Why would I want to change a person's belief if they already value philosophical solutions?  I think people should value philosophical solutions. I value them.

Maybe I'm misunderstanding your question.

It seemed like the poster above stated they do not value philosophical solutions.  The paper isn't really aimed at converting a person that doesn't value 'the why' into a person that does.  It is aimed at people which already do care about 'the why' and are looking to further reinforce/challenge their beliefs about what induction is capable of doing.

The principle of uniformity of nature is something we need to assume if we are going to declare we have evidence that the tenth swan to come out of the box would be white (in the situation where we have a box of ten swans and have observed 9 of them come out of the box and be white).  Hume successfully convinced me that this can't be done without assuming the principle of uniformity in nature.

What I am claiming though, is that although we have no evidence to support the assertion 'The 10th swan will be white.' we do have evidence to support the assertion 'All ten swans in the box will be white.' (an assertion made before we opened the box.).  This justification is not dependent upon assuming the principle of uniformity of nature.

In general, it is a clarification specifically about what induction is capable of producing justification for.

Future observation instances?  No.

But general statements?  I think this is plausible.

It's really just an inquiry into what counts as justification.

Necessary or sufficient evidence.

It sounds like they are simply suggesting I accept the principle of uniformity of nature as an axiom.

Although I agree that this is the crux of the issue, as it has been discussed for decades, it doesn't really address the points I aim to urge the reader to consider.

This is a good question.

I agree that you can't justify a prediction until it happens, but I'm urging us to consider what it actually means for a prediction to happen.  This can become nuanced when you consider predictions that are statements which require multiple observations to be justified.

If I predict that a box (that we all know contains 10 swans) contains 10 white swans (My prediction is 'There are ten white swans in this box.').  When does that prediction actually 'happen'?  When does it become 'justified'?

I think we all agree that after we've witnessed the 10th white swan, my assertion is justified. But am I justified at all to believe I am more likely to be correct after I've only witnessed 8 or 9 white swans? 

This is controversial.

This was a paper I wrote 8 - 10 years ago while taking a philosophy of science course primarily directed at Hume and Popper.  Sorry about the math, I'll try to fix it when I have a moment.

The general point is this:

I am trying to highlight a distinction between two cases.

Case A - We say 'All swans are white.' and mean something like, 'There are an infinite number of swans in the Universe and all of them are white.'.

Hume's primary point, as I interpreted him, is that since there are an infinite number of observations that would need to be made to justify this assertion, making a single observation of a white swan doesn't make any sort of dent in the list of observations we would need to make.  If you have an infinitely long 'to do list', then checking off items from your list, doesn't actually make any progress on completing your list.

Case B - We say 'All swans are white.' and mean something like, 'There are a finite number of swans (n) in the Universe and all of them are white.' (and (n) is going to be really big.).

If we mean this instead, then we can see that no matter how large (n) is, each observation makes comprehensive and calculable progress towards justifying that (n) swans are indeed white.  I'm saying that, no matter how long your finite 'to do list' is, checking off an item is calculable progress towards the assertion that (n) swans are white.

In general, I think Hume did a great job of demonstrating why we can't justify assertions like the one in case A.  I agree with him on that.  What I'm saying, is that we shouldn't make statements like the one in case A.  They are absurd (in the formal sense). 

What I'm saying is that, yes, observations of instances can't provide any justification for general claims about infinite sets, but they can provide justification of general claims about finite sets (as large as you would like to make them) and that is important to consider.

Well, that looks absolutely horrible.

I promise, it looked normal until I hit the publish button..

It will not take a long time if we use collective intelligence to do it together.  The technology is already here.  I've been trying to share it with others that understand the value of doing this before AI learns to do it on its own.  If you want to learn more about that, feel free to look me up on the 'X' platform @therealkrantz.

I understood the context provided by your 4 color problem example.

What I'm unsure about is how that relates to your question.

Maybe I don't understand the question you have.

I thought it was, "What should happen if both (1) everything it says makes sense and (2) you can't follow the full argument?".

My claim is "Following enough of an argument  to agree is precisely what it means for something to make sense.".

In the case of the four color problem, it sounds like for 20 years there were many folks that did not follow the full argument because it was too long for them to read.  During that time, the conclusion did not make sense to them.  Then, in 1995 a new shorter argument came along.  One that they could follow.  It included propositions that describe how the computer proofing system works. 

For your latter question, "What would it take for me to trust an AI's reasoning over my own beliefs when I'm unable to actually verify the AI's reasoning?".  My answer is "A leap of faith.".  I would highly recommend that people not take leaps of faith.  In general, I would not trust an AI's reasoning if I were not able to actually verify the AI's reasoning.  This is why mechanistic interpretability is critical in alignment.

I'm not sure what the hypothetical Objectivist 'should do', but I believe the options they have to choose from are:

(1) Choose to follow the full argument (in which case everything that it said made sense)

and they are no longer an Objectivist

or

(2) Choose to not follow the full argument (in which case some stuff didn't make sense)

and they remain an Objectivist

In some sense, this is the case already.  People are free to believe whatever they like.  They can choose to research their beliefs and challenge them more.  They might read things that convince them to change their position.  If they do, are they "compelled" are they "forced"?  I think they are in a way.  I think this is a good type of control.  Control by rational persuasion.

For the question of whether an external agent should impose its beliefs onto an agent choosing option (2), I think the answer is 'no'.  This is oppression.

I think the question you are getting at is, "Should a digital copy of yourself be able to make you do what you would be doing if you were smarter?". 

Most would say no, for obvious reasons.  Nobody wants their AI bossing them around.  This is mostly because we typically control other agents (boss them around) by force.  We use rules and consequences. 

What I'm suggesting, is that we will get so much better at controlling things through rational persuasion, that force will not be required for control.  All that the 'smarter version of yourself' does is tell you what you probably need to hear.  When you need to hear it.  Like your conscience.  

It's important to retain the right to choose to listen to it.

In general, I see the alignment problem as a category error.  There is no way to align artificial intelligence.  AI isn't really what we want to build.  We want to build an oracle that can tell us everything. That's a collective intelligence. A metaphorical brain that represents society by treating each member as a nerve on its spinal cord.

I'm not sure I can imagine a concrete example of an instance where both (1) everything that it said made sense and (2) I am not able to follow the full argument.

Maybe you could give me an example of a scenario?

I believe, if the alignment bandwidth is high enough, it should be the case that whatever an external agent does could be explained to 'the host' if that were what the host desired.