It is surprising to find someone on a site dedicated to the Art of Rationality who cannot imagine impersonal norms, since rationality is a set of impersonal norms. You are not compelled to be rational, to be moral, or to play chess. But if you are being rational, you should avoid contradictions—that is a norm. If you are being moral, you should avoid doing unto others what you would not wish done unto you. If you are playing chess, you should avoid placing the bishop on a square that cannot be reached diagonally from the current one. No-one makes you follow those rules, but there is a logical relationship between following the rules and playing the game: you cannot break the rules and still play the game. In that sense, you must follow
the rules to stay in the game. But that is not an edict coming from a person or Person.
ETA:
You may well need agents to have values. I don’t require morality to be free of values.
To expound on JoshuaZ’s point, would chess have rules even if there were no minds?
Are the rules of chess objective and independent of anyone actually, y’know, knowing them?
ETA: Furthermore, if two agents in a place where chess has never existed come across a chess set, and they have a disagreement about what the rules might be, is one of them right and the other wrong?
There’s exactly one function which is objectively the function which returns 1 for just those moves where a pawn moves one space, or two spaces on the first move, or the bishop moves diagonally, or the king moves one space, where none of the moves intersect other pieces without capturing, etc...
As I said, not every mind will care to evaluate this function.
As for whether mathematical objects exist… is this important? It really adds up to the same thing, either way.
There’s exactly one function which is objectively the function which returns 1 for just those moves where a pawn moves one space, or two spaces on the first move, or the bishop moves diagonally, or the king moves one space, where none of the moves intersect other pieces without capturing, etc...
Yes, of course. I wasn’t arguing anything else. The person I was contending with is a moral realist, who would say that the function which represents those rules, the rules under which we play chess now, is the correct set of rules, and that this correctness is objective and independent of the minds of chess players.
This person would, I presume, argue that if suddenly every chess player in the world at the same time agreed to eliminate en passant from the game of chess, that they would then be playing the game “wrong”.
That is the position which I find nonsensical. I’m not arguing for anything bizarre here. I’m a Bayesian rationalist and a reductionist and yes I have read the sequences.
The person I was contending with is a moral realist, who would say that the function which represents those rules, the rules under which we play chess now, is the correct set of rules, and that this correctness is objective and independent of the minds of chess players.
I explained the point I was making and that wasn’t it: The point was what obligation/compulsion means. It doesn’t mean it is physically impossible to
do what is morally forbidden. It doesn’t mean it is an edict you will be punished for
disobeying. It does mean that it is logically impossible to be moral (or rational or a chess player) after having significantly departed from the rules.
This person would, I presume, argue that if suddenly every chess player in the world at the same time agreed to eliminate en passant from the game of chess, that they would then be playing the game “wrong”.
They would be playing a different game..chess 2.0 or chess++. Plainly,
you can’t have one player using the revised rules and her opponent the old ones.
With your chess analogy, those moves that are forbidden are set by human minds and decisions. The game of chess itself is a product of human intelligence, and they can change the rules over time, and indeed they have.
Are you saying that morality works the same way? That what is morally forbidden are those things which most people find objectionable / assign negative value to?
They would be playing a different game..chess 2.0 or chess++. Plainly, you can’t have one player using the revised rules and her opponent the old ones.
Dude, you just said a minute ago that the word “chess” could be a family of different but related rulesets when I asked about castling, but now when it comes to changing en passant the game becomes something else entirely? I think you should respond to my question on that thread about a precise explanation of what you mean by “chess”, as I cannot figure out why some things count and others do not.
If you vary the way games work too much, you end with useless non-games (winning is undefinable, one player always wins...)
If you vary the way rationality works too much, you end up with paradox, quodlibet etc.
If you vary the rules of meta ethics too much, you end up with anyone being allowed to do anything, or nobody being allowed to do anything.
“The rules are made up” doesn’t mean the rules are abitrary.
There is a family of chess-type games, and they are different games, because they
are not intersubstitutable.
One could identify many different sets of rules for chess mathematically, but is one of them objectively the “correct” set of rules?
I find that perplexing. Perhaps you mean many sets of rules could be used to play games with chess boards and pieces. But they are not all chess. Chess is its rules.
Same rules+differrent pieces=same game. Different rules+same pieces=different game.
Chess is its rules. Same rules+differrent pieces=same game. Different rules+same pieces=different game.
This isn’t strictly speaking true. Note that there have many different games called chess. For example, pawns being able to move 2 squares on their first move, en passant, castling, and the queen being able to move as she can, are all recent innovations. But let’s put that aside and explore your analogy. If there’s one thing called “morality” then I fail to see how that isn’t but one game among many. You seem to be treating morality like chess (in that there’s an objective thing that is or is not chess) but are then bringing along for the particular game called “morality” all sorts of assumptions about whether or not people should play it or expect to play it. This seems akin to asserting that because there’s only one objective game called “chess” that entities “should” play it.
In Italy one can still find older chess players who use an alternative castling rule, from when castling was first being introduced, called “free castling” in which the rook can take any of the squares between itself and the king, or the king’s position, rather than the single permitted position (depending on the side) of the more common castling rules we play with today.
Is one of these versions the “correct” way to play chess? Or does it depend entirely on the subjective viewpoint of the chess players?
Which way is the correct way to play “chess” depends on which definition of the word chess you are using. In general, we resolve ambiguities like that by looking at the speaker’s intent. (The speaker does not have to be one of the players.)
Which way is the correct way to play “chess” depends on which definition of the word chess you are using. In general, we resolve ambiguities like that by looking at the speaker’s intent. (The speaker does not have to be one of the players.)
Yes, I know that. I’m asking rhetorical questions to Peter who is a moral realist.
Alright, this is your analogy, and instead of dancing around and arguing definitions can you explain, in precise terms, what you mean when you say chess?
I’ll take the bait: A place where the idea of chess had never been thought of couldn’t, by definition, contain a chess set. It could contain an artifact physically identical to one and which we could call one if we weren’t being precise, but it would have to have come from some origin besides humans intending to build a chess set. Thus would be perfectly reasonable for the two to speculate (and be right or wrong) about what (if any) use it was meant for by its actual builders (if any).
It could contain an artifact physically identical to one and which we could call one if we weren’t being precise, but it would have to have come from some origin besides humans intending to build a chess set.
Do you seriously mean to imply that something identical to chess set is not a chess set? The words “chess set” as I used them above are meant only to connect to a physical object, not intentions.
Thus would be perfectly reasonable for the two to speculate (and be right or wrong) about what (if any) use it was meant for by its actual builders (if any).
In practical terms I agree completely. My argument with Peter wasn’t actually about chess though, so it doesn’t make a ton of sense when you focus on particulars of the analogy, especially an analogy so flawed as this one.
Do you think we disagree on any issue of substance? If so, where?
I’m familiar with it anyway. The point is that things like history, prvenance and cultural
significance are built into the way we think about things, part of the connotational cloud. That doesn;t contradict QM, but it does schemes to lossllessly reduce meaning to physics.
I’m sorry Peter, but I do not subscribe to your flights of non-empirical philosophy. We have been around this over and over. I could sit here and explain to you how the chess analogy fails, how the rationality analogy fails, et cetera and so on.
You embody Hollywood rationality. Your conception of belief and thought is entirely verbal and anthropocentric. You focus too hard on philosophy and not enough on physics. As a result, you can be seen almost palpably grasping at straws.
I avoid doing unto others what I would not wish done unto me because that policy, when shared by social animals like humans, leads to results I prefer. I have evolved that preference. I voluntarily cooperate because it is in my direct interest, i.e. fulfills my values and preferences.
I could sit here and explain to you how the chess analogy fails, how the rationality analogy fails, et cetera and so on.
I would find it easier to believe you could if you had.
I avoid doing unto others what I would not wish done unto me because that policy, when shared by social animals like humans, leads to results I prefer. I have evolved that preference. I voluntarily cooperate because it is in my direct interest, i.e. fulfills my values and preferences.
I don’t deny that you can reason about preferences. All I’m saying is that to make a decision about whether to keep, discard, or modify your own preferences, the only metrics you have to check against are your own existing values and preferences. There are no moral facts out there in the universe to check against.
Do you disagree?
I would find it easier to believe you could if you had.
It turns out that I couldn’t walk away so easily, and so I, and several others, have.
Next I’ll be saying that mathematicians can come up with objectively true theorems without checking them against Paul Erdos’s Book..
Values and preferences can be re-evaluated according to norms of rationality, such as consistency. We generally deem the outputs of reasoning processes to be objective,
even absent the existence of a domain of things to be checked against.
Next I’ll be saying that mathematicians can come up with objectively true theorems without checking them against Paul Erdos’s Book..
First, that book only has the elegant proofs. Second this totally misses the point: whether a statement is a theorem of a given formal system is objectively true or false is a distinct claim from the claim that some set of axioms is objectively a set of axioms that is somehow worth paying attention to. Even if two mathematicians disagree about whether or not one should include the Axiom of Choice in set theory, they’ll both agree that doing so is equivalent to including Zorn’s Lemma.
You aren’t just claiming that there are “theorems” from some set of moral axioms, but seem to be claiming that some sets of axioms are intrinsically better than others. You keep making this sort of leap and keep giving it no substantial justification other than the apparent reasoning that you want to be able to say things like “Gandhi was good” or “genocide is bad” and feel that there’s objective weight behind it. And we all empathize with that desire, but that doesn’t make those statements more valid in any objective sense.
I haven’t said anything is intriniscally better: I have argued that the choice of basic principles in maths, morlaity, etc is constrained by what we expect to be able to do with those things.
If you vary the way games work too much, you end with useless non-games (winning is undefinable, one player always wins...)
If you vary the way rationality works too much, you end up with paradox, quodlibet etc.
If you vary the rules of meta ethics too much, you end up with anyone being allowed to do anything, or nobody being allowed to do anything.
Yes. I do want to be able to say murder is wrong. I should want to be able to say that. It’s a feature. not a bug.. What use is a new improved rationalised system of mathematics which can’t support 2+2=4?
Peter, how do you reconcile this statement with your statement such as the one’s here where you say that
I think most moral nihilists are not evil. But the point is that if he really does think murder is not wrong, he has a bad glitch in his thinking; and if he does think murder is wrong, but feels unable to say so, he has another glitch.
How can you say someone has a glitch if they simply aren’t adopting your system which you acknowledge is arbitrary?
By arbitrarily declaring what qualifies as a glitch. (Which is only partially arbitrary if you have information about typical or ‘intended’ behaviour for an agent.)
I said he has a glitch if he can’t see that murder is wrong. I didn’t say he had to arrive at it the way I arrived at it.. I am selling a meta ethical theory. I am not selling 1-st order system of morality like Roman Catholicism or something. I use core intuitions, common
to all 1st order systems, as test cased. If you can’t get them out of your metaethical principles, you are doing something wrong.
What use is a new improved rationalised system of mathematics which can’t support 2+2=4?
So morality is like chess, but there’s some sort of grounding for why we should play it? I am confused as to what your position is.
What use is a new improved rationalised system of mathematics which can’t support 2+2=4?
I’m not sure what you mean by that. If I’m following your analogy correctly then this is somewhat wrong. Any reasonable general philosophy of metamathematics would tell you that 2+2=4 is only true in certain axiomatic systems. For example, if I used as an axiomatic system all the axioms of ZFC but left out the axiom of infinity and the axiom of replacement, I cannot then show that + is a well-defined operation. But this is an interesting system which has been studied. Moreover, nothing in my metamathematics tells me that that I should be more interested in ZFC or Peano Arithmetic. I am more interested in those systems, but that’s due to cultural and environmental norms. And one could probably have a whole career studying weak systems where one cannot derive 2+2=4 for the most natural interpretations of “2”, “+”,”=” and “4” in that system.
To return to the original notion, just because a metaethical theory has to support that someone within their more and ethical framework has “murder is wrong” doesn’t mean that the metaethical system must consider that to be a non-arbitrary claim. This is similar to just because our metamathetical theory can handle 2+2=4 doesn’t mean it needs to assert that 2+2=4 in some abstract sense.
For example, if I used as an axiomatic system all the axioms of ZFC but left out the axiom of infinity and the axiom of replacement, I cannot then show that + is a well-defined operation.
I know this is a sidetrack, but I don’t think that’s right, unless we’re omitting the axiom of pairing as well. Can’t we use pairing to prove the finite version of replacement? (This needs an induction, but that doesn’t require the axioms of replacement or infinity.) Hence, can’t we show that addition of finite ordinals is well-defined, at least in the sense that we have a class Plus(x,y,z) satisfying the necessary properties?
(Actually, I think it ought to be possible to show that addition is well-defined even without pairing, because power set and separation alone (i.e. together with empty set and union) give us all hereditarily finite sets. Perhaps we can use them to prove that {x,y} exists when x and y are hereditarily finite.)
I know this is a sidetrack, but I don’t think that’s right, unless we’re omitting the axiom of pairing as well. Can’t we use pairing to prove the finite version of replacement? (This needs an induction, but that doesn’t require the axioms of replacement or infinity.)
If we don’t have the axiom of infinity then addition isn’t a function (since its domain and range aren’t necessarily sets).
Sure, in the sense that it’s not a set. But instead we can make do with a (possibly proper) “class”. We define a formula Plus(x,y,z) in the language of set theory (i.e. using nothing other than set equality and membership + logical operations), then we prove that for all finite ordinals x and y there exists a unique finite ordinal z such that Plus(x,y,z), and then we agree to use the notation x + y = z instead of Plus(x,y,z).
This is not an unusual situation in set theory. For instance, cardinal exponentiation and ‘functions’ like Aleph are really classes (i.e. formulas) rather than sets.
Yes. But in ZFC we can’t talk about classes. We can construct predicates that describe classes, but one needs to prove that those predicates make sense. Can we in this context we can show that Plus(x,y,z) is a well-defined predicate that acts like we expect addition to act (i.e. associative, commutative and has 0 as an identity)?
In practice we tend to throw them around even when working in ZFC, on the understanding that they’re just “syntactic sugar”. For instance, if f(x,y) is a formula such that for all x there exists unique y such that f(x,y), and phi is some formula then rather than write “there exists y such that f(x,y) and phi(y)” it’s much nicer to just write “phi(F(x))” even though strictly speaking there’s no such object as F.
Can we in this context we can show that Plus(x,y,z) is a well-defined predicate that acts like we expect addition to act (i.e. associative, commutative and has 0 as an identity)?
I think the proofs go through almost unchanged (once we prove ‘finite replacement’).
Well, we could define Plus(x,y,z) by “there exists a function f : x → z with successor(max(codomain(f))) = z, which preserves successorship and sends 0 to y”. (ETA: This only works if x > 0 though.)
And then we just need to do loads of inductions, but the basic induction schema is easy:
Suppose P(0) and for all finite ordinals n, P(n) implies P(n+1). Suppose ¬P(k). Let S = {finite ordinals n : ¬P(n) and n ⇐ k}. By the axiom of foundation, S has a smallest element m. Then ¬P(m). But then either m = 0 or P(m-1), yielding a contradiction in either case.
Sure, but we still have a “class”. “Classes” are either crude syntactic sugar for “formulae” (as in ZFC) or they’re a slightly more refined syntactic sugar for “formulae” (as in BGC). In either case, classes are ubiquitous—for instance, ordinal addition isn’t a function either, but we prove things about it just as if it was.
But if you are being rational, you should avoid contradictions—that is a norm. If you are being moral, you should avoid doing unto others what you would not wish done unto you. If you are playing chess, you should avoid placing the bishop on a square that cannot be reached diagonally from the current one. No-one makes you follow those rules, but there is a logical relationship between following the rules and playing the game: you cannot break the rules and still play the game. In that sense, you must follow the rules to stay in the game.
Are you asserting that being “moral” is just like a game with a set of agreed upon rules? That doesn’t fit with your earlier claims (e.g. this remark)and on top of that seems to run into the problems of people not agreeing what the rules are. Note incidentally, that it is extremely unlikely that any random intelligence will either know or have any desire to play chess. If you think the same applies about your notion of morality then there’s much less disagreement, but that doesn’t seem to be what you are asserting. I am confused.
Agreed upon? Most of the game is in making up rules and forcing them on others despite their disagreement!
Although that happens with other games also, when there’s a disagreement about the rules. It just seems to be a smaller fraction of the game and something that everyone tries to avoid. There are some games that explicitly lampshade this. The official rules of Munchkin say something like (paraphrase) ” in a rules dispute whoever shouts loudest is right.”
Although it would be unpleasant, I think, to be the loud guy at the party who no one wants to be there. Still, I overreacted, I think. It was a relatively small number of my posts that were received negatively, and absent an explanation of why they were, all I can do is work on refining my rationality and communication skills.
Edit: Downvoted lol
Further edit: This could be like rejection therapy for karma. Everyone downvote this post!
I’m arguing that there is a sense in which one “should” follow rules which has nothing to do with human-like agents laying down the law, thereby refuting NMJ’s attempt at a link between objective morality and theism.
There are constraints on the rules games can have (eg fairness, a clear winner after finite time).
There are constraints on rationality (eg avoidance of quodlibet).
Likewise, there are constraints on the rules of moral reasoning. (eg. people cannot just make up their own morality and do what they want). Note that I am talking about
metaethics here.
I’m arguing that there is a sense in which one “should” follow rules which has nothing to do with human-like agents laying down the law, thereby refuting NMJ’s attempt at a link between objective morality and theism.
So this is the exact opposite of a chess game. So what do you mean by your analogy?
It is surprising to find someone on a site dedicated to the Art of Rationality who cannot imagine impersonal norms, since rationality is a set of impersonal norms. You are not compelled to be rational, to be moral, or to play chess. But if you are being rational, you should avoid contradictions—that is a norm. If you are being moral, you should avoid doing unto others what you would not wish done unto you. If you are playing chess, you should avoid placing the bishop on a square that cannot be reached diagonally from the current one. No-one makes you follow those rules, but there is a logical relationship between following the rules and playing the game: you cannot break the rules and still play the game. In that sense, you must follow the rules to stay in the game. But that is not an edict coming from a person or Person.
ETA: You may well need agents to have values. I don’t require morality to be free of values.
To expound on JoshuaZ’s point, would chess have rules even if there were no minds?
Are the rules of chess objective and independent of anyone actually, y’know, knowing them?
ETA: Furthermore, if two agents in a place where chess has never existed come across a chess set, and they have a disagreement about what the rules might be, is one of them right and the other wrong?
The rules of chess would certainly exist, as much as any other mathematical object does. Of course, not every mind would care to follow them...
One could identify many different sets of rules for chess mathematically, but is one of them objectively the “correct” set of rules?
Or does selecting a set of rules from the possibilities always require the action of a subjective mind?
Edit: Also...
… that’s a whole other rabbit hole, no?
There’s exactly one function which is objectively the function which returns 1 for just those moves where a pawn moves one space, or two spaces on the first move, or the bishop moves diagonally, or the king moves one space, where none of the moves intersect other pieces without capturing, etc...
As I said, not every mind will care to evaluate this function.
As for whether mathematical objects exist… is this important? It really adds up to the same thing, either way.
(By the way, have you read the metaethics sequence?)
Yes, of course. I wasn’t arguing anything else. The person I was contending with is a moral realist, who would say that the function which represents those rules, the rules under which we play chess now, is the correct set of rules, and that this correctness is objective and independent of the minds of chess players.
This person would, I presume, argue that if suddenly every chess player in the world at the same time agreed to eliminate en passant from the game of chess, that they would then be playing the game “wrong”.
That is the position which I find nonsensical. I’m not arguing for anything bizarre here. I’m a Bayesian rationalist and a reductionist and yes I have read the sequences.
I explained the point I was making and that wasn’t it: The point was what obligation/compulsion means. It doesn’t mean it is physically impossible to do what is morally forbidden. It doesn’t mean it is an edict you will be punished for disobeying. It does mean that it is logically impossible to be moral (or rational or a chess player) after having significantly departed from the rules.
They would be playing a different game..chess 2.0 or chess++. Plainly, you can’t have one player using the revised rules and her opponent the old ones.
With your chess analogy, those moves that are forbidden are set by human minds and decisions. The game of chess itself is a product of human intelligence, and they can change the rules over time, and indeed they have.
Are you saying that morality works the same way? That what is morally forbidden are those things which most people find objectionable / assign negative value to?
Dude, you just said a minute ago that the word “chess” could be a family of different but related rulesets when I asked about castling, but now when it comes to changing en passant the game becomes something else entirely? I think you should respond to my question on that thread about a precise explanation of what you mean by “chess”, as I cannot figure out why some things count and others do not.
If you vary the way games work too much, you end with useless non-games (winning is undefinable, one player always wins...) If you vary the way rationality works too much, you end up with paradox, quodlibet etc. If you vary the rules of meta ethics too much, you end up with anyone being allowed to do anything, or nobody being allowed to do anything. “The rules are made up” doesn’t mean the rules are abitrary.
There is a family of chess-type games, and they are different games, because they are not intersubstitutable.
I find that perplexing. Perhaps you mean many sets of rules could be used to play games with chess boards and pieces. But they are not all chess. Chess is its rules. Same rules+differrent pieces=same game. Different rules+same pieces=different game.
This isn’t strictly speaking true. Note that there have many different games called chess. For example, pawns being able to move 2 squares on their first move, en passant, castling, and the queen being able to move as she can, are all recent innovations. But let’s put that aside and explore your analogy. If there’s one thing called “morality” then I fail to see how that isn’t but one game among many. You seem to be treating morality like chess (in that there’s an objective thing that is or is not chess) but are then bringing along for the particular game called “morality” all sorts of assumptions about whether or not people should play it or expect to play it. This seems akin to asserting that because there’s only one objective game called “chess” that entities “should” play it.
In Italy one can still find older chess players who use an alternative castling rule, from when castling was first being introduced, called “free castling” in which the rook can take any of the squares between itself and the king, or the king’s position, rather than the single permitted position (depending on the side) of the more common castling rules we play with today.
Is one of these versions the “correct” way to play chess? Or does it depend entirely on the subjective viewpoint of the chess players?
Which way is the correct way to play “chess” depends on which definition of the word chess you are using. In general, we resolve ambiguities like that by looking at the speaker’s intent. (The speaker does not have to be one of the players.)
Yes, I know that. I’m asking rhetorical questions to Peter who is a moral realist.
Chess might be a small and closely related family of rule-sets. That doesn’t affect anything.
Alright, this is your analogy, and instead of dancing around and arguing definitions can you explain, in precise terms, what you mean when you say chess?
I’ll take the bait: A place where the idea of chess had never been thought of couldn’t, by definition, contain a chess set. It could contain an artifact physically identical to one and which we could call one if we weren’t being precise, but it would have to have come from some origin besides humans intending to build a chess set. Thus would be perfectly reasonable for the two to speculate (and be right or wrong) about what (if any) use it was meant for by its actual builders (if any).
Do you seriously mean to imply that something identical to chess set is not a chess set? The words “chess set” as I used them above are meant only to connect to a physical object, not intentions.
In practical terms I agree completely. My argument with Peter wasn’t actually about chess though, so it doesn’t make a ton of sense when you focus on particulars of the analogy, especially an analogy so flawed as this one.
Do you think we disagree on any issue of substance? If so, where?
A duplicate of the Mona Lisa wouldn’t be the Mona Lisa.
Have you read the quantum physics sequence? Are you familiar with the experimental evidence on particle indistinguishability?
I’m familiar with it anyway. The point is that things like history, prvenance and cultural significance are built into the way we think about things, part of the connotational cloud. That doesn;t contradict QM, but it does schemes to lossllessly reduce meaning to physics.
Nothing I have to say about morality or metaethics hinges on that one way or the other.
Then clearly we have badly miscommunicated.
I’m sorry Peter, but I do not subscribe to your flights of non-empirical philosophy. We have been around this over and over. I could sit here and explain to you how the chess analogy fails, how the rationality analogy fails, et cetera and so on.
You embody Hollywood rationality. Your conception of belief and thought is entirely verbal and anthropocentric. You focus too hard on philosophy and not enough on physics. As a result, you can be seen almost palpably grasping at straws.
I avoid doing unto others what I would not wish done unto me because that policy, when shared by social animals like humans, leads to results I prefer. I have evolved that preference. I voluntarily cooperate because it is in my direct interest, i.e. fulfills my values and preferences.
I would find it easier to believe you could if you had.
Reasoning about preferences is still reasoning.
I don’t deny that you can reason about preferences. All I’m saying is that to make a decision about whether to keep, discard, or modify your own preferences, the only metrics you have to check against are your own existing values and preferences. There are no moral facts out there in the universe to check against.
Do you disagree?
It turns out that I couldn’t walk away so easily, and so I, and several others, have.
Next I’ll be saying that mathematicians can come up with objectively true theorems without checking them against Paul Erdos’s Book..
Values and preferences can be re-evaluated according to norms of rationality, such as consistency. We generally deem the outputs of reasoning processes to be objective, even absent the existence of a domain of things to be checked against.
First, that book only has the elegant proofs. Second this totally misses the point: whether a statement is a theorem of a given formal system is objectively true or false is a distinct claim from the claim that some set of axioms is objectively a set of axioms that is somehow worth paying attention to. Even if two mathematicians disagree about whether or not one should include the Axiom of Choice in set theory, they’ll both agree that doing so is equivalent to including Zorn’s Lemma.
You aren’t just claiming that there are “theorems” from some set of moral axioms, but seem to be claiming that some sets of axioms are intrinsically better than others. You keep making this sort of leap and keep giving it no substantial justification other than the apparent reasoning that you want to be able to say things like “Gandhi was good” or “genocide is bad” and feel that there’s objective weight behind it. And we all empathize with that desire, but that doesn’t make those statements more valid in any objective sense.
I haven’t said anything is intriniscally better: I have argued that the choice of basic principles in maths, morlaity, etc is constrained by what we expect to be able to do with those things.
If you vary the way games work too much, you end with useless non-games (winning is undefinable, one player always wins...) If you vary the way rationality works too much, you end up with paradox, quodlibet etc. If you vary the rules of meta ethics too much, you end up with anyone being allowed to do anything, or nobody being allowed to do anything.
Yes. I do want to be able to say murder is wrong. I should want to be able to say that. It’s a feature. not a bug.. What use is a new improved rationalised system of mathematics which can’t support 2+2=4?
Peter, how do you reconcile this statement with your statement such as the one’s here where you say that
I don’t see the problem. What needs reconciling with what?
How can you say someone has a glitch if they simply aren’t adopting your system which you acknowledge is arbitrary?
By arbitrarily declaring what qualifies as a glitch. (Which is only partially arbitrary if you have information about typical or ‘intended’ behaviour for an agent.)
Yet again: I never said morality was arbitrary.
I said he has a glitch if he can’t see that murder is wrong. I didn’t say he had to arrive at it the way I arrived at it.. I am selling a meta ethical theory. I am not selling 1-st order system of morality like Roman Catholicism or something. I use core intuitions, common to all 1st order systems, as test cased. If you can’t get them out of your metaethical principles, you are doing something wrong.
What use is a new improved rationalised system of mathematics which can’t support 2+2=4?
So morality is like chess, but there’s some sort of grounding for why we should play it? I am confused as to what your position is.
I’m not sure what you mean by that. If I’m following your analogy correctly then this is somewhat wrong. Any reasonable general philosophy of metamathematics would tell you that 2+2=4 is only true in certain axiomatic systems. For example, if I used as an axiomatic system all the axioms of ZFC but left out the axiom of infinity and the axiom of replacement, I cannot then show that + is a well-defined operation. But this is an interesting system which has been studied. Moreover, nothing in my metamathematics tells me that that I should be more interested in ZFC or Peano Arithmetic. I am more interested in those systems, but that’s due to cultural and environmental norms. And one could probably have a whole career studying weak systems where one cannot derive 2+2=4 for the most natural interpretations of “2”, “+”,”=” and “4” in that system.
To return to the original notion, just because a metaethical theory has to support that someone within their more and ethical framework has “murder is wrong” doesn’t mean that the metaethical system must consider that to be a non-arbitrary claim. This is similar to just because our metamathetical theory can handle 2+2=4 doesn’t mean it needs to assert that 2+2=4 in some abstract sense.
I know this is a sidetrack, but I don’t think that’s right, unless we’re omitting the axiom of pairing as well. Can’t we use pairing to prove the finite version of replacement? (This needs an induction, but that doesn’t require the axioms of replacement or infinity.) Hence, can’t we show that addition of finite ordinals is well-defined, at least in the sense that we have a class Plus(x,y,z) satisfying the necessary properties?
(Actually, I think it ought to be possible to show that addition is well-defined even without pairing, because power set and separation alone (i.e. together with empty set and union) give us all hereditarily finite sets. Perhaps we can use them to prove that {x,y} exists when x and y are hereditarily finite.)
If we don’t have the axiom of infinity then addition isn’t a function (since its domain and range aren’t necessarily sets).
Sure, in the sense that it’s not a set. But instead we can make do with a (possibly proper) “class”. We define a formula Plus(x,y,z) in the language of set theory (i.e. using nothing other than set equality and membership + logical operations), then we prove that for all finite ordinals x and y there exists a unique finite ordinal z such that Plus(x,y,z), and then we agree to use the notation x + y = z instead of Plus(x,y,z).
This is not an unusual situation in set theory. For instance, cardinal exponentiation and ‘functions’ like Aleph are really classes (i.e. formulas) rather than sets.
Yes. But in ZFC we can’t talk about classes. We can construct predicates that describe classes, but one needs to prove that those predicates make sense. Can we in this context we can show that Plus(x,y,z) is a well-defined predicate that acts like we expect addition to act (i.e. associative, commutative and has 0 as an identity)?
In practice we tend to throw them around even when working in ZFC, on the understanding that they’re just “syntactic sugar”. For instance, if f(x,y) is a formula such that for all x there exists unique y such that f(x,y), and phi is some formula then rather than write “there exists y such that f(x,y) and phi(y)” it’s much nicer to just write “phi(F(x))” even though strictly speaking there’s no such object as F.
I think the proofs go through almost unchanged (once we prove ‘finite replacement’).
I’m not as confident but foundations is very much not my area of expertise. I’ll try to work out the details and see if I run into any issues.
Well, we could define Plus(x,y,z) by “there exists a function f : x → z with successor(max(codomain(f))) = z, which preserves successorship and sends 0 to y”. (ETA: This only works if x > 0 though.)
And then we just need to do loads of inductions, but the basic induction schema is easy:
Suppose P(0) and for all finite ordinals n, P(n) implies P(n+1). Suppose ¬P(k). Let S = {finite ordinals n : ¬P(n) and n ⇐ k}. By the axiom of foundation, S has a smallest element m. Then ¬P(m). But then either m = 0 or P(m-1), yielding a contradiction in either case.
Yes, this seems to work.
Sure, but we still have a “class”. “Classes” are either crude syntactic sugar for “formulae” (as in ZFC) or they’re a slightly more refined syntactic sugar for “formulae” (as in BGC). In either case, classes are ubiquitous—for instance, ordinal addition isn’t a function either, but we prove things about it just as if it was.
Are you asserting that being “moral” is just like a game with a set of agreed upon rules? That doesn’t fit with your earlier claims (e.g. this remark)and on top of that seems to run into the problems of people not agreeing what the rules are. Note incidentally, that it is extremely unlikely that any random intelligence will either know or have any desire to play chess. If you think the same applies about your notion of morality then there’s much less disagreement, but that doesn’t seem to be what you are asserting. I am confused.
Agreed upon? Most of the game is in making up rules and forcing them on others despite their disagreement!
Although that happens with other games also, when there’s a disagreement about the rules. It just seems to be a smaller fraction of the game and something that everyone tries to avoid. There are some games that explicitly lampshade this. The official rules of Munchkin say something like (paraphrase) ” in a rules dispute whoever shouts loudest is right.”
Upvoted for levity! Whew, we needed it.
I am tremendously confused as to why this and the parent were downvoted. Clearly I should just stop posting.
Or quit caring about the voting system.
That is also an option.
Although it would be unpleasant, I think, to be the loud guy at the party who no one wants to be there. Still, I overreacted, I think. It was a relatively small number of my posts that were received negatively, and absent an explanation of why they were, all I can do is work on refining my rationality and communication skills.
Edit: Downvoted lol
Further edit: This could be like rejection therapy for karma. Everyone downvote this post!
I’m arguing that there is a sense in which one “should” follow rules which has nothing to do with human-like agents laying down the law, thereby refuting NMJ’s attempt at a link between objective morality and theism.
There are constraints on the rules games can have (eg fairness, a clear winner after finite time). There are constraints on rationality (eg avoidance of quodlibet). Likewise, there are constraints on the rules of moral reasoning. (eg. people cannot just make up their own morality and do what they want). Note that I am talking about metaethics here.
So this is the exact opposite of a chess game. So what do you mean by your analogy?