Oh, and the Liar Paradox makes much more sense once we overcome our obsession about recursion: If we take the equally valid stance of viewing it as an iteration, it is easy to see that the whole problem is that the proposition does not converge; that's all there is to it.

I think the trouble about "Have you stopped beating your wife?" is that it is not about a state but about a state transition. It asks "10?", and the answer "no" really leaves three possibilities open (including that the questionee has recently started beating his wife). The sentence structure implies a false choice between answers 10 and 11, because we are used to asking (and answering) yes/no questions about 1-bit issues while here we deal with a 2-bit issue. But you probably knew all that... =)

[having read the comments]

Kriti et al: I'd recommend this and this to anybody who hasn't already read it. Otherwise I have not much idea for introductory texts right now.

[Without having read the comments]

WTF? You say: [...] I was actually advised to post something "fun", but I'd rather not [...]

I think it was fun!

BTW could we increase the probability of people being honest by basing reward not on individual choices, but on the log-likelihood over a sample of similar choices? (For a given meaning of similar.)

tcpkac: The important caveat is : 'boundaries around where concentrations of unusually high probability density lie, to the best of our knowledge and belief' . All the imperfections in categorisation in existing languages come from that limitation.

This strikes me as a rather bold statement, but "to the best of our knowledge and belief" might be fuzzy enough to make it true. Some specific factors that distort our language (and consequently our thinking) might be: * Probability shifts in thingspace invalidating previously useful clusterings. Natural languages need time adapt, and dictionary writers tend to be conservative. * Cognitive biases that distort our perception of thingspace. Very on topic here, I suppose. ^_^ * Manipulation (intended and unintended). Humans treat articulations from other humans as evidence. That can go so far that authentic contrary evidence is explained away using confirmation bias.

Other problems in categorisation, [...] do not come from language problems in categorisation, [...] but from different types of cognitive compromise.

Well, lack of consistency in important matters seems to me to be a rather bad sign.

It would also lack words for the surprising but significant improbable phenomenon. Like genius, or albino. Then again, once you get around to saying you will have words for significant low hills of probability, the whole argument blows away.

I don't think so. Once the most significant hills have been named, we go on and name the next significant hills. We just choose longer names.

Okay, now let's code those factory objects! 1 bit for blue not red 1 bit for egg not cube 1 bit for furred not smooth 1 bit for flexible not hard 1 bit for opaque not translucent 1 bit for glows not dark 1 bit for vanadium not palladium

Nearly all objects we encounter code either 1111111 or 0000000. So we compress all objects into two categories and define: 1 bit for blegg (1111111) not rube (0000000). But, alas, the compression is not lossless, because there are objects which are neither perfect bleggs nor rubes: A 1111110 object will be innocently accused of containing vanadium, because it is guilty by association with the bleggs, subjected to unfair kin liability! Still, in an enviroment where our survival depends on how faithfully we can predict unobserved features of those objects we stand good chances:

Nature: "I have here an x1x1x1x object, what is at it's core?" We suspect a blegg and guess Vanadium - and with 98% probability we are right, and nature awards us a pizza and beer.

Now the evil supervillain, I-can-define-any-way-I-like-man (Icdawil-man, for short), comes by and says: "I will define my categories thus: 1 bit for regg (0101010) not blube (1010101)" While he will achieve the same compression ratio, he looses about 1/2 of the information in the process. He has failed to carve at the joint. So much the worse for Icdawil-man.

Nature: "I have here an x1x1x1x object, what is at it's core?" Icdawil-man suspects a regg, guesses Palladium, and with 98% probability starts coughing blood...

Next along comes the virtuous and humble I-refuse-to-compress-man:

Nature: "I have here an x1x1x1x object, what is at it's core?" Irtc-man refuses to speculate and is awarded a speck in his eye.

Next along comes the brainy I-have-all-probabilities-stored-here-because-I-can-man:

Nature: "I have here an x1x1x1x object, what is at it's core?" Ihapshbic-man also gets a pizza and beer, but will sooner be hungry again than we will. That's because of all the energy he needs for his humongous brain which comes in an extra handcart.

Any more contenders? =)

Just a small one, because I can't hold it: You can't judge the usefulness of a definition without specifying what you want it to be useful for. And now I'm off to bed... =)

Hi, am back from the city, and a bit sleepy. I'll try my best with my comment. =) Michael: I was not so much commenting on this specific post as on the whole series. Your example seems to me to boil down to a case of bait-and-switch. Eliezer: ,,When people start violently arguing over their communication signals while they (a) understand what each other are trying to say'' Here the problem is already at full swing, and it's the same as philosophers arguing about the "real" definition of X. As soon as you have managed to get your point across, any further insistance, or even "violent arguing" only shows lack of insight or sincerity. ,,and (b) are trying to do an inference that they could theoretically do as single players, something has gone wrong'' I see no problem about inferences as long as it's clear to everyone what the inference is about (and nobody tries to sneak a switch later).

Ben: I think you're right, we are on the same page! =) How about "Useful definitions will still be distorted by our mental mechanisms. Malignant and careless definitions are bad no matter what."?

Rolf: ,,What do you think of, say, philosophers' endless arguments of what the word "knowledge" *really* means?'' I think meh! ,,This seems to me one example where many philosophers don't seem to understand that the word doesn't have any intrinsic meaning apart from how people define it.'' Well, if they like to do so, let 'em. At least they're off the streets. =) What's worse is the kind of philosophers who flourish by sidestepping honest debate by complicating matters until nobody (including themselves) can possibly tell a left hand from a right foot anymore, and then go on to declare victory. Definitions belong to their toolset, too. But are we going to argue against knifes because the malignant can hurt others with them, and the ignorant or plain unlucky even themselves? We need them to carve the turkey, so if we want turkey slices we'll just have to operate carefully. I, for one, want to keep my knife! ,,Presumably Eliezer would ask, "for what purpose do we want to answer the question?" However, many philosophers would prefer to unconstructively argue what semantics are "correct". So my personal experience is that I don't think Eliezer's attacking a straw man here.'' He is if he is going to spill the baby with the bath. He'd have to write "Careless/malignant use of definitions is bad." not just "Definitions are bad." (which is my perception).