I think this answer contains something important--

Not so much an answer to the problem, but a clue to the reason WHY we intuitively, as humans, know to respond in a way which seems un-mathematical.

It seems like a Game Theory problem to me. Here, we're calling the opponents' bluff. If we make the decision that SEEMINGLY MAXIMIZES OUR UTILITY, according to game theory we're set up for a world of hurt in terms of indefinite situations where we can be taken advantage of. Game Theory already contains lots of situations where reasons exist to take action that seemingly does not maximize your own utility.

and they don't understand that there has never been a common ancestor of all and only the monkeys

This fact though -- that monkeys are paraphyletic -- argues in favour of (not against) the view that the common ancestor of monkeys and apes was itself monkey-like...

If you think about when the "ape traits" must have evolved, it would be after the new-world monkeys had already diverged away. The common ancestor of monkeys and apes wouldn't have had them, but must have had those traits common to both old and new-world monkeys. It itself has to be basically a monkey.

(I drew out a phylogenetic tree for this but couldn't get it to format, alas...)

There's a discussion post that mentions the fundraiser here, along with other news: http://lesswrong.com/r/discussion/lw/o0d/miri_ama_plus_updates/

To be honest, your comments confuse me. I knew about the link but I didn't see a connection between the link and experimental method and where the citations in the link came from. I am not sure what you mean by "anything like that" in your last comment and I am not very interested in it.

But I prefer to keep the original problem: If looking up a result in a math book could count as an experiment what is the (broader) definition of an experiment, then?

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?

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 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)

Hi, I am a mathematician and I guess most mathematicians would not agree with this. I am quite new here and I am looking forward to reactions of rationalists :-)

I, personally, distinguish "real world" and "mathematical world". In real world, I could be persuaded that 2+2=3 by experience. There is no way to persuade me that 2+2=3 in mathematical world unless somebody shows me a proof of it. But I already have a proof of 2+2=4, so it would lead into great reform of mathematics, similar to the reform after Russel paradox. Just empirical experience would definitely not suffice. The example of 2+2=4 looks weird because the statement holds in both "worlds" but there are other paradoxes which demonstrate the difference better.

For example, there is so called Banach-Tarski paradox, (see Wikipedia). It is proven (by set theory) that a solid ball can be divided into finitely many parts and then two another balls of the same size as the original one can be composed from the pieces. It is a physical nonsense, mass is not preserved. Yet, there is a proof... What can we do with that? Do we say that physics is right and mathematics is wrong?

Reasonable explanation: The physical interpretation of the mathematical theorem is just oversimplified. This part of mathematics does not fit to this part of physics. The false statement about physics is just different from the true mathematical statement.

But the Banach-Tarski paradox has no physical equivalent. We can not test it empirically, we can just believe the proof. This is probably what I would think if my experiences showed me that 2+2=3. It would appear that in our real mysterious world just 2+2=3 but in mathematical world, which was designed to be simple and reasonable, still 2+2=4.

Similarly, we can guess whether and how the physical universe is curved, yet the Euclidean space will be straight and infinite by definition, no matter what we will experience.

Sure, it can be argued that if mathematics does not reflect the real world then it is useless. Well, set theory is a base for almost all math fields. Even though the particular result called Banach-Tarski paradox have no practical use, more complicated objects in the mathematical universe are used in physics well. Restriction to just "empirically testable" objects in mathematics is a counter-intuitive useless obstacle. In such view, there is no sixth Ackermann number or the twin prime conjecture has no meaning. I can barely imagine such mathematics.

I understand that you may want a simple way to handle theists but abandoning abstract mathematics (or calling it "false") is definitely not a wise one.

The reason I went for the Forum was to find a pathway through my problems. Here I wasn't judged or disrespected. I liked the concept and it helped me with a few things in my current life. I was depressed as I failed my exams and have been aloof since. This course taught me how to be self-expressive. I haven't seen much of a difference yet but am looking forward to a few good changes in life. I haven't recommended this course to anyone yet, but you can go ahead if you need to talk about something in particular. I witnessed a few disappointed people in my batch but they were taken care of later.

Thanks for letting me know.

Here's the correct link: http://scienceblogs.com/gnxp/2006/07/06/stupid-feels-might-good-am-i-i/

Fortunately, I didn't need an archive, I just made a good guess about the correct title of the article and searched.

I have no idea where that php in the original link came from.

I still recommend the article-- Razib does irrational ranting for fun and offers a vivid description of how much fun it is.

Initial reaction: "That's news?".

That said, your link seems to be dead, with no archive. Do you have it saved?

Fixed, thanks.

Sure, that explains why the story was written with this flaw, but it doesn't remove the flaw. But I don't have a better suggestion.