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.
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.