The vocabulary of the constructed language Lojban seems, to me, to be, overall, much more useful; this seems to result naturally from the language's simplicity and lack of irregularity and arbitrary restrictions, which make it difficult to naturally think of verbs in terms of multiple arguments. selbri, Lojban's equivalent of verbs, regularly make direct use of more than one, and even two, arguments. For example, {zdile} (note: the Lojban community uses the convention of using braces to quote Lojban text inside English text) is the translation of "fun". Its definition is "x1 (abstract) is amusing/entertaining to x2 in property/aspect x3; x3 is what amuses x2 about x1."
It's difficult to construe, in a way that's rigorous to at least a useful degree, any usefully meaningful interpretation of "fun" without any notion of a subject or experiencer in contexts in which it commonly occurs, whether the result is based on a fixed subject or not. (It is this reason, by the way, for which I hope that the fun sequence, which I haven't yet read, makes it really clear that our utility functions may not necessarily preserve our system of "fun"; it's a property of us, not of the universe, so we may find another way to experience "fun" more valuable; it' s entirely the result of our own minds. An essay which goes on in great detail about similar ideas is the one at http://abolitionist.com/, which, on a personal note, largely represents my cur rent views, with the exception that, while "happiness" is likely-to-me one of the most important factors in our utility function, it is not our only value (I don't remember whether this was laid out by David Pearce); regardless, eliminating suffering is extremely important to me. (Any conception in which our universe, or mathematics in general, is somehow fundamentally associated with an absolute moral, value, or goal structure, seems, to me, to be the result of confusion.) The essay had a dramatic emotional impact on me when I read it three years ago (I was 15 at the time, had never heard of Less Wrong, and had not yet conceived of the abstract notions of systemic cognitive processes that reliably increase the accuracy of beliefs and reality and of optimizing for utility; I still believe that the principles I remember from David Pearce's writings remain consistent with what I've learned from Less Wrong; I was, in fact pleasently surprised to find a link to them on the LW wiki article of the fun theory sequence as an external link.).)
Another example is that of the very concept discussed in this essay, that of "beauty". The closest single-world translation in Lojban (I'm referring to the dialect defined by the CLL and the updates formally accepted by the BPFK) is {melbi}, whose definition is "x1 (abstract) is amusing/entertaining to x2 in property/aspect x3; x3 is what amuses x2 about x1.". In order for this concept, by this definition (which happens to be meaningful and correspond very closely to our own, of "beauty"), to be meaningful, there needs to be a subjective e xperiencer, the second argument to the function {melbi}.
Lojban is far from being any supposed "perfect" language; it's the result of arbitrary principles and unpredictable complexity. Still, it's based on really useful principles; this is why I like it much more than I like any other language of which I'm aware. I am, however, only slightly hesitant to commit to learning it, which requires an immense investment of time, for the same reaso ns I'm hesitant to commit to learning and using a language that regularly appeals to practicality to the extent that Haskell does; there are many ways to approach the problem, some of which are dramatically worse, by some goal structures, than others, and none of which are based on a perfect system, one that is consistent and complete. As a language for humans, though, Lojban is reall y nice and well designed, often even in areas that aren't necessitated by its principles (its vocabulary, particularly its definitions, for example).
I suspect that, while putting serious effort into learning Lojban, for most people, enables them to think in a slightly more rigorous way, using the system of Lojban; learning, say, Agda will be useful to a much greater extent. Unfortunately, very few people would be capable of and motivated to do the latter, which is p art of why I think it'd be nice if Lojban were thought of as important to learn as English.
(By the way, I've also been happy to see rigorous distinction between quotation and referent briefly mentioned in several places around Less Wrong. In my experience, learning Lojban has helped members of the community learn this distinction if they hadn't already. In Lojban, there is no ambiguity, in neither writing nor speech, between a quote and a referent; you would sound quite si lly if you said {la bairyn cu se cmene mi}, rather than {zo bairyn cu se cmene mi}, as Byron is my name; the notion of Byron the person being my name is quite silly indeed, and the difference is quite obvious in Lojban, the arbitrarily designed human language. If a person hasn't internalized the distinction, I suspect Lojban would be likely to help them do so, whether they deliberatel y attempt to or not. I would also like to point out that there are often many ways to dereference a quotation; obvious examples include interpreting a word and converting a variable, such as {k o'a}, to the sumti, the latter of which depends on the environment.)
While it'd be trivial to arbitrarily define a Lojban selbri in a rather meaningless way, it seems that the designers were careful to construct only rigorously meaningful gismu. I never (thought much)[http://lesswrong.com/lw/nu/taboo_your_words/] about a rigorous meaning of "should" until I tried to translate it while speaking in Lojban; it turned out that this had been a problem faced by many speakers, many of whom just gave up, it seems.
Meditation: Some time after that, I finally understood how I could more formally understand how I interpreted "should", which was, quite simply,
... ... ...
Reply: "optimal for some goal structure", which, of course, depends on the goal structure in question; our own human values is an obvious implicit x2. (I haven't yet read the metaethics sequenc e, but I expect it contains essays describing topics similar to that of this discovery). Perhaps translating into Lojban is often a good strategy for Tabooing ideas. (Thanks, Eliezer, for the meditation idea!)
I have previously spoken of the ancient, pulp-era magazine covers that showed a bug-eyed monster carrying off a girl in a torn dress; and about how people think as if sexiness is an inherent property of a sexy entity, without dependence on the admirer.
"Of course the bug-eyed monster will prefer human females to its own kind," says the artist (who we'll call Fred); "it can see that human females have soft, pleasant skin instead of slimy scales. It may be an alien, but it's not stupid—why are you expecting it to make such a basic mistake about sexiness?"
What is Fred's error? It is treating a function of 2 arguments ("2-place function"):
As though it were a function of 1 argument ("1-place function"):
If Sexiness is treated as a function that accepts only one Entity as its argument, then of course Sexiness will appear to depend only on the Entity, with nothing else being relevant.
When you think about a two-place function as though it were a one-place function, you end up with a Variable Question Fallacy / Mind Projection Fallacy. Like trying to determine whether a building is intrinsically on the left or on the right side of the road, independent of anyone's travel direction.
An alternative and equally valid standpoint is that "sexiness" does refer to a one-place function—but each speaker uses a different one-place function to decide who to kidnap and ravish. Who says that just because Fred, the artist, and Bloogah, the bug-eyed monster, both use the word "sexy", they must mean the same thing by it?
If you take this viewpoint, there is no paradox in speaking of some woman intrinsically having 5 units of Fred::Sexiness. All onlookers can agree on this fact, once Fred::Sexiness has been specified in terms of curves, skin texture, clothing, status cues etc. This specification need make no mention of Fred, only the woman to be evaluated.
It so happens that Fred, himself, uses this algorithm to select flirtation targets. But that doesn't mean the algorithm itself has to mention Fred. So Fred's Sexiness function really is a function of one object—the woman—on this view. I called it Fred::Sexiness, but remember that this name refers to a function that is being described independently of Fred. Maybe it would be better to write:
Fred::Sexiness == Sexiness_20934
It is an empirical fact about Fred that he uses the function Sexiness_20934 to evaluate potential mates. Perhaps John uses exactly the same algorithm; it doesn't matter where it comes from once we have it.
And similarly, the same woman has only 0.01 units of Sexiness_72546, whereas a slime mold has 3 units of Sexiness_72546. It happens to be an empirical fact that Bloogah uses Sexiness_72546 to decide who to kidnap; that is, Bloogah::Sexiness names the fixed Bloogah-independent mathematical object that is the function Sexiness_72546.
Once we say that the woman has 0.01 units of Sexiness_72546 and 5 units of Sexiness_20934, all observers can agree on this without paradox.
And the two 2-place and 1-place views can be unified using the concept of "currying", named after the mathematician Haskell Curry. Currying is a technique allowed in certain programming language, where e.g. instead of writing
you can also write
So plus is a 2-place function, but currying plus—letting it eat only one of its two required arguments—turns it into a 1-place function that adds 2 to any input. (Similarly, you could start with a 7-place function, feed it 4 arguments, and the result would be a 3-place function, etc.)
A true purist would insist that all functions should be viewed, by definition, as taking exactly 1 argument. On this view, plus accepts 1 numeric input, and outputs a new function; and this new function has 1 numeric input and finally outputs a number. On this view, when we write plus(2, 3) we are really computing plus(2) to get a function that adds 2 to any input, and then applying the result to 3. A programmer would write this as:
This says that plus takes an int as an argument, and returns a function of type int—> int.
Translating the metaphor back into the human use of words, we could imagine that "sexiness" starts by eating an Admirer, and spits out the fixed mathematical object that describes how the Admirer currently evaluates pulchritude. It is an empirical fact about the Admirer that their intuitions of desirability are computed in a way that is isomorphic to this mathematical function.
Then the mathematical object spit out by currying Sexiness(Admirer) can be applied to the Woman. If the Admirer was originally Fred, Sexiness(Fred) will first return Sexiness_20934. We can then say it is an empirical fact about the Woman, independently of Fred, that Sexiness_20934(Woman) = 5.
In Hilary Putnam's "Twin Earth" thought experiment, there was a tremendous philosophical brouhaha over whether it makes sense to postulate a Twin Earth which is just like our own, except that instead of water being H20, water is a different transparent flowing substance, XYZ. And furthermore, set the time of the thought experiment a few centuries ago, so in neither our Earth nor the Twin Earth does anyone know how to test the alternative hypotheses of H20 vs. XYZ. Does the word "water" mean the same thing in that world, as in this one?
Some said, "Yes, because when an Earth person and a Twin Earth person utter the word 'water', they have the same sensory test in mind."
Some said, "No, because 'water' in our Earth means H20 and 'water' in the Twin Earth means XYZ."
If you think of "water" as a concept that begins by eating a world to find out the empirical true nature of that transparent flowing stuff, and returns a new fixed concept Water_42 or H20, then this world-eating concept is the same in our Earth and the Twin Earth; it just returns different answers in different places.
If you think of "water" as meaning H20 then the concept does nothing different when we transport it between worlds, and the Twin Earth contains no H20.
And of course there is no point in arguing over what the sound of the syllables "wa-ter" really means.
So should you pick one definition and use it consistently? But it's not that easy to save yourself from confusion. You have to train yourself to be deliberately aware of the distinction between the curried and uncurried forms of concepts.
When you take the uncurried water concept and apply it in a different world, it is the same concept but it refers to a different thing; that is, we are applying a constant world-eating function to a different world and obtaining a different return value. In the Twin Earth, XYZ is "water" and H20 is not; in our Earth, H20 is "water" and XYZ is not.
On the other hand, if you take "water" to refer to what the prior thinker would call "the result of applying 'water' to our Earth", then in the Twin Earth, XYZ is not water and H20 is.
The whole confusingness of the subsequent philosophical debate, rested on a tendency to instinctively curry concepts or instinctively uncurry them.
Similarly it takes an extra step for Fred to realize that other agents, like the Bug-Eyed-Monster agent, will choose kidnappees for ravishing based on SexinessBEM(Woman), not SexinessFred(Woman). To do this, Fred must consciously re-envision Sexiness as a function with two arguments. All Fred's brain does by instinct is evaluate Woman.sexiness—that is, SexinessFred(Woman); but it's simply labeled Woman.sexiness.
The fixed mathematical function Sexiness_20934 makes no mention of Fred or the BEM, only women, so Fred does not instinctively see why the BEM would evaluate "sexiness" any differently. And indeed the BEM would not evaluate Sexiness_20934 any differently, if for some odd reason it cared about the result of that particular function; but it is an empirical fact about the BEM that it uses a different function to decide who to kidnap.
If you're wondering as to the point of this analysis, we shall need it later in order to Taboo such confusing words as "objective", "subjective", and "arbitrary".