God vs AI scientifically

Why call it an assumption at all?

Partly because I was worried about follow-up comments that were kind of like "so you say you can prove it - well, why aren't you doing it then?".

And partly because I don't make a strict distinction between "things I assume" and "things I have convinced myself of, or proved to myself, based on things I assume". I do see there as sort of being a distinction along such lines, but I see it as blurry.

Something that is derivable from axioms is usually called a theorem.

If I am to be nitpicky, maybe you meant "derived" and not "derivable".

From my perspective there is a lot of in-between between these two:

• "we've proved this rigorously (with mathemathical proofs, or something like that) from axiomatic assumptions that pretty much all intelligent humans would agree with"
• "we just assume this without reason, because it feels self-evident to us"

Like, I think there is a scale of sorts between those two.

I'll give an extreme example:

Person A: "It would be technically possible to make a website that works the same way as Facebook, except that its GUI is red instead of blue."

Person B: "Oh really, so have you proved that then, by doing it yourself?"

Person A: "No"

Person B: "Do you have a mathemathical proof that it's possible"

Person A: "Not quite. But it's clear that if you can make Facebook like it is now, you could just change the colors by changing some lines in the code."

Person B: "That's your proof? That's just an assumption!"

Person A: "But it is clear. If you try to think of this in a more technical way, you will also realize this sooner or later."

Person B: "What's your principle here, that every program that isn't proven as impossible is possible?"

Person A: "No, but I see very clearly that this program would be possible."

Person B: "Oh, you see it very clearly? And yet, you can't make it, or prove mathemathically that it should be possible."

Person A: "Well, not quite. Most of what we call mathemathical proofs, are (from my point of view) a form of rigorous argumentation. I think I understand fairly well/rigorously why what I said is the case. Maybe I could argue for it in a way that is more rigorous/formal than I've done so far in our interaction, but that would take time (that I could spend on other things), and my guess is that even if I did, you wouldn't look carefully at my argumentation and try hard to understand what I mean."

The example I give here is extreme (in order to get across how the discussion feels to me, I make the thing they discuss into something much simpler). But from my perspective it is sort of similar to discussion in regards the The Orthogonality Thesis. Like,  The Orthogonality Thesis is imprecisely stated, but I "see" quite clearly that some version of it is true. Similar to how I "see" that it would be possible to make a website that technically works like Facebook but is red instead of blue (even though - as I mentioned - that's a much more extreme and straight-forward example).

Do I understand correctly that you do not agree with this?

Because any proposition is possible while not disproved according to Hitchens's razor.

Could you share reasons?

It seems that 2 + 2 = 4 is also an assumption for you.

Yes (albeit a very reasonable one).

Not believing (some version) of that claim would make typically make minds/AGIs less "capable", and I would expect more or less all AGIs to hold (some version of) that "belief" in practice.

I don't think it is possible to find consensus if we do not follow the same rules of logic.

Here are examples of what I would regard to be rules of logic: https://en.wikipedia.org/wiki/List_of_rules_of_inference (the ones listed here don't encapsulate all of the rules of inference that I'd endorse, but many of them). Despite our disagreements, I think we'd both agree with the rules that are listed there.

I regard Hitchens's razor not as a rule of logic, but more as an ambiguous slogan / heuristic / rule of thumb.

Best wishes from my side as well :)

:)