"It will no longer be correct to say that something is (a color or similar property). One must say it "seems" a color, as well as to whom. Not "Snow is white", rather, "Snow seems white to me"."

I´d say this is not needed, when people say "Snow is white" we know that it really means "Snow seems white to me", so saying it as "Snow seems white to me" adds length without adding information.

My first fixes to english would be to unite spoken and written english with same letters always meaning same sounds, and getting rid of adding "the" to places where it does not add information (where sentence would mean same even without "the").

I didn't mean to imply nonlinear functions are bad. It's just how humans are.

Picking gambles 1A and 2B, on the other hand, cannot be described by any utility function.

Prospect Theory describes this and even has a post here on lesswrong. My understanding is that humans have both a non-linear utility function as well as a non-linear risk function. This seems like a useful safeguard against imperfect risk estimation.

[Insurance is] not a Dutch Book in the usual sense: it doesn't guarantee either side a profit.

If you setup your books correctly, then it is guaranteed. A dutch book doesn't need to work with only one participant, and in fact many dutch books only work with on populations rather than individuals, in the same way insurance only guarantees a profit when properly spread across groups.

The point of the Allais paradox is less about how humans violate the axiom of independence and more about how our utility functions are nonlinear, especially with respect to infinitesimal risk.

There is an existing Dutch Book for eliminating infinitesimal risk, and it's called insurance.

In reality, the fact that parallel lines do not intersect does follow from the definition of the word "parallel". Therefore, the error results in several of the paragraphs in the original post being meaningless or untrue.

The trouble is that in 2-D Euclidean space, there are many equivalent definitions of "parallel". It just so happens that straight lines that don't intersect also have the same slope,will intersect any transverse line at congruent angles, and are always the same distance apart (and vice versa). However, these properties need not be equivalent in non-Euclidean geometry.

The OP's issue seems to be that defining parallel lines as those which do not intersect is artificial. It's a workaround Euclid developed to smooth over his presentation. He could not use local properties of lines and angles to prove parallel lines didn't intersect. So, he defined them as lines that don't intersect, introduced the parallel postulate, and then used those to prove the other properties of parallel lines. Later mathematicians found this to be rather inelegant and tried to prove parallel lines didn't intersect using only properties of lines and angles.

Sure, it's an error if you use Euclid's definition of parallel, but I wouldn't call the discussion meaningless. It touches on a very important issue of how to define things and what properties we want to retain when we generalize a notion.

I've always enjoyed Lewis Carroll's talk of maps:

"That's another thing we've learned from your Nation," said Mein Herr, "map-making. But we've carried it much further than you. What do you consider the largest map that would be really useful?"

"About six inches to the mile."

"Only six inches!" exclaimed Mein Herr. "We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!"

"Have you used it much?" I enquired.

"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.

From Sylvie and Bruno Concluded by Lewis Carroll, first published in 1893.

In morals, as in logic, you can't explain something by appealing to something else unless the chain terminates in an axiom.

The question "why is it bad to rape and murder?" can be rephrased as, "how can we determine if a thing is bad, in the case of rape and murder?"

The answer "rape and murder are bad by definition" may be unsatisfying, but at least it's a workable way: everything on the list is bad, everything else is not. But the answer "because they make others sad" assumes you can determine making others sad is bad. You substitute one question for another, and unless we keep asking why, we won't have answered the original question.

This doesn't answer the question. Why is doing things Joe doesn't like, or making his friends sad, bad? Consequentialism isn't a moral system by itself; you need axioms or goals.

It occurs to me that we can express this problem in the following isomorphic way:

1. Omega makes an identical copy of you.

2. One copy exists for a week. You get to pick whether that week is torture or nirvana.

3. The other copy continues to exist as normal, or maybe is unconscious for a week first, and depending on what you picked for step 2, it may lose or receive lots of money.

I'm not sure how enlightening this is. But we can now tie this to the following questions, which we also don't have answers to: is an existence of torture better than no existence at all? And is an existence of nirvana good when it does not have any effect on the universe?

Sometimes people will argue that if you would pay a lot to save your own life from a fatal illness, that means you don't value lives equally but prefer your own, and therefore you should sign up for cryonics. But this argument seems a bit problematic to me, because it assumes my preference to save my life in the case of the fatal illness is ideal. In reality it might not be ideal at all. I am certainly not Zachary Baumkletterer, but it's likely I would be a better person if I were. If this is the case, the problem is not that I am unwilling to sign up for cryonics, but that I would pay to save myself from the fatal illness instead of giving the money away. And this argument does not mean that if I don't want to sign up for cryonics, instead I have to start donating all my money to charity. It just means I am doing the best I feel that I can, and if I signed up for cryonics I would be doing even worse (by doing less for others.)

Please Don't Fight the Hypothetical. I agree with you if you are only 99% sure, but the premise is that you know Omega is right with certainty. Obviously that is implausible, but so is the entire situation with an omniscient being asking people to commit suicide, or oracles that can predict if you will die.

But if you like you can have a lesser cost, like Omega asking you to pay $10,000. Or some amount of money significant enough to seriously consider just giving away.