The pie example appears to treat “fair” as a 1-place word
‘Beautiful’ needs 2 places because our concept of beauty admits of perceptual variation. ‘Fairness’ does not grammatically need an ‘according to whom?’ argument place, because our concept of fairness is not observer-relative. You could introduce a function that takes in a person X who associates a definition with ‘fairness,’ takes in a situation Y, and asks whether X would call Y ‘fair.’ But this would be a function for ‘What does the spoken syllable FAIR denote in a linguistic community?‘, not a function for ‘What is fair?’ If we applied this demand generally, ‘beautiful’ would became 3-place (‘what objects X would some agent Y say some agent Z finds ‘beautiful’?‘), as would logical terms like ‘plus’ (‘how would some agent X perform the operation X calls “addition” on values Y and Z?’), and indeed all linguistic acts.
intuitions reflect their ancestral environment, and [...] those intuitions can be variable.
Yes, but a given intuition cannot vary limitlessly, because there are limits to what we would consider to fall under the same idea of ‘fairness.’ Different people may use the spoken syllables FAIR, PLUS, or BEAUTIFUL differently, but past a certain point we rightly intuit that the intension of the words, and not just their extension, has radically changed. Thus even if ‘fairness’ is disjunctive across several equally good concepts of fairness, there are semantic rules for what gets to be in the club. Plausibly, ‘fairness is whatever makes RobbBB happiest’ is not a semantic candidate for what English-speakers are logically pinpointing as ‘fairness.’
This article reads like you’re trying to move your stone tablet from your head into the world of logic, where it can be as universal as the concept of primes.
You hear ‘Oh no, he’s making morality just as objective as number theory!’ whereas I hear ‘Oh good, he’s making morality just as subjective as number theory.’ If we can logically pinpoint ‘fairness,’ then fairness can be rigorously and objectively discussed even if some species find the concept loathsome; just as if we can logically pinpoint ‘prime number,’ we can rigorously and objectively discuss the primes even with a species S who finds it unnatural to group 2 with the other primes, and a second species S* who finds it unnatural to exclude 1 from their version of the primes. Our choice of whether to consider 2 prime, like our choice of which semantic value to assign to ‘fair,’ is both arbitrary and unimpeachably objective.
Or do you think that number theory is literally writ into the fabric of reality somewhere, that Plato’s Heaven is actually out there and that we therefore have to be very careful about which logical constructs we allow into the club? This reluctance to let fairness into an elite Abstraction Club, even if some moral codes are just as definable in logical terms as is number theory, reminds me of Plato’s neurotic reluctance (in the Parmenides) to allow for the possibility that there might be Forms “of hair, mud, dirt, or anything else which is vile and paltry.” Constructible is constructible; there is not a privileged set of Real Constructs distinct from the Mere Fictions, and the truths about Sherlock Holmes, if defined carefully enough, get the same epistemic and metaphysical status as the truths about Graham’s Number.
If your sense of elegance is admittedly subjective, why are we supposing a Platonic form of elegance out in the world of logic?
You’re confusing epistemic subjectivity with ontological subjectivity. Terms that are defined via or refer to mind- or brain-states may nevertheless be defined with so much rigor that they admit no indeterminacy, i.e., an algorithm could take in the rules for certain sentences about subjectivity and output exactly which cases render those sentences true, and which render them false.
Isn’t this basically the error where one takes a cognitive algorithm that recognizes whether or not something is a horse and turns it into a Platonic form of horseness floating in the world of logic?
What makes you think that the ‘world of logic’ is Platonic in the first place? If logic is a matter of mental construction, not a matter of us looking into our metaphysical crystal balls and glimpsing an otherworldly domain of Magical Nonspatiotemporal Thingies, then we cease to be tempted by Forms of Horsehood for the same reason we cease to be tempted by Forms of Integerhood.
‘Beautiful’ needs 2 places because our concept of beauty admits of perceptual variation. ‘Fairness’ does not grammatically need an ‘according to whom?’ argument place, because our concept of fairness is not observer-relative.
What? It seems to me that fairness and beauty are equally subjective, and the intuition that says “but my sense of fairness is objectively correct!” is the same intuition that says “but my sense of beauty is objectively correct!”
If we can logically pinpoint ‘fairness,’ then fairness can be rigorously and objectively discussed even if some species find the concept loathsome
I agree that we can logically pinpoint any specific concept; to use the pie example, Yancy uses the concept of “splitting windfalls equally by weight” and Zaire uses the concept of “splitting windfalls equally by desire.” What I disagree with is the proposition that there is this well-defined and objective concept of “fair” that, in the given situation, points to “splitting windfalls equally by weight.”
One could put forward the axiom that “splitting windfalls equally by weight is fair”, just like one can put forward the axiom that “zero is not the successor of any number,” but we are no closer to that axiom having any decision-making weight; it is just a model, and for it to be used it needs to be a useful and appropriate model.
What I disagree with is the proposition that there is this well-defined and objective concept of “fair” that, in the given situation, points to “splitting windfalls equally by weight.”
“Fair”, quoted, is a word. You don’t think it’s plausible that in English “fair” could refer to splitting windfalls equally by weight? (Or rather to something a bit more complicated that comes out to splitting windfalls equally by weight in the situation of the three travellers and the pie.)
I agree that someone could mean “splitting windfalls equally by weight” when they say “fair.” I further submit that words can be ambiguous, and someone else could mean “splitting windfalls equally by desire” when they say “fair.” In such a case, where the word seems to adding more heat than light, I would scrap it and go with the more precise phrases.
What? It seems to me that fairness and beauty are equally subjective
I don’t know what you mean by ‘subjective.’ But perhaps there is a (completely non-denoting) concept of Objective Beauty in addition to the Subjective Beauty (‘in the eye of the beholder’) I’m discussing, and we’re talking past each other about the two. So let’s pick a simpler example.
‘Delicious’ is clearly two-place, and ordinary English-language speakers routinely consider it two-place; we sometimes elide the ‘delicious for whom?’ by assuming ‘for ordinary humans,’ but it would be controversial to claim that speaking of deliciousness automatically commits you to a context-independent property of Intrinsic Objective Tastiness.
Now, it sounded like you were claiming that fairness is subjective in much the same way as deliciousness; no claim about fairness is saturated unless it includes an argument place for the evaluater. But this seems to be false simply given how people conceive of ‘fair’ and ‘delicious’. People don’t think there’s an implicit ‘fairness-relative-to-a-judge-thereof’ when we speak of ‘fairness,’ or at least it don’t think it in the transparent way they think of ‘deliciousness’ as always being ‘deliciousness-relative-to-a-taster.’ (‘Beauty,’ perhaps, is an ambiguous case straddling these two categories.) So is there some different sense in which fairness is ‘subjective’? What is this other sense?
What I disagree with is the proposition that there is this well-defined and objective concept of “fair” that, in the given situation, points to “splitting windfalls equally by weight.”
Are you claiming that Eliezer lacks any well-defined concept he’s calling ‘fairness’? Or are you claiming that most English-speakers don’t have Eliezer’s well-defined fairness in mind when they themselves use the word ‘fair,’ thus making Eliezer guilty of equivocation?
People argue about how best to define a term all the time, but we don’t generally conclude from this that any reasoning one proceeds to carry out once one has stipulated a definition for the controversial term is for that reason alone ‘subjective.’ There have been a number of controversies in the history of mathematics — places where people’s intuitions simply could not be reconciled by any substantive argument or proof — and mathematicians responded by stipulating precisely what they meant by their terms, then continuing on from there. Are you suggesting that this same method stops being useful or respectable if we switch domains from reasoning about this thing we call ‘quantity’ to reasoning about this thing we call ‘fairness’?
we are no closer to that axiom having any decision-making weight
What would it mean for an axiom to have “decision-making weight”? And do you think Eliezer, or any other intellectually serious moral realist, is honestly trying to attain this “decision-making weight” property?
That the judgments of “fair” or “beautiful” don’t come from a universal source, but from a particular entity. I have copious evidence that what I consider “beautiful” is different from what some other people consider “beautiful;” I have copious evidence that what I consider “fair” is different from what some other people consider “fair.”
‘Delicious’ is clearly two-place, and ordinary English-language speakers routinely consider it two-place;
It is clear to me that delicious is two-place, but it seems to me that people have to learn that it is two-place, and evidence that it is two-place is often surprising and potentially disgusting. Someone who has not learned through proverbs and experience that “beauty is in the eye of the beholder” and “there’s no accounting for taste” would expect that everyone thinks the same things are beautiful and tasty.
But this seems to be false simply given how people conceive of ‘fair’ and ‘delicious’.
There are several asymmetries between them. Deliciousness generally affects one person, and knowing that it varies allows specialization and gains from trade (my apple for your banana!). Fairness generally requires at least two people to be involved, and acknowledging that your concept of fairness does not bind the other person puts you at a disadvantage. Compare Xannon’s compromise to Yancy’s hardlining.
People thinking that something is objective is not evidence that it is actually objective. Indeed, we have plenty of counterevidence in all the times that people argue over what is fair.
Are you claiming that Eliezer lacks any well-defined concept he’s calling ‘fairness’?
No? I’m arguing that Eliezer::Fair may be well-defined, but that he has put forward no reason that will convince Zaire that Zaire::Fair should become Eliezer::Fair, just like he has put forward no reason why Zaire::Favorite Color should become Eliezer::Favorite Color.
Are you suggesting that this same method stops being useful or respectable if we switch domains from reasoning about this thing we call ‘quantity’ to reasoning about this thing we call ‘fairness’?
There are lots of possible geometries out there, and mathematicians can productively discuss any set of non-contradictory axioms. But only a narrow subset of those geometries correspond well with the universe that we actually live in; physicists put serious effort into understanding those, and the rest are curiosities.
(I think that also answers your last two questions, but if it doesn’t I’ll try to elaborate.)
I have copious evidence that what I consider “beautiful” is different from what some other people consider “beautiful;” I have copious evidence that what I consider “fair” is different from what some other people consider “fair.”
But there is little upshot to people having differnt notions of beauty, since people can arrange their own environents to suit
their own aesthetics. However, resources have to be apportioned one way or another. So we need, and have discussion
about how to do things fairly. (Public architecture is a bit of an exception to what I said about beauty, but lo and behold, we have debates at that too).
the judgments of “fair” or “beautiful” don’t come from a universal source, but from a particular entity.
I don’t understand what this means. To my knowledge, the only things that exist are particulars.
I have copious evidence that what I consider “beautiful” is different from what some other people consider “beautiful;” I have copious evidence that what I consider “fair” is different from what some other people consider “fair.”
I have copious evidence that others disagree with me about ¬¬P being equivalent to P. And I have copious evidence that others disagree with me about the Earth’s being more than 6,000 years old. Does this imply that my belief in Double Negation Elimination and in the Earth’s antiquity is ‘subjective’? If not, then what extra premises are you suppressing?
It is clear to me that delicious is two-place, but it seems to me that people have to learn that it is two-place
Well, sure. But, barring innate knowledge, people have to learn everything at some point. 3-year-olds lack a theory of mind; and those with a new theory of mind may not yet understand that ‘beautiful’ and ‘delicious’ are observer-relative. But that on its own gives us no way to conclude that ‘fairness’ is observer-relative. After all, not everything that we start off thinking is ‘objective’ later turns out to be ‘subjective.’
And even if ‘fairness’ were observer-relative, there have to be constraints on what can qualify as ‘fairness.’ Fairness is not equivalent to ‘whatever anyone decides to use the word “fairness” to mean,’ as Eliezer rightly pointed out. Even relativists don’t tend to think that ‘purple toaster’ and ‘equitable distribution of resources’ are equally legitimate and plausible semantic candidates for the word ‘fairness.’
Deliciousness generally affects one person
That’s not true. Deliciousness, like fairness, affects everyone. For instance, my roommate is affected by which foods I find delicious; it changes where she ends up going to eat.
Perhaps you meant something else. You’ll have to be much more precise. The entire game when it comes to as tricky a dichotomy as ‘objective/subjective’ is just: Be precise. The dichotomy will reveal its secrets and deceptions only if we taboo our way into its heart.
and knowing that it varies allows specialization and gains from trade (my apple for your banana!).
What’s fair varies from person to person too, because different people, for instance, put different amounts of work into their activities. And knowing about what’s fair can certainly help in trade!
acknowledging that your concept of fairness does not bind the other person puts you at a disadvantage
Does not “bind” the other person? Fairness is not a physical object; it cannot bind people’s limbs. If you mean something else by ‘bind,’ please be more explicit.
Eliezer::Fair may be well-defined, but that he has put forward no reason that will convince Zaire that Zaire::Fair should become Eliezer::Fair
What would it mean for Zaire::Fair to become Eliezer::Fair? Are you saying that Eliezer’s fairness is ‘subjective’ because he can’t give a deductive argument from the empty set of assumptions proving that Zaire should redefine his word ‘fair’ to mean what Eliezer means by ‘fair’? Or are you saying that Eliezer’s fairness is ‘subjective’ because he can’t give a deductive argument from the empty set of assumptions proving that Zaire should pretend that Zaire’s semantic value for the word ‘fair’ is the same as Eliezer’s semantic value for the word ‘fair’? Or what? By any of these standards, there are no objective truths; all truths rely on fixing a semantic value for your linguistic atoms, and no argument can be given for any particular fixation.
There are lots of possible geometries out there, and mathematicians can productively discuss any set of non-contradictory axioms.
They can also productively discuss sets of contradictory axioms, especially if their logic be paraconsistent.
But only a narrow subset of those geometries correspond well with the universe that we actually live in; physicists put serious effort into understanding those, and the rest are curiosities.
So, since we don’t live in Euclidean space, Euclidean geometry is merely a ‘curiosity.’ Is it, then, subjective? If not, what ingredient, what elemental objectivium, distinguishes Euclidean geometry from Yudkowskian fairness?
Does this imply that my belief in Double Negation Elimination and in the Earth’s antiquity is ‘subjective’? If not, then what extra premises are you suppressing?
Your choice of logical system and your belief in an old Earth reside in your mind, and that you believe them only provides me rather weak evidence that they are beliefs I should hold. (I do hold both of those beliefs, but because of other evidence.) It is not clear to me that attaching the label of “subjective” or “objective” would materially improve my description.
That’s not true.
When I write the word “generally,” I mean it as a qualifier that acknowledges many objections could be raised that do not materially alter the point. Generally, at restaurants, you and your roommate are not required to eat the same meal, and the effects of, say, the unpleasant-to-her smell of your meal are smaller than the effects of the pleasant-to-her taste of her meal. Of course there are meals you could eat and restaurants you could choose where that is not case, but the asymmetry between the impact of your tastes on your roommate and the impact of your sense of fairness on your roommate remains in the general case.
Does not “bind” the other person? Fairness is not a physical object; it cannot bind people’s limbs. If you mean something else by ‘bind,’ please be more explicit.
Consider:
The priest walks by the beggar without looking. The beggar calls up to him, “Matthew 25!” Matthew is not the priest’s name, but still he stops, decides, and then gives the beggar his sack lunch.
The practical use of moral and ethical systems is as a guide to decision-making. Moral systems typically specialize in guiding decisions in a way that increases the positive benefit to others and decreases the negative cost to them. Moral and ethical systems are only relevant insofar as they are used to make decisions.
So, since we don’t live in Euclidean space, Euclidean geometry is merely a ‘curiosity.’
The space we live in corresponds well (obviously, not perfectly) with Euclidean space, and so it receives significant attention from physicists. The space we live in doesn’t correspond well with the Poincare disk hyperbolic geometry; the most likely place a non-mathematician has seen it is M.C.Escher.
Is it, then, subjective?
Models of Euclidean geometry exist in minds, and one person’s model of it may not agree with another’s, but there is currently an established definition (i.e. blueprint for a model), and not using that definition correctly makes conversation about that topic difficult with humans who use the established definition. Comparing it to beauty, models of beauty exist in minds, and those models can differ, but there is not an established blueprint to construct a model of beauty.
Your choice of logical system and your belief in an old Earth reside in your mind, and that you believe them only provides me rather weak evidence that they are beliefs I should hold.
I didn’t ask you whether my believing them gives you evidence to think they’re objectively true. I asked whether other people not believing them gives me evidence to think they’re merely subjective. If not, then you can’t use disagreement over ‘fairness,’ on its own, to demonstrate the subjectivity of fairness.
It is not clear to me that attaching the label of “subjective” or “objective” would materially improve my description.
So is it your view that “The Earth is over 6,000 years old” is neither subjective nor objective? Why not say, then, that claims about fairness are neither subjective nor objective?
When I write the word “generally,” I mean it as a qualifier that acknowledges many objections could be raised that do not materially alter the point.
That’s great for you, but the fact that you believe you could meet all the objections to your assertion (if you didn’t, why would you be asserting it?) doesn’t give me much reason to believe what you’re saying. Generally.
Generally, at restaurants, you and your roommate are not required to eat the same meal, and the effects of, say, the unpleasant-to-her smell of your meal are smaller than the effects of the pleasant-to-her taste of her meal.
Just like the effects of an unfair situation I’m in (generally!) impact me more than they impact my roommate. Again, it’s not clear what work you’re trying to do, either when you note similarities between deliciousness and fairness or when you note dissimilarities. You’ve provided us with no principled way to treat ‘fairness’ any different than we treat the old-Earth hypothesis or 0.999… = 1; and you’ve given us no principled way to sort the ‘subjective’ claims from the ‘objective’ ones, nor explained why it matters which of the categories we put moral concepts under.
The priest walks by the beggar without looking. The beggar calls up to him, “Matthew 25!” Matthew is not the priest’s name, but still he stops, decides, and then gives the beggar his sack lunch.
So your claim is that fairness is subjective because it has an impact on people’s decision-making? Don’t objective things have an impact on people’s decision-making too?
Models of Euclidean geometry exist in minds, and one person’s model of it may not agree with another’s, but there is currently an established definition (i.e. blueprint for a model), and not using that definition correctly makes conversation about that topic difficult with humans who use the established definition.
You didn’t answer my question. Is Euclidean geometry subjective? I’m just trying to get you to make your criticism of Eliezer explicit, but every time we come close to you giving a taboo’d version of what troubles you about treating fairness in the same way we treat geometry, you shift to a different topic without explaining its relevance to the ‘subjectivity!’ charge.
Comparing it to beauty, models of beauty exist in minds, and those models can differ, but there is not an established blueprint to construct a model of beauty.
What does it take for a blueprint to be “estabished”? Does a certain percentage of the human race have to agree on the same definition of the term? Or a certain percentage of academia? Or does an organization or individual just have to explicitly note their definition? Are you suggesting that when you criticize Eliezer for treating ‘subjective’ fairness as though it were ‘objective,’ all you’re really saying is that Eliezer is treating ambiguous fairness as though it were unambiguous, i.e., eliding the multiple semantic candidates? In that case ‘fairness,’ defined in Eliezer’s sense, would only be as subjective as, say, the term “causal model” is, since “cause” and “model” can likewise mean different things in different contexts.
I’m just trying to get you to make your criticism of Eliezer explicit, but every time we come close to you giving a taboo’d version of what troubles you about treating fairness in the same way we treat geometry, you shift to a different topic without explaining its relevance to the ‘subjectivity!’ charge.
That is because it’s not clear to me that “subjective” evokes the same concept for each of us, and so I’d rather taboo subjective and talk about object-level differences than classifications.
Are you suggesting that when you criticize Eliezer for treating ‘subjective’ fairness as though it were ‘objective,’ all you’re really saying is that Eliezer is treating ambiguous fairness as though it were unambiguous, i.e., eliding the multiple semantic candidates?
That looks like my objection.
I want to make clear that the linguistic claim is amplified by the relevance to decision-making. It is of little relevance to me whether others classify my actions as blegg or not; it is of great relevance to me whether others classify my actions as fair or not, and the same is true for enough people that putting forth an algorithm and stating “fairness points to this algorithm” is regarded as a power grab. Saying “geometry with the parallel postulate is Euclidean” is not regarded a power grab because the axioms and their consequences are useful or useless independent of the label ascribed to them. That communication is simply text; with labeling something ‘fair,’ there is the decision-making subtext “you should do this.”
Originally, it sounded like you were making one of these claims:
(a) There is no semantic candidate for the word ‘fairness.’ It’s just noise attempting to goad people into behaving a certain way.
(b) No semantic candidate for ‘fairness’ can be rendered logically precise.
(c) Even if we precisify a candidate meaning for ‘fairness,’ it won’t really be a Logical Idea, because the subject matter of morality is intrinsically less logicy than the subject matter of mathematics.
(d) Metaphysically speaking, there are quantitative universals or Forms in Plato’s Heaven, but there are no moral universals or Forms.
(e) No semantic candidate for ‘fairness’ can avoid including an argument place for a judge-of-fairness.
(f) No logically precise semantic candidate for ‘fairness’ can avoid including such an argument place.
All of these claims are implausible. But now it sounds like you’re instead just claiming: (g) There are multiple semantic candidates for ‘fairness,’ and I’m not totally clear on which one Eliezer is talking about. So I’d appreciate it if he were a bit clearer about what he means.
If (g) is all you meant to argue this whole time, then we’re in agreement. Specificity is of course a virtue.
Saying “geometry with the parallel postulate is Euclidean” is not regarded a power grab because the axioms and their consequences are useful or useless independent of the label ascribed to them.
Mathematical definitions are a power grab just as moral definitions are; the only difference is that people care more about the moral power-grabs than about the mathematical ones. Mathematical authorities assert their dominance, assert their right to participate in establishing General Mathematical Practice regarding definitions, inference rules, etc., every time they endorse one usage as opposed to another. It’s only because their authority goes relatively unchallenged that we don’t see foundational disputes over mathematical definitions as often as we see foundational disputes over moral definitions. Each constrains practice, after all.
(c) Even if we precisify a candidate meaning for ‘fairness,’ it won’t really be a Logical Idea, because the subject matter of morality is intrinsically less logicy than the subject matter of mathematics.
[...]All of these claims are implausible
This inspired me to write Morality Isn’t Logical, and I’d be interested to know what you think.
Saying “geometry with the parallel postulate is Euclidean” is not regarded a power grab because the axioms and their consequences are useful or useless independent of the label ascribed to them
Mathematical definitions are a power grab just as moral definitions are; the only difference is that people care more about the moral power-grabs than about the mathematical ones. Mathematical authorities assert their dominance, assert their right to participate in establishing General Mathematical Practice regarding definitions, inference rules, etc., every time they endorse one usage as opposed to another. It’s only because their authority goes relatively unchallenged that we don’t see foundational disputes over mathematical definitions as often as we see foundational disputes over moral definitions. Each constrains practice, after all.
Very few mathematical definitions are about General Mathematical Practice. Euclidean and Riemannian (or projective) geometry are in perfect peaceful coexistence, and in general, new forms of mathematics expand the territory rather than fight over an existing patch of territory.
Very few mathematical definitions are about General Mathematical Practice. Euclidean and Riemannian (or projective) geometry are in perfect peaceful coexistence,
I think you underestimate the generality of my claim. (Perhaps the phrase ‘power grab’ is poorly chosen.) Relatively egalitarian power grabs are still power grabs, inasmuch as they use the weight of consensus and tradition to marginalize non-egalitarian views. There is no proof that both geometries are equally ‘true’ or ‘correct’ or ‘legitimate’ or ‘valid;’ so we could equally well have decided that only Euclidean geometry is correct; or that only project geometry is; or that neither is. There is no proof that one of the latter options is superior; but nor is there a proof that one is inferior. It’s a pragmatic and/or arbitrary choice, and settling such decisions depends on an initially minority viewpoint coming to exert its consensus-establishing authority over majority practice. Egalitarianism is about General Mathematical Practice. (And sometimes it’s very clearly sociological, not logical, in character; for instance, the desire to treat conventional and intuitionistic systems as equally correct but semantically disjoint is a fine way to calm down human disagreement, but as a form of mathematical realism it is unmotivated, and in fact leads to paradox.)
in general, new forms of mathematics expand the territory rather than fight over an existing patch of territory.
That depends a great deal on how coarse-grainedly you instantiate “forms”. Mathematical results get overturned all the time; not just in the form of entire fields being rejected or revised from the ground up (like the infinitesimal calculus), and not just in the discovery of internal errors in proofs past, but in the rejection of definitions and axioms for a given discourse.
Mathematical results get overturned all the time; not just in the form of entire fields being rejected or revised from the ground up (like the infinitesimal calculus), and not just in the discovery of internal errors in proofs past, but in the rejection of definitions and axioms for a given discourse.
I’m just a 2 year math Ph.D. program drop-out from 35 years ago, but I got quite a different take on it. As I experienced it, most mathematics is like “Let X be a G-space where G-space is defined as having ”. and then you might spend years proving whatever those axioms imply, and defining umpteen specializations of a G-space, like a G2-space which has , and teasing out and proving the consequences of having those axioms. At no point do you say these axioms are true—that’s an older, non-mathematical use of the word “axiom” as something (supposedly) self-evidently true. You just say if these axioms are true for X, then this and this and this follows.
Mathematicians simply don’t say that the axioms of Euclidean geometry are true. It is all about, “if an object (which is a purely mental construct) has these properties, then it most have these other properties.
By the “infinitesimal calculus”, being overturned, I assume you mean dropping the use of infinitesimals in favor of delta-epsilon type definitions in calculus/real analysis, it’s not such a good illustration that revision from the ground up happens all the time, since really, that goes back to the late 19th century, and I really don’t think such things do happen all the time though another big redefining project happened in the early 20th century.
If (g) is all you meant to argue this whole time, then we’re in agreement. Specificity is of course a virtue.
I don’t think (g) is quite right. It is clear to me which candidate Eliezer is putting forward (in this case, at least): splitting windfalls equally by weight.
I think the closest of the ones you suggest is (e). Trying to put my view of my claim in similar terms to your other options, I think I would go with something like “We can create logically precise candidates for fairness, but this leaves undone the work of making those candidates relevant to decision-makers,” with the motivation that the reason to have moral systems / concepts like ‘fairness’ is because they are relevant to decision-makers.
That is, we can imagine numbers being ‘prime’ without a mathematician looking at them and judging them prime, but we should not imagine piles of pebbles occurring in prime numbers without some force that shifts pebbles based on their pile size.
“We can create logically precise candidates for fairness, but this leaves undone the work of making those candidates relevant to decision-makers,”
(a) Do you think Eliezer is trying to make his terms ‘relevant to decision-makers’ in the requisite sense?
(b) Why would adding an argument place for ‘the person judging the situation as fair’ help make fairness more relevant to decision-makers?
we can imagine numbers being ‘prime’ without a mathematician looking at them and judging them prime, but we should not imagine piles of pebbles occurring in prime numbers without some force that shifts pebbles based on their pile size.
I don’t believe in a fundamental physical force that calculates how many pebbles are in a pile, and adds or subtracts a pebble based specifically on that fact. But I do believe that pebbles can occur in piles of 3, and that 3 is a prime number. Similarly, I don’t believe in a magical Moral Force, but I do believe that people care about equitable distributions of resources, and that ‘fairness’ is a perfectly good word for picking out that property we care about. I still don’t see any reason to add an argument place; and if there were a need for a second argument place, I still don’t see why an analogous argument wouldn’t force us to add a third argument to ‘beautiful,’ so that some third party can judge whether another person is perceiving something as beautiful. (Indeed, if we took this requirement seriously, it would produce an infinite regress, making no language expressible.)
Why would adding an argument place for ‘the person judging the situation as fair’ help make fairness more relevant to decision-makers?
Do you see why a 2-place beauty would be more relevant than a 1-place beauty?
I don’t believe in a fundamental physical force that calculates how many pebbles are in a pile, and adds or subtracts a pebble based specifically on that fact. But I do believe that pebbles can occur in piles of 3, and that 3 is a prime number.
I was unclear; I didn’t mean “that some piles will have prime membership” but that “most or all piles of pebbles will have prime membership.”
I do believe that people care about equitable distributions of resources
Do you see why a 2-place beauty would be more relevant than a 1-place beauty?
Relevant to what?
I would have no objection to a one-place beautyₐ, where ‘beautyₐ’ is an exhaustively physically specifiable idea like ‘producing feelings of net aesthetic pleasure when encountered by most human beings’. I would also have no objection to a two-place beauty₂, where ‘beauty₂’ means ‘aesthetically appealing to some person X.’ Neither one of these is more logically legitimate than the other, and neither one is less logically legitimate than the other. The only reason we prefer beauty₂ over beautyₐ is that it’s (a) more user-friendly to calculate, or that it’s (b) a more plausible candidate for what ordinary English language users mean when they say the word ‘beauty.’
What I want to see is an argument for precisely what the analogous property ‘fairness₂’ would look like, and why this is a more useful or more semantically plausible candidate for our word ‘fairness’ than a one-place ‘fairnessₐ’ would be. Otherwise your argument will just as easily make ‘plus’ three-place (‘addition-according-to-someone’) or ‘bird’ two-place (‘being-a-bird-according-to-someone’). This is not only impractical, but dangerous, since it confuses us into thinking that what we want when we speak of ‘objectivity’ is not specificity, but merely making explicit reference to some subject. As though mathematics would become more ‘objective,’ and not less, if we were to relativize it to a specific mathematician or community of mathematicians.
“most or all piles of pebbles will have prime membership.”
So is your worry that having a one-place ‘fairness’ predicate will make people think that most situations are fair, or that there’s a physically real fundamental law of karma promoting fairness?
I think I’m going to refer you to this post again. Having a beautyₐ which implicitly rather than explicitly restricts itself to humans runs the risk of being applied where its not applicable. Precision in language aids precision in thought.
I think I’m also going to bow out of the conversation at this point; we have both typed a lot and it’s not clear that much communication has gone on, to the point that I don’t expect extending this thread is a good use of either of our times.
Yes. Clearly I was being unclear. Just as saying “Eating broccoli is good” I think assumes a tacit answer to “Good for whom?” and/or “Good for what?”, saying “Hamburgers are delicious” assumes a tacit “Delicious to whom?”, even if the answer is “To everyone!”. I have a hard time understanding what it means to visualize a possible world where everything is delicious and there are no organisms or sentients. I think of ‘beauty’ the same way, but perhaps not everyone does; and if some people think of ‘fairness’ as intrinsically—because of the concept itself, and not just because of our metaphysical commitments or dialectical goals—demanding an implicit argument place for a ‘judge of fairness,’ I’d like to hear more about why. Or is this just a metaphysical argument, not a conceptual one?
‘Beautiful’ needs 2 places because our concept of beauty admits of perceptual variation. ‘Fairness’ does not grammatically need an ‘according to whom?’ argument place, because our concept of fairness is not observer-relative. You could introduce a function that takes in a person X who associates a definition with ‘fairness,’ takes in a situation Y, and asks whether X would call Y ‘fair.’ But this would be a function for ‘What does the spoken syllable FAIR denote in a linguistic community?‘, not a function for ‘What is fair?’ If we applied this demand generally, ‘beautiful’ would became 3-place (‘what objects X would some agent Y say some agent Z finds ‘beautiful’?‘), as would logical terms like ‘plus’ (‘how would some agent X perform the operation X calls “addition” on values Y and Z?’), and indeed all linguistic acts.
Yes, but a given intuition cannot vary limitlessly, because there are limits to what we would consider to fall under the same idea of ‘fairness.’ Different people may use the spoken syllables FAIR, PLUS, or BEAUTIFUL differently, but past a certain point we rightly intuit that the intension of the words, and not just their extension, has radically changed. Thus even if ‘fairness’ is disjunctive across several equally good concepts of fairness, there are semantic rules for what gets to be in the club. Plausibly, ‘fairness is whatever makes RobbBB happiest’ is not a semantic candidate for what English-speakers are logically pinpointing as ‘fairness.’
You hear ‘Oh no, he’s making morality just as objective as number theory!’ whereas I hear ‘Oh good, he’s making morality just as subjective as number theory.’ If we can logically pinpoint ‘fairness,’ then fairness can be rigorously and objectively discussed even if some species find the concept loathsome; just as if we can logically pinpoint ‘prime number,’ we can rigorously and objectively discuss the primes even with a species S who finds it unnatural to group 2 with the other primes, and a second species S* who finds it unnatural to exclude 1 from their version of the primes. Our choice of whether to consider 2 prime, like our choice of which semantic value to assign to ‘fair,’ is both arbitrary and unimpeachably objective.
Or do you think that number theory is literally writ into the fabric of reality somewhere, that Plato’s Heaven is actually out there and that we therefore have to be very careful about which logical constructs we allow into the club? This reluctance to let fairness into an elite Abstraction Club, even if some moral codes are just as definable in logical terms as is number theory, reminds me of Plato’s neurotic reluctance (in the Parmenides) to allow for the possibility that there might be Forms “of hair, mud, dirt, or anything else which is vile and paltry.” Constructible is constructible; there is not a privileged set of Real Constructs distinct from the Mere Fictions, and the truths about Sherlock Holmes, if defined carefully enough, get the same epistemic and metaphysical status as the truths about Graham’s Number.
You’re confusing epistemic subjectivity with ontological subjectivity. Terms that are defined via or refer to mind- or brain-states may nevertheless be defined with so much rigor that they admit no indeterminacy, i.e., an algorithm could take in the rules for certain sentences about subjectivity and output exactly which cases render those sentences true, and which render them false.
What makes you think that the ‘world of logic’ is Platonic in the first place? If logic is a matter of mental construction, not a matter of us looking into our metaphysical crystal balls and glimpsing an otherworldly domain of Magical Nonspatiotemporal Thingies, then we cease to be tempted by Forms of Horsehood for the same reason we cease to be tempted by Forms of Integerhood.
What? It seems to me that fairness and beauty are equally subjective, and the intuition that says “but my sense of fairness is objectively correct!” is the same intuition that says “but my sense of beauty is objectively correct!”
I agree that we can logically pinpoint any specific concept; to use the pie example, Yancy uses the concept of “splitting windfalls equally by weight” and Zaire uses the concept of “splitting windfalls equally by desire.” What I disagree with is the proposition that there is this well-defined and objective concept of “fair” that, in the given situation, points to “splitting windfalls equally by weight.”
One could put forward the axiom that “splitting windfalls equally by weight is fair”, just like one can put forward the axiom that “zero is not the successor of any number,” but we are no closer to that axiom having any decision-making weight; it is just a model, and for it to be used it needs to be a useful and appropriate model.
“Fair”, quoted, is a word. You don’t think it’s plausible that in English “fair” could refer to splitting windfalls equally by weight? (Or rather to something a bit more complicated that comes out to splitting windfalls equally by weight in the situation of the three travellers and the pie.)
I agree that someone could mean “splitting windfalls equally by weight” when they say “fair.” I further submit that words can be ambiguous, and someone else could mean “splitting windfalls equally by desire” when they say “fair.” In such a case, where the word seems to adding more heat than light, I would scrap it and go with the more precise phrases.
I don’t know what you mean by ‘subjective.’ But perhaps there is a (completely non-denoting) concept of Objective Beauty in addition to the Subjective Beauty (‘in the eye of the beholder’) I’m discussing, and we’re talking past each other about the two. So let’s pick a simpler example.
‘Delicious’ is clearly two-place, and ordinary English-language speakers routinely consider it two-place; we sometimes elide the ‘delicious for whom?’ by assuming ‘for ordinary humans,’ but it would be controversial to claim that speaking of deliciousness automatically commits you to a context-independent property of Intrinsic Objective Tastiness.
Now, it sounded like you were claiming that fairness is subjective in much the same way as deliciousness; no claim about fairness is saturated unless it includes an argument place for the evaluater. But this seems to be false simply given how people conceive of ‘fair’ and ‘delicious’. People don’t think there’s an implicit ‘fairness-relative-to-a-judge-thereof’ when we speak of ‘fairness,’ or at least it don’t think it in the transparent way they think of ‘deliciousness’ as always being ‘deliciousness-relative-to-a-taster.’ (‘Beauty,’ perhaps, is an ambiguous case straddling these two categories.) So is there some different sense in which fairness is ‘subjective’? What is this other sense?
Are you claiming that Eliezer lacks any well-defined concept he’s calling ‘fairness’? Or are you claiming that most English-speakers don’t have Eliezer’s well-defined fairness in mind when they themselves use the word ‘fair,’ thus making Eliezer guilty of equivocation?
People argue about how best to define a term all the time, but we don’t generally conclude from this that any reasoning one proceeds to carry out once one has stipulated a definition for the controversial term is for that reason alone ‘subjective.’ There have been a number of controversies in the history of mathematics — places where people’s intuitions simply could not be reconciled by any substantive argument or proof — and mathematicians responded by stipulating precisely what they meant by their terms, then continuing on from there. Are you suggesting that this same method stops being useful or respectable if we switch domains from reasoning about this thing we call ‘quantity’ to reasoning about this thing we call ‘fairness’?
What would it mean for an axiom to have “decision-making weight”? And do you think Eliezer, or any other intellectually serious moral realist, is honestly trying to attain this “decision-making weight” property?
That the judgments of “fair” or “beautiful” don’t come from a universal source, but from a particular entity. I have copious evidence that what I consider “beautiful” is different from what some other people consider “beautiful;” I have copious evidence that what I consider “fair” is different from what some other people consider “fair.”
It is clear to me that delicious is two-place, but it seems to me that people have to learn that it is two-place, and evidence that it is two-place is often surprising and potentially disgusting. Someone who has not learned through proverbs and experience that “beauty is in the eye of the beholder” and “there’s no accounting for taste” would expect that everyone thinks the same things are beautiful and tasty.
There are several asymmetries between them. Deliciousness generally affects one person, and knowing that it varies allows specialization and gains from trade (my apple for your banana!). Fairness generally requires at least two people to be involved, and acknowledging that your concept of fairness does not bind the other person puts you at a disadvantage. Compare Xannon’s compromise to Yancy’s hardlining.
People thinking that something is objective is not evidence that it is actually objective. Indeed, we have plenty of counterevidence in all the times that people argue over what is fair.
No? I’m arguing that Eliezer::Fair may be well-defined, but that he has put forward no reason that will convince Zaire that Zaire::Fair should become Eliezer::Fair, just like he has put forward no reason why Zaire::Favorite Color should become Eliezer::Favorite Color.
There are lots of possible geometries out there, and mathematicians can productively discuss any set of non-contradictory axioms. But only a narrow subset of those geometries correspond well with the universe that we actually live in; physicists put serious effort into understanding those, and the rest are curiosities.
(I think that also answers your last two questions, but if it doesn’t I’ll try to elaborate.)
But there is little upshot to people having differnt notions of beauty, since people can arrange their own environents to suit their own aesthetics. However, resources have to be apportioned one way or another. So we need, and have discussion about how to do things fairly. (Public architecture is a bit of an exception to what I said about beauty, but lo and behold, we have debates at that too).
I don’t understand what this means. To my knowledge, the only things that exist are particulars.
I have copious evidence that others disagree with me about ¬¬P being equivalent to P. And I have copious evidence that others disagree with me about the Earth’s being more than 6,000 years old. Does this imply that my belief in Double Negation Elimination and in the Earth’s antiquity is ‘subjective’? If not, then what extra premises are you suppressing?
Well, sure. But, barring innate knowledge, people have to learn everything at some point. 3-year-olds lack a theory of mind; and those with a new theory of mind may not yet understand that ‘beautiful’ and ‘delicious’ are observer-relative. But that on its own gives us no way to conclude that ‘fairness’ is observer-relative. After all, not everything that we start off thinking is ‘objective’ later turns out to be ‘subjective.’
And even if ‘fairness’ were observer-relative, there have to be constraints on what can qualify as ‘fairness.’ Fairness is not equivalent to ‘whatever anyone decides to use the word “fairness” to mean,’ as Eliezer rightly pointed out. Even relativists don’t tend to think that ‘purple toaster’ and ‘equitable distribution of resources’ are equally legitimate and plausible semantic candidates for the word ‘fairness.’
That’s not true. Deliciousness, like fairness, affects everyone. For instance, my roommate is affected by which foods I find delicious; it changes where she ends up going to eat.
Perhaps you meant something else. You’ll have to be much more precise. The entire game when it comes to as tricky a dichotomy as ‘objective/subjective’ is just: Be precise. The dichotomy will reveal its secrets and deceptions only if we taboo our way into its heart.
What’s fair varies from person to person too, because different people, for instance, put different amounts of work into their activities. And knowing about what’s fair can certainly help in trade!
Does not “bind” the other person? Fairness is not a physical object; it cannot bind people’s limbs. If you mean something else by ‘bind,’ please be more explicit.
What would it mean for Zaire::Fair to become Eliezer::Fair? Are you saying that Eliezer’s fairness is ‘subjective’ because he can’t give a deductive argument from the empty set of assumptions proving that Zaire should redefine his word ‘fair’ to mean what Eliezer means by ‘fair’? Or are you saying that Eliezer’s fairness is ‘subjective’ because he can’t give a deductive argument from the empty set of assumptions proving that Zaire should pretend that Zaire’s semantic value for the word ‘fair’ is the same as Eliezer’s semantic value for the word ‘fair’? Or what? By any of these standards, there are no objective truths; all truths rely on fixing a semantic value for your linguistic atoms, and no argument can be given for any particular fixation.
They can also productively discuss sets of contradictory axioms, especially if their logic be paraconsistent.
So, since we don’t live in Euclidean space, Euclidean geometry is merely a ‘curiosity.’ Is it, then, subjective? If not, what ingredient, what elemental objectivium, distinguishes Euclidean geometry from Yudkowskian fairness?
Your choice of logical system and your belief in an old Earth reside in your mind, and that you believe them only provides me rather weak evidence that they are beliefs I should hold. (I do hold both of those beliefs, but because of other evidence.) It is not clear to me that attaching the label of “subjective” or “objective” would materially improve my description.
When I write the word “generally,” I mean it as a qualifier that acknowledges many objections could be raised that do not materially alter the point. Generally, at restaurants, you and your roommate are not required to eat the same meal, and the effects of, say, the unpleasant-to-her smell of your meal are smaller than the effects of the pleasant-to-her taste of her meal. Of course there are meals you could eat and restaurants you could choose where that is not case, but the asymmetry between the impact of your tastes on your roommate and the impact of your sense of fairness on your roommate remains in the general case.
Consider:
The priest walks by the beggar without looking. The beggar calls up to him, “Matthew 25!” Matthew is not the priest’s name, but still he stops, decides, and then gives the beggar his sack lunch.
The practical use of moral and ethical systems is as a guide to decision-making. Moral systems typically specialize in guiding decisions in a way that increases the positive benefit to others and decreases the negative cost to them. Moral and ethical systems are only relevant insofar as they are used to make decisions.
The space we live in corresponds well (obviously, not perfectly) with Euclidean space, and so it receives significant attention from physicists. The space we live in doesn’t correspond well with the Poincare disk hyperbolic geometry; the most likely place a non-mathematician has seen it is M.C. Escher.
Models of Euclidean geometry exist in minds, and one person’s model of it may not agree with another’s, but there is currently an established definition (i.e. blueprint for a model), and not using that definition correctly makes conversation about that topic difficult with humans who use the established definition. Comparing it to beauty, models of beauty exist in minds, and those models can differ, but there is not an established blueprint to construct a model of beauty.
I didn’t ask you whether my believing them gives you evidence to think they’re objectively true. I asked whether other people not believing them gives me evidence to think they’re merely subjective. If not, then you can’t use disagreement over ‘fairness,’ on its own, to demonstrate the subjectivity of fairness.
So is it your view that “The Earth is over 6,000 years old” is neither subjective nor objective? Why not say, then, that claims about fairness are neither subjective nor objective?
That’s great for you, but the fact that you believe you could meet all the objections to your assertion (if you didn’t, why would you be asserting it?) doesn’t give me much reason to believe what you’re saying. Generally.
Just like the effects of an unfair situation I’m in (generally!) impact me more than they impact my roommate. Again, it’s not clear what work you’re trying to do, either when you note similarities between deliciousness and fairness or when you note dissimilarities. You’ve provided us with no principled way to treat ‘fairness’ any different than we treat the old-Earth hypothesis or 0.999… = 1; and you’ve given us no principled way to sort the ‘subjective’ claims from the ‘objective’ ones, nor explained why it matters which of the categories we put moral concepts under.
So your claim is that fairness is subjective because it has an impact on people’s decision-making? Don’t objective things have an impact on people’s decision-making too?
You didn’t answer my question. Is Euclidean geometry subjective? I’m just trying to get you to make your criticism of Eliezer explicit, but every time we come close to you giving a taboo’d version of what troubles you about treating fairness in the same way we treat geometry, you shift to a different topic without explaining its relevance to the ‘subjectivity!’ charge.
What does it take for a blueprint to be “estabished”? Does a certain percentage of the human race have to agree on the same definition of the term? Or a certain percentage of academia? Or does an organization or individual just have to explicitly note their definition? Are you suggesting that when you criticize Eliezer for treating ‘subjective’ fairness as though it were ‘objective,’ all you’re really saying is that Eliezer is treating ambiguous fairness as though it were unambiguous, i.e., eliding the multiple semantic candidates? In that case ‘fairness,’ defined in Eliezer’s sense, would only be as subjective as, say, the term “causal model” is, since “cause” and “model” can likewise mean different things in different contexts.
That is because it’s not clear to me that “subjective” evokes the same concept for each of us, and so I’d rather taboo subjective and talk about object-level differences than classifications.
That looks like my objection.
I want to make clear that the linguistic claim is amplified by the relevance to decision-making. It is of little relevance to me whether others classify my actions as blegg or not; it is of great relevance to me whether others classify my actions as fair or not, and the same is true for enough people that putting forth an algorithm and stating “fairness points to this algorithm” is regarded as a power grab. Saying “geometry with the parallel postulate is Euclidean” is not regarded a power grab because the axioms and their consequences are useful or useless independent of the label ascribed to them. That communication is simply text; with labeling something ‘fair,’ there is the decision-making subtext “you should do this.”
Originally, it sounded like you were making one of these claims:
(a) There is no semantic candidate for the word ‘fairness.’ It’s just noise attempting to goad people into behaving a certain way.
(b) No semantic candidate for ‘fairness’ can be rendered logically precise.
(c) Even if we precisify a candidate meaning for ‘fairness,’ it won’t really be a Logical Idea, because the subject matter of morality is intrinsically less logicy than the subject matter of mathematics.
(d) Metaphysically speaking, there are quantitative universals or Forms in Plato’s Heaven, but there are no moral universals or Forms.
(e) No semantic candidate for ‘fairness’ can avoid including an argument place for a judge-of-fairness.
(f) No logically precise semantic candidate for ‘fairness’ can avoid including such an argument place.
All of these claims are implausible. But now it sounds like you’re instead just claiming: (g) There are multiple semantic candidates for ‘fairness,’ and I’m not totally clear on which one Eliezer is talking about. So I’d appreciate it if he were a bit clearer about what he means.
If (g) is all you meant to argue this whole time, then we’re in agreement. Specificity is of course a virtue.
Mathematical definitions are a power grab just as moral definitions are; the only difference is that people care more about the moral power-grabs than about the mathematical ones. Mathematical authorities assert their dominance, assert their right to participate in establishing General Mathematical Practice regarding definitions, inference rules, etc., every time they endorse one usage as opposed to another. It’s only because their authority goes relatively unchallenged that we don’t see foundational disputes over mathematical definitions as often as we see foundational disputes over moral definitions. Each constrains practice, after all.
This inspired me to write Morality Isn’t Logical, and I’d be interested to know what you think.
Very few mathematical definitions are about General Mathematical Practice. Euclidean and Riemannian (or projective) geometry are in perfect peaceful coexistence, and in general, new forms of mathematics expand the territory rather than fight over an existing patch of territory.
I think you underestimate the generality of my claim. (Perhaps the phrase ‘power grab’ is poorly chosen.) Relatively egalitarian power grabs are still power grabs, inasmuch as they use the weight of consensus and tradition to marginalize non-egalitarian views. There is no proof that both geometries are equally ‘true’ or ‘correct’ or ‘legitimate’ or ‘valid;’ so we could equally well have decided that only Euclidean geometry is correct; or that only project geometry is; or that neither is. There is no proof that one of the latter options is superior; but nor is there a proof that one is inferior. It’s a pragmatic and/or arbitrary choice, and settling such decisions depends on an initially minority viewpoint coming to exert its consensus-establishing authority over majority practice. Egalitarianism is about General Mathematical Practice. (And sometimes it’s very clearly sociological, not logical, in character; for instance, the desire to treat conventional and intuitionistic systems as equally correct but semantically disjoint is a fine way to calm down human disagreement, but as a form of mathematical realism it is unmotivated, and in fact leads to paradox.)
That depends a great deal on how coarse-grainedly you instantiate “forms”. Mathematical results get overturned all the time; not just in the form of entire fields being rejected or revised from the ground up (like the infinitesimal calculus), and not just in the discovery of internal errors in proofs past, but in the rejection of definitions and axioms for a given discourse.
I’m just a 2 year math Ph.D. program drop-out from 35 years ago, but I got quite a different take on it. As I experienced it, most mathematics is like “Let X be a G-space where G-space is defined as having ”. and then you might spend years proving whatever those axioms imply, and defining umpteen specializations of a G-space, like a G2-space which has , and teasing out and proving the consequences of having those axioms. At no point do you say these axioms are true—that’s an older, non-mathematical use of the word “axiom” as something (supposedly) self-evidently true. You just say if these axioms are true for X, then this and this and this follows.
Mathematicians simply don’t say that the axioms of Euclidean geometry are true. It is all about, “if an object (which is a purely mental construct) has these properties, then it most have these other properties.
By the “infinitesimal calculus”, being overturned, I assume you mean dropping the use of infinitesimals in favor of delta-epsilon type definitions in calculus/real analysis, it’s not such a good illustration that revision from the ground up happens all the time, since really, that goes back to the late 19th century, and I really don’t think such things do happen all the time though another big redefining project happened in the early 20th century.
ZFC set theory? Peano arithmetics?
I don’t think (g) is quite right. It is clear to me which candidate Eliezer is putting forward (in this case, at least): splitting windfalls equally by weight.
I think the closest of the ones you suggest is (e). Trying to put my view of my claim in similar terms to your other options, I think I would go with something like “We can create logically precise candidates for fairness, but this leaves undone the work of making those candidates relevant to decision-makers,” with the motivation that the reason to have moral systems / concepts like ‘fairness’ is because they are relevant to decision-makers.
That is, we can imagine numbers being ‘prime’ without a mathematician looking at them and judging them prime, but we should not imagine piles of pebbles occurring in prime numbers without some force that shifts pebbles based on their pile size.
(a) Do you think Eliezer is trying to make his terms ‘relevant to decision-makers’ in the requisite sense?
(b) Why would adding an argument place for ‘the person judging the situation as fair’ help make fairness more relevant to decision-makers?
I don’t believe in a fundamental physical force that calculates how many pebbles are in a pile, and adds or subtracts a pebble based specifically on that fact. But I do believe that pebbles can occur in piles of 3, and that 3 is a prime number. Similarly, I don’t believe in a magical Moral Force, but I do believe that people care about equitable distributions of resources, and that ‘fairness’ is a perfectly good word for picking out that property we care about. I still don’t see any reason to add an argument place; and if there were a need for a second argument place, I still don’t see why an analogous argument wouldn’t force us to add a third argument to ‘beautiful,’ so that some third party can judge whether another person is perceiving something as beautiful. (Indeed, if we took this requirement seriously, it would produce an infinite regress, making no language expressible.)
Do you see why a 2-place beauty would be more relevant than a 1-place beauty?
I was unclear; I didn’t mean “that some piles will have prime membership” but that “most or all piles of pebbles will have prime membership.”
Generally?
Relevant to what?
I would have no objection to a one-place beautyₐ, where ‘beautyₐ’ is an exhaustively physically specifiable idea like ‘producing feelings of net aesthetic pleasure when encountered by most human beings’. I would also have no objection to a two-place beauty₂, where ‘beauty₂’ means ‘aesthetically appealing to some person X.’ Neither one of these is more logically legitimate than the other, and neither one is less logically legitimate than the other. The only reason we prefer beauty₂ over beautyₐ is that it’s (a) more user-friendly to calculate, or that it’s (b) a more plausible candidate for what ordinary English language users mean when they say the word ‘beauty.’
What I want to see is an argument for precisely what the analogous property ‘fairness₂’ would look like, and why this is a more useful or more semantically plausible candidate for our word ‘fairness’ than a one-place ‘fairnessₐ’ would be. Otherwise your argument will just as easily make ‘plus’ three-place (‘addition-according-to-someone’) or ‘bird’ two-place (‘being-a-bird-according-to-someone’). This is not only impractical, but dangerous, since it confuses us into thinking that what we want when we speak of ‘objectivity’ is not specificity, but merely making explicit reference to some subject. As though mathematics would become more ‘objective,’ and not less, if we were to relativize it to a specific mathematician or community of mathematicians.
So is your worry that having a one-place ‘fairness’ predicate will make people think that most situations are fair, or that there’s a physically real fundamental law of karma promoting fairness?
In general, yes, generally.
To decision-makers.
I think I’m going to refer you to this post again. Having a beautyₐ which implicitly rather than explicitly restricts itself to humans runs the risk of being applied where its not applicable. Precision in language aids precision in thought.
I think I’m also going to bow out of the conversation at this point; we have both typed a lot and it’s not clear that much communication has gone on, to the point that I don’t expect extending this thread is a good use of either of our times.
Grammatically, neither does “beautiful”. “Alice is beautiful” is a perfectly grammatical English sentence.
Yes. Clearly I was being unclear. Just as saying “Eating broccoli is good” I think assumes a tacit answer to “Good for whom?” and/or “Good for what?”, saying “Hamburgers are delicious” assumes a tacit “Delicious to whom?”, even if the answer is “To everyone!”. I have a hard time understanding what it means to visualize a possible world where everything is delicious and there are no organisms or sentients. I think of ‘beauty’ the same way, but perhaps not everyone does; and if some people think of ‘fairness’ as intrinsically—because of the concept itself, and not just because of our metaphysical commitments or dialectical goals—demanding an implicit argument place for a ‘judge of fairness,’ I’d like to hear more about why. Or is this just a metaphysical argument, not a conceptual one?