Something that helps me understand reductionism is defining "hands" not as a set of quarks in some state, but as a range of possible sets of quarks in a range of possible states. Replace quarks by whatever fundamental thing reality is made of.

I don't think you've responded to my linked comment. But OK, looking up a result in a math book could count as an experiment, as could any method by which you might learn about dyslexia or whatever you suspect might be confusing you. If you don't believe anything like that could happen to you, either you made that judgement based on experience and science or you are very badly misguided.

(I think this may have came across a bit more confrontational than was optimal)

((Also, on that note, mirefek, if I came across as more confrontational than seemed appropriate, apologies.))

Please, be more specific. I am not sure exactly what are you responding to. Do you mean that a math proof (or knowledge of it) can be considered as experimental method in some sense?

Replace quarks by whatever fundamental thing reality is made of.

That's the kicker, isn't it. We'd like to be able to look at an arbitrary model of the world, and see if it has any observers in it who might experience "hands".

Ahem. I can think of many ways that some broadly defined "experimental method" could come into play there.

I think that I got the point, "I know that I know nothing" is a well known quote.

It's actually a somewhat different point he's trying to make (it's spaced out over several blogposts) - the idea is not to say "all knowledge is fallible." You should be very confident in math proofs that have been well vetted. It's useful to have a sense of how certain your knowledge is. (like, could you make 100 similar statements without being wrong once? 1,000? 10,000?)

(i.e. "the sun will rise tomorrow" is a probability, not a certainty, and "Ghosts could be real" is a probability, not a certainty, but they are very different probabilities.)

If you're interested, I do recommend the sequences in more detail - a lot of their points build on each other. (For example, there are multiple other posts that argue about what it's useful to think in probabilities, and how to apply that to other things).

He is saying that things that are not actual, yet "possible", are exactly the same, as far as the universe is concerned, as things that are not actual and not "possible". Specifically, they are all nonexistent. Hence possibility is not fundamental in any ontological sense.

But the laws of the universe demarcate possible things from impossible things: so can you dismiss the reality of possibilities without dismissing the reality of laws?

I see. It seemed to me that it was about the experimental method which did not fit to a mathematical statement. I understand the possibility of being mistaken. I was mistaken many times, I am not sure with some proofs and I know some persuasive fake proofs... Despite this, I am not very convinced that I should do such things with my probability estimates. After all, it is just an estimate. Moreover it is a bit self-referencing when the estimate uses a more complicated formula then the statement itself. If I say that I am 1-sure, that 1 is not 1/2, it is safe, isn't it? :-D Well, it does not matter :-) I think that I got the point, "I know that I know nothing" is a well known quote.

The point was less about the physical world applications of 2+2=4, and more about the fact that any belief you have is ultimately based on the evidence you've encountered. In the case of purely theoretical proofs, it's still based on your subjective experience of having read and understood the proofs.

Humans are sometimes literally insane (for example, not being able to tell that they're missing an arm). Also, even the best of us sometimes misunderstand or misremember things. So you need to leave probability mass for having misunderstood the proof in the first place.

(The followup to this post is this one: http://lesswrong.com/lw/mo/infinite_certainty/ which addresses this in some more detail)