer," as I believe we would need to test this to confirm it.
The human brain is amazing not just for its intelligence, but its efficiency. A computer can do more processing for example, but its energy cost shoots through the roof. The fact we can think at the level we do without overheating ourselves or using more energy than we do, cannot be beat. Its easy to forget, but we thinking things that had to evolve in a world where danger and scarcity once existed at much greater levels.
This means we are not innately beings who are situated to think deeply about new experiences, or reorganize thought patterns. Doing so is inefficient. Thinking heavily about something takes concentration, energy, and time. Reprocessing your entire structure of thinking is even more difficult. So when we think about human intelligence, we shouldn't that its a font of reason, but a font of efficient processing.
So then, what does an efficient thinker focus on? Getting a result with as little thought as possible. Too little thought, and you fail to understand the situation and make a potentially lethal or tragic mistake. Too much thought, and you spend an inordinate amount of time and energy on a situation and are isolated from social groups, starve, or miss the window to act.
As such, humans are not wired for excellence, or the ideal. We are wires for, "Just enough". As a quick aside, doing more than "Just enough" is an expression of status. To do more than "Just enough" you must have excessive resources, be remarkably more efficient than others, or in a place of immense privilege. To spend time on inefficient matters and demonstrate mastery over them is an expression of one's status in society.
So then back to your point. One person has a paradigm, or set of distinctive and applicable knowledge that works for their life. They come across another person or group of people that a set of distinctive and applicable knowledge that works for their context. Why should one bother with the other paradigm?
My hypothesis is its about cost vs benefit. Maybe paradigm A is more accurate, but less efficient. Despite being more accurate, it doesn't provide much more benefit than paradigm B which is much more efficient. So society uses paradigm A in special circumstances where more accuracy is needed for a substantial benefit, vs usually using paradigm B for most other cases.
Religion is a great example of this. An atheist might have proof that there is no God, and go to a religion to persuade them to abandon their faith. The atheist may have a more accurate and cohesive world view. But what does the religious group gain? As it is now, they have group cohesion, and a community that cares about one another. They have a higher purpose that motivates them to volunteer and try to make the world a better place. The simple view motivates them and helps them when they're sad and down.
If they decided to take the atheistic standpoint, sure, it might be more accurate. But at what cost? A loss of community and purpose? A loss of motivation to care about others? People do not fight for the truth. They fight for the good that a certain viewpoint provides for their lives. If reality lets them have this viewpoint and benefits with few contradictions, why change?
Perhaps this is part of the 'intuition' you speak about. It is a mistake to think that our thought processes are for logic and truth. They are for efficient benefits to ourselves and society. And sometimes we can't voice that, but its there, under the surface.
I'll let this rest for now. What do you think about the topics? is starting to touch the surface of what you're thinking about, or is there another direction we need to go? I appreciate your thoughts.