The statement “Mozart’s music is better than Beethoven’s” is usually considered a subjective opinion.

But this statement has the same form as “Mozart’s music is better than the music of the three-year old girl who lives upstairs from me and bangs on her toy piano sometimes.”

Is this latter statement also subjective? Calling it “subjective” or “a matter of opinion” feels wrong; someone who disagrees with me on this issue would be weird in a way someone who disagrees with me about chocolate vs. vanilla ice cream isn’t. But the girl-upstairs question seems similar enough to the Beethoven question that admitting the existence of an objective answer here seems to force belief in an objective answer about the relative merit of Beethoven.

And of course part of the answer here is the extent of human variation. For whatever reasons – different genetics, different life experiences, whatever – people have different tastes in music. The human music-appreciating-organ varies enough that some people can prefer Mozart to Beethoven and other people can express the opposite preference. But it doesn’t vary enough that any person’s music-appreciating-organ could prefer the girl upstairs.

Or to give another example, for whatever reason some people’s taste buds prefer vanilla and other people’s taste buds prefer chocolate, but basic regularities in human design – like the evolutionary need for sugar and the neural connections between sugar receptors and pleasure pathways – suggest that pretty much everyone will prefer either of those to horseradish ice cream.

But let’s take another example: was Mozart’s music more original than Beethoven’s? This question sounds a lot like the first question of whether Mozart’s music was better. And it shares the same sort of weird half-subjective half-objectiveness (let’s call it ambijectivity) – it seems completely open to disagreement whether Mozart or Beethoven was more original, but there are other questions – like “Was Mozart’s music more original than that of the average Elvis impersonator?” for which no sane disagreement is possible.

But it’s a lot harder to believe there’s an originality-detecting organ in the brain than that there’s a music-appreciation-organ or a taste-detecting-organ. Even for the very vague and sloppy definition of “organ” being used here.

Or another question: is Pluto a planet? The correct answer is “meh, stop arguing about definitions, whether something is a planet or not isn’t an objective fact about the universe”. But is my left foot a planet? Here the correct answer is “no”.

So I think of ambijective statements as being undefined over a whole set of possible meanings. For example, “is X a planet” is undefined over:

1. is X larger than most moons, but smaller than most stars?
2. is X spherical under its own gravity?
3. does X orbit a star directly?
4. does X have a regular orbit in terms of ellipticalness and orientation to the plane?
5. is X a natural body made of rock and gas and stuff like that?

Pluto satisfies 2, 3, and 5, but arguably not 1 and 4, therefore it’s “subjective” whether or not it’s a planet insofar as you can choose which of these definitions you want to use. My left foot doesn’t satisfy any of these criteria, so anyone claiming it’s a planet doesn’t have a leg to stand on.

Moving back to the first question: whose music is better, Mozart’s or Beethoven’s? We can cash out “better” in several ways:

1. I enjoy it more
2. You enjoy it more
3. More people prefer it
4. It’s more famous
5. It satisfies the sorts of rules music theorists talk about more precisely

Worse, each of these definitions is itself underspecified. For example, criteria 1 could vary based on which song we’re talking about – do I have to enjoy Beethoven’s best song more than Mozart’s best song, or the average Beethoven song more than the average Mozart song?

It could vary based on when you’re asking the question – maybe Mozart speaks to me when I’m sad, but Beethoven when I’m happy; is this averaged over all possible moods, and are we weighting it for the moods I’m most likely to have?

It could vary based on what you mean by “enjoy” – maybe Mozart creates more powerful emotions in me, but I am more impressed by Beethoven’s technical precision, plus maybe Mozart only produces sad emotions in me and Beethoven inspires me to love, and what if I am impelled to listen to Mozart songs more often but when I do listen to Beethoven I find I like him better but that mysteriously fails to translate into more Beethoven-listening time?

We could probably break even these sub-sub-questions down, and go through the same procedure for each of our original five criteria, until we have hundreds or thousands of extremely specific questions. Eventually we will bottom out in objective questions, the sort you could solve by scientific experiment if you wanted to – for example, if we decided on a very specific rating system for songs, we could ask me to rate a specific performance of one randomly chosen Beethoven song and one randomly chosen Mozart song each morning when I woke up.

(In practice, maybe there are infinitely many questions, but at some point the questions become so similar that the difference between them become noise that we no longer care about. For example, “do I prefer Beethoven at 10:00 AM” and “do I prefer Beethoven at 10:00 AM + 1 microsecond”.)

So suppose we have 1000 objective questions which all combine to form the question “Who is better, Beethoven or Mozart?” The “subjectivity” comes in not just in who we’re talking about (eg my music-appreciation-organ which is a little different from your music-appreciation-organ) but in how we weight these different questions in composing the meta-question “better”. This is a purely linguistic problem – if we have any disputes after this, we’re arguing about definitions.

This explains why it’s not “subjective” that Mozart is better than my upstairs neighbor. All those 1000 questions are very closely correlated, so it may be that my upstairs neighbor doesn’t win on any of them, and therefore there’s no way to compose the term “better” in which my neighbor could possibly be better than Mozart. Or maybe my neighbor only wins on two of the thousand questions, and no one has a definition of “better” which weights those questions higher than the remaining 998.

This post is mostly just so I have a word to refer to this kind of thinking quickly next time I get stuck in a subjective vs. objective dispute.

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34 Responses to Ambijectivity

  1. Pingback: is “it’s all subjective” a quagmire? | Useful Rung

  2. Hey! Long time fan of your writing, first time poster.

    I think this is great, and a really solid elaboration on the cluster concepts (empirical clusters in thingspace/conceptspace) that lesswrongers are so familiar with (bleggs and rubes, do dolphins belong in the fish category, cardinals are more birdy than ostriches, but they’re both birds).

    From this, I think we could elaborate even a little further and say that we have a spectrum from subjective to objective, where pure objectivity satisfies the criterion that no reasonable criteria (or extremely few) for the question could ever differ with all the others (Mozart and the toddler) and subjectivity is where they could all go either way. In your example, objective is when the thousand questions all get answered the same way, subjective gets you around 500 one way, 500 another. And then we have a whole spectrum in between.
    I think this is a really useful way of thinking about these things.

    • Scott Alexander says:

      Hi Chana. I like your blog too. And I just learned you’re the same Chana who knows Alicorn’s sister at UChicago and whom I occasionally hear interesting stories about. Hi!

  3. Ben Nader says:

    I’d say you’re just playing on a broken intuition to try and make Mozart obviously better than the girl next door. Well, actually to clarify, if you think better can reasonably include more original, influential, complex etc., then obviously I accept we could probably agree on some objective measures, and under those it’s highly unlikely the three year old is better. But I don’t really think any of those strike at goodness at all when it comes to music, they’re their own thing. I’d say goodness has to be evocation of enjoyment, the aesthetic feeling, emotion etc., and there’s no reason why the child couldn’t be more effect in that respect!

    In fact, two eleven year old girls recorded an album in the 70s that gives me a stronger aesthetic experience than many excellent compositions in the western art music tradition ( Some melodies, harmonies, rhythms, timbres are inexplicably (or arbitrarily explicably) more powerful than others to an individual, and it may just be that Mozart hits on these less reliably than your neighbour. I admit that I find it unlikely there are many individuals for which this is the case, but I also don’t think aesthetic quality has anything to do with majority rule.

    • David Gerard says:

      “Better” is relative in itself: better for what? This comes down to what music is for, and who it’s that thing for. Remembering that culture is only tangentially and locally about aesthetics; .

    • Richard Gadsden says:

      Bear in mind that a significant number of people detest western art music, and therefore will prefer the three-year-old to Mozart simply for that reason.

      I don’t hold with that position, but it certainly seems to be a real aesthetic position.

  4. Sam Rosen says:

    Why are people more inclined to say, “Mozart is better than Beethoven” as opposed to “I prefer Mozart” or “People tend to prefer Mozart”?

    Even if these latter claims are underspecified, they are far more clear claims about reality.

    There seems to be something deeply intuitive about saying, “Mozart, intrinsically, has the property of being better.”

    My hunch is that although human minds can make Locke’s “Primary quality versus secondary quality” distinction ( they can only do so slowly and consciously. Our minds don’t intuitively make the distinction.

    In Kahneman’s terminology: Whereas our system 2 can differentiate primary and secondary qualities, our system 1 cannot. Our system 1 treats all properties as primary.

    • Paul Torek says:

      My system 2 can’t differentiate primary and secondary qualities either. It keeps saying the distinction doesn’t have a leg to stand on.

      • Sam Rosen says:

        Do you think there is a difference between the wavelength of a beam of light and its color?

        Its wavelength is a fact about it, its color is a fact about how our brains work. Gamma rays have a wavelength, but because our eyes and brains don’t process them, they don’t have a color. There is not an objective fact about a gamma ray’s color. This is an objective fact about its wavelength.

        • Sam Rosen says:

          There is an objective fact about its wavelength.*

        • Yushatak says:

          A gamma ray does have a color, just not one we can see. That’s how I look at wavelength v. color and equate the two absolutely. If you specify “normal-human-visible color” I’d no longer equate them.

  5. Pingback: Raikoth: Laws, Language, and Society | Slate Star Codex

  6. komponisto says:

    My understanding of the liberal educated consensus is that you’re not allowed to actually say that Mozart is better than the three-year old girl, because that would make you a “snob”; but if you just accidentally happen to spend more of your time and effort on Mozart’s music than that of the three-year old, no one will go after you for that (so long as you don’t make too much of a fuss about how much you like Mozart, because then people will infer that you don’t like other things, unless you include explicit disclaimers to the contrary; and definitely don’t criticize anyone else for elevating the three-year-old’s music, even at the expense of Mozart).

    • David Gerard says:

      I’d really need a good enough citation to show that said “liberal educated consensus” is not as made of straw as your description sounds.

      (The error I see in practice in discourse at the far end of what was once rock’n’roll tends to the opposite problem: aggressively objective declarations about matters that are clearly heavily subjective. The writer knows this and is doing it deliberately, but it’s still annoying. Which is why we do it.)

  7. komponisto says:

    A note on musical terminology:

    A song is a vocal composition (usually for one or more solo singers — as opposed to chorus — with or without instrumental accompaniment). The term does not include purely instrumental works (unless they happen to have deliberately self-contradictory titles, such as Mendelsshohn’s Songs Without Words).

    Both Mozart and Beethoven wrote a number of very fine songs, but they also wrote much, much more.

    (In other words, you presumably meant to write “piece” or “work” or “composition” when you wrote “song” in the post.)

  8. TeaMug says:

    Interestingly, Luna satisfies all the planetary criteria you listed, but it’s still called ‘the moon’ instead of a planet, so the ambijectivity runs both ways.

    • g says:

      I don’t think Scott would count it as “orbit[ing] a star directly“.

      • TeaMug says:

        That’s the fun part – the Sun’s gravity on Luna has more than twice the effect of Earth’s gravity. (Are Wikipedia links kosher? Their double planet article has a good explanation)

        • g says:

          It also gives some examples of cases (actually instantiated in our solar system) where the same thing is true but it doesn’t seem like anyone would want to use the term “double planet” rather than “moon”.

          (I agree that there’s a case to be made for calling Earth + Luna a double planet rather than a planet and its moon.)

  9. Doug S. says:

    I’ve never had horseradish ice cream. It actually sounds kinda tasty. 😉

  10. Max says:

    “But it’s a lot harder to believe there’s an originality-detecting organ in the brain than that there’s a music-appreciation-organ or a taste-detecting-organ. ”

    Really? I would guess the opposite. Detecting originality seems to me like a matter of pattern recognition, since it comes down to discerning degrees of similarity to other works. On the other hand, I have no idea what’s behind music appreciation. If I didn’t know we had it, I don’t think I would ever have predicted it in advance.

  11. David Schaengold says:

    Great post. Your account of the Mozart vs. Beethoven vs. 3-yrd-old reminds me of Kant’s account of aesthetic judgments. Like you, Kant puts aesthetic judgments somewhere between purely subjective or personal judgments like “chocolate ice cream is better than vanilla” and purely objective or demonstrable judgments. He also linked this fact to “basic regularities in human design.” I won’t try to summarize his view exhaustively, but one important part of it was that when you say something like “Mozart’s music is more beautiful than this 3-yr-old kid’s music” you’re implying that everyone else should think so too, whereas when you say “I find broccoli distasteful” you shouldn’t expect everyone else to agree. I think something like Kant’s view and yours is what is meant by the term “intersubjectivity,” though I’ve never gotten a concise definition of it.

    I don’t think Kant would have put the question about whether Pluto was a planet into this category of judgment, however.

    • David Gerard says:

      “Intersubjectivity” is the word for this, yes. Anyone who likes music and thinks about liking music a lot has experienced the thing we’re talking about here. It’s because it’s a sort of language, an example of an intersubjective phenomenon that people who aren’t so deeply into critical discourse about music will readily understand.

    • David Gerard says:

      The key point is that if you think you need a neologism, you probably don’t.

  12. Berry says:

    For the record, horseradish ice cream is delicious. You might want to change the example there.

  13. arrowpker20 says:

    I think ambijectivity comes into play whenever you have to play the prisoner’s dilemma between what you like and what you expect other people to like. There’s no reason an alien wouldn’t prefer the girl upstairs to any genius, but if you openly expect humans to, then you sound really weird. I guess that makes it objective within a certain parameter of human mind-space, but subjective from an outside view?

  14. g says:

    The hyperlink to the “Diseased Thinking” post is b0rked: you’ve got a right-angle-bracket where you need a left one.

  15. g says:

    Pedantic note: the basis on which Pluto isn’t now officially considered a planet isn’t its size or the eccentricity of its orbit, but the fact that it hasn’t “cleared the neighbourhood around its orbit”.

    The eight Official Planets all have the property that there’s basically nothing sharing the same orbital region as them, other than their moons and other things they’re gravitationally “in control” of like Jupiter’s “Trojan asteroids”. That’s far from being true for Pluto.

    Admittedly, that’s largely because Pluto is small. (It’s about 1/6 the mass of our moon.)

    • Daniel Armak says:

      It’s funny how this and other definitions of planet-hood depend on facts, not about the alleged planet or its primary, but about other satellites of the primary.

      “Has X cleared its orbit of other bodies?” So if I move a bunch of asteroids into Earth orbit, or build space stations at the Lagrange points, Earth will stop being a planet?

      “Does X have a regular orbit in terms of ellipticalness and orientation to the plane?” So a star with two bodies orbiting in different planes has zero planets? And if I add enough new satellites to the Sun, all orbiting in a new common plane, the old ones like Earth will lose their planethood by majority vote?

      • g says:

        My impression is that the people coming up with definitions of planethood were looking for definitions that (1) fit reasonably well with their intuitions while (2) not explicitly including ad hoc things like “at least such-and-such a fraction of the mass of the earth”.

        Of course the difficulty is (and this is kinda the point of Scott’s posting) that those intuitions are complicated things derived from a bunch of examples and a lot of fuzzy thinking, rather than from any precise definition that one might hope to recapture. It’s not terribly surprising if when someone tries to reverse-engineer them into a precise definition, it turns out to be one that goes wrong in cases far removed from the examples that gave rise to the intuitions.

        Though, actually, I think the current standaofficial definition holds up OK in the face of the particular cases you describe. The eight now-canonical planets have cleared their orbits and this will remain true even if someone deliberately unclears them again. Also, the definition of “clearing” allows for smaller bodies orbiting or at the Lagrange points; otherwise the earth wouldn’t have “cleared its orbit” on account of the Moon, etc. And the official definition doesn’t say anything about the eccentricity or inclination of the orbit, so if it were possible — I don’t know whether it is — to have two sets of planets in different orbital planes, they wouldn’t be disqualified on that count.

      • endoself says:

        They do tend to carve reality at its joins though. I don’t remember the numbers, so most of this is guessing, but all planets comprise at least something like 99.9% of the mass in their orbit, while non-planets comprise less than something like 0.3%. The cases that you mention have to be constructed artificially, but the words are defined in order to classify what occurs naturally.

  16. Jonathan Graehl says:

    You accidentally a word.

    (“This post is mostly just so I a word to refer to”)

    And yes, you covered it. Just like you can imagine a utility function with individualized weightings, so can you imagine a “liking music” function that depends on the man and the time (“where’s the drop?”).