About Morality

by hilzoy

Once upon a time, I went to a gathering of liberals and conservatives that was intended to promote dialogue and understanding between the two groups; and I was struck by the fact that whenever someone learned that I was an ethicist, they immediately assumed that I was a conservative. This seemed odd to me: it was several decades over a decade* ago, before 'moral values' had emerged as a political term, and at that point I couldn't imagine why anyone would suppose that conservatives had a lock on moral values.

(This was not just partisanship, or a reflection of the fact that my moral beliefs underwrite my political views. It was also due to my having spent several decades being lectured by conservatives about my "excessively idealistic" views -- e.g., about how it was silly to think that we shouldn't support, say, Guatemala in the early '80s "just" because it was murderous and repressive. It was genuinely surprising to discover that the very people who had made these arguments were regarded as champions of morality.)

These days it's more obvious why someone might think that. But it's deeply regrettable. There is a straightforward moral case to be made not just against the current crop of Republican politicians, but also, I think, for liberal values. But as long as we cede moral language to conservatives, we will not be able to make this case effectively. Nor will we be able to speak to the legitimate fears of people who (correctly) think that morality is extremely important, who are worried that it's under seige, and who (mistakenly) suppose that only conservatives are willing to speak up for them, or that defending morality involves an obsession with preventing gay marriage, or something like that.

If we want to reclaim moral language, however, we need to get comfortable with the idea of making moral judgments. Some of you already are, of course, but some of the reactions to my Evil post made me think that some of you are not. Therefore, I have written a short primer. It's meant for those who are not fully comfortable making moral judgments, or using the language of morality. Many of you probably don't need it. It also contains only the issues that happened to occur to me. I'll write about others on request.

1) What is the point of thinking about morality?

I'll consider two possible reasons for thinking about morality, which I will tendentiously refer to as "the right view" and "the wrong view."

The right way: We all perform actions. And whether or not we reflect on the kinds of actions we think we should perform, the kinds of principles we think we should live by, or the kinds of persons we think we should be, we will end up performing some actions and not others, living in accordance with certain principles, and developing a particular character. It will be true of one person that she ruthlessly pursues her own interests; of another that she drifts along, allowing her actions to be determined by the preferences of those around her; of another that she tries to preserve her image of herself as 'virtuous' only as long as it is not too inconvenient to do so; and of another that she tries to respond to others with generosity and honesty and respect, even when this is difficult. Even someone who tries to live by no principles at all -- say, by flipping coins instead of making choices -- still lives by the principle of allowing her actions to be determined by chance.

This being the case, it makes sense to try to figure out which principles we think should try to live by and which sorts of persons we think we should try to be, just as the fact that we will probably have to earn our living by doing something gives us reason to try to figure out which job we want and to try to get it. If we don't think about which job we would like to end up with, we might find ourselves spending eight hours a day doing something we hate, when a little forethought would have prevented this. Similarly, if we do not try to figure out which principles should guide our actions, we could wind up needlessly living by principles we find odious.

On the right view, the ultimate object of moral reasoning is always to give us guidance in leading our lives; and (in so doing) to lead us to greater self-knowledge. And on this view, we make moral judgments about other people for two reasons. First, having developed moral concepts for use in our own lives, we can apply them to others. If, for instance, we are talking with another person about morality, we may have occasion to make such judgments. Second, we make them in order to clarify our own views about right and wrong, and to see more clearly how we can achieve the former and avoid the latter.

This might not seem to give us much of a reason to judge, say, torturers: on the one hand, torture seems clearly wrong, so our attitudes are not in need of clarification; on the other, with any luck none of us will be faced with the possibility of becoming a torturer, so why bother trying to figure out how to avoid doing so? But it does. Thinking about other people, and trying to understand why they act as they do, can lead us to see connections between what they did and attitudes or character traits which we might have, even when the possibility of our performing the very same act which they performed is remote. For example, consider this quote from Primo Levi's Survival In Auschwitz:

"Many people -- many nations -- can find themselves holding, more or less wittingly, that 'every stranger is an enemy'. For the most part this conviction lies deep down like some latent infection; it betrays itself only in random, disconnected acts, and does not lie at the base of a system of reason. But when this does come about ... then, at the end, there is the lager. Here is the product of a conception of the world carried rigorously to its logical conclusion; so long as the conception subsists, the conclusion remains to threaten us. The story of the death camps should be understood by everyone as a sinister alarm-signal."

One can make moral judgments, and engage in moral reasoning, in order to become aware of such 'alarm signals', and to understand more clearly what they warn of. Analogously, thinking about people or actions we regard as good can lead us to understand more clearly what goodness is, and how we might try to achieve it, even if the person we are thinking about seems to us to have a kind of heroic virtue which we doubt we could ever attain.

The wrong view: if we say that someone acted wrongly, we may do so in order to demonstrate, to ourselves and to others, how marvelously virtuous we are, and how morally perceptive. We shudder in horror at the thought that awful they did ghastly that, and in so doing remind ourselves of how very different wonderful we are. To judge another's actions in this spirit is to indulge in a sneaky sort of self-congratulation.

The right view and the wrong view are deeply opposed to one another. For one thing, only the right view requires us to try to understand other people and their actions accurately. We can learn from others only to the extent that our ideas about what led them to act as they did are correct. The wrong view, on the other hand, uses morality for the purpose of self-congratulation; and self-congratulation requires only that we believe that we are virtuous. Whether or not this belief is correct is irrelevant. The wrong view is therefore compatible with self-deception and hypocrisy; the right view is not.

The two views also favor different views of the people we judge. The wrong view leads us to view the people we disapprove of as very different from ourselves. Ideally, they should have horns; if this cannot be arranged, we should at least view their actions as revealing some appalling inner corruption which is not so much as a possibility for us. The right view, by contrast, will lead us to try to understand these people as recognizably human beings who behave in more or less comprehensible ways; as, in some broad sense, like us. Otherwise their actions will have no lessons for our lives. Because the right view involves a commitment to accuracy, it will not insist on viewing an action as humanly comprehensible even when it really doesn't seem to be; if the person who performed it really does seem to have horns, moral reasoning undertaken for this motive can recognize this fact. But, unlike self-congratulatory moral reasoning, it will accept such explanations only as a last resort, and with bewilderment.

I probably don't need to say that I do not think that self-congratulation is a good motive for making moral judgments. People sometimes seem to assume that it is the only motive for engaging in moral reasoning; that whenever anyone reaches any conclusion about the morality of someone else's actions, they must be putting themselves on a pedestal, claiming that they would never do such a horrible thing, etc. I do not think that when one concludes that some act is wrong one must believe that one would not perform it, or that that conclusion is incompatible with a vivid appreciation of one's own fallibility. Such an appreciation can motivate moral reasoning: those who set out to sea in tiny fragile boats have every reason to note precisely where, and why, others were shipwrecked; and not because they want to laugh at the misfortunes of others.

Moreover, a genuine commitment to morality leads to the right view, and away from the wrong one. Each of us is responsible for making one person as good as possible: him- or herself. Our own failings, not those of others, should always be our primary concern. For this reason, a preoccupation with (as opposed to an ability to recognize) the sins of other people is likely to be a distraction from the task at hand: oneself. Besides, on most accounts of morality, a desire to prop up one's own conception of oneself by vilifying others is not high on the list of desirable motivations; and self-deception and hypocrisy are not among the characteristics we ought to tolerate, let alone cultivate.

(You can often tell a lot about someone's view of morality by asking: does this person seem to focus more on her own failings, or on those of of others? Is her primary concern making herself a better person, or distancing herself from those she regards as bad? Morality generally requires the first answer to each question.)

Does thinking about morality make you self-righteous?

It will if you think about it in the wrong way, as described above. Self-righteousness is practically the wrong way's middle name. But thinking about morality in the right way generally precludes self-righteousness, for several reasons. First, and most obviously, the harder you try to live a decent life, the more likely it is that you will discover that you have flaws. Some of them may be familiar to you, but some of them may be ones you didn't know you had. And the more important you think morality is, the more serious these flaws will seem. (Samuel Johnson once wrote: "I have now begun the sixtieth year of my life. How the last year has passed I am unwilling to terrify myself with thinking." Only the thought that it really matters whether you're a good person or not can make could one find the thought of how one spent one's last year not just disheartening or disappointing, but terrifying.) This will help to undermine any temptation to self-righteousness that you might have had.

Second, if you think that there is such a thing as the right thing to do, and that it matters to do that thing, an obvious question to ask is: do I know what exactly the right thing to do is? For most people, the answer will be, roughly: there are some things I feel confident about, some things I believe but am not really sure of, and some things I just don't know.

The more important you think morality is, the more important actually being right about these questions will seem to be, and the less tolerable the idea of just convincing yourself that you're right to make yourself seem good will be to you. For this reason, I have always thought that a real commitment to morality ought to lead us to seek out people who disagree with us and try to learn from them, since it's in that way that we're most likely to see things we might have overlooked, or to reconsider things we have hitherto taken for granted. I say more about this here.

In general, though, if you make a real effort to actually live a decent life, that effort will directly work against self-righteousness, both by providing you with vivid proof of your own faults and by making the idea of convincing yourself that you're a wonderful person with a complete grasp of the truth about morality seem both absurd and intolerable. (Unless, of course, you are a wonderful person with a complete grasp of the truth about morality. One would have to be very wary about accepting any such conclusion -- the possibility of self-deception is presumably obvious -- but if, after long and careful reflection, it really does seem to you true, then morality will not require that you lie to yourself, though it will counsel against resting on your laurels.)

Isn't making moral judgments, well, kind of mean?

No, for several reasons. For one thing, not all moral judgments are negative. However, let's restrict ourselves to negative moral judgments for the moment. Here it's important to separate three things: (a) how you express a moral judgment; (b) how you form it (e.g., how careful you are, where you take the burden of proof to lie, etc.), and third, the judgment itself.

(a) There are times when expressing a given moral judgment is wrong, even if that judgment is true. An example I sometimes use in class: suppose that you walk out in front of a bus without looking, and get run over. As you lie there bleeding in the street, I come up to you and start to lecture you on how dumb you were. Here it's not the judgment that's at fault. What I say is true: it is dumb to walk out into the street without looking. The problem is what I do with that judgment: it is heartless of me to stand there lecturing you instead of calling an ambulance, or trying to stop the bleeding, or in some other way trying to help.

(b) There are ways of making moral judgments that are themselves wrong. Making any negative judgment about a person is something that we should be careful about. Holding any false belief involves a mistake; but thinking ill of someone when it's not true is in addition unfair, and possibly deeply insulting, to that person. As a result, a decent person will want to be especially sure that she's right before making such a judgment.

Consider, for example, concluding that someone is a rapist. A rapist is a terrible thing to be, and the judgment that some particular person is a rapist is a terrible thing to conclude about that person. Because it's a terrible thing to think about someone, any decent person will think long and hard before reaching the conclusion that someone is a rapist. And if (for instance) I saw a woman come out of a man's apartment in tears and leapt to the conclusion that the man raped her, without considering any of the other possible explanations for what I saw, I would be wrong.

There is, however, a difference between recognizing that you have to think hard before concluding that someone is a rapist and thinking that concluding that someone is a rapist just shows that you're mean and ungenerous. After all, some people are rapists, and while no one should ever leap to the conclusion that a particular person is one of them, arriving at that conclusion when you're presented with compelling evidence that it's true is not an inherently mean thing to do.

Most negative moral judgments are a lot less damning than concluding that someone is a rapist. Just as there's a difference between getting one problem on a math exam wrong and getting a failing grade, there's a difference between having some flaw, or doing one wrong action, and being a miserable failure as a person. Here again, it helps to use morality primarily on oneself: in one's own case, it's generally obvious that there's a fair amount of room between some negative moral judgment being true (which is true of all of us) and being a horrible person (which is not.)

Still, we should always be reluctant to think the worst of someone, both because it's insulting to them and because morality requires generosity of us.

I think that people who believe that there's something mean about making moral judgments tend to focus either on the possibility that those who make them might be uncharitable -- leaping to bad conclusions about people rather than asking whether what they did might be explained in some non-damning way -- or on how that judgment is expressed. In either case, what's wrong is not that the person forms moral judgments; it's how those judgments are formed and/or expressed. If you form negative moral judgments only reluctantly, and if you try to subject your own impulse to express them (or not to) to the same moral scrutiny as the rest of your actions, then you will be a lot less likely to be mean about it.

Some of the temptation to think that negative moral judgments are mean might also come from unclarity about what point they might serve, other than allowing us to tot up other people's failings and pass judgment on them. I tried to answer this above (see "the right way"). Trying to understand why other people do what they do, and whether what they do is right or wrong, is immensely useful in trying to become a decent person oneself.

Moreover, it's worth noting that if the other person wants to become a decent person herself, then you might find yourself needing to talk about what you think of her conduct with her. If you think she's doing something wrong, this might be unpleasant, the way saying you don't like someone's writing is. But it can be very much worth saying nonetheless, and for many of the same reasons.

In my family, we all read one another's written work, and we all took it for granted that while it was never fun to be critical of one another, it was much, much better to find out about the problems with your written work before rather than after publication, and from someone you know loves you and has your best interests at heart, rather than from some critic who might or might not be thoughtful or kind. (This got me into trouble later: it had never crossed my mind that I should not be honest, though as kind as possible, in assessing other people's work, and so naturally the discovery that some people give out their work for entirely different reasons was as much a shock to me as I imagine my comments were to them. Oops.) Moral criticism, when it's called for and when you are not hasty or uncharitable in making your judgments, can be just as useful.

In order to make moral judgments about others, do I have to understand why they acted as they did?

Of course, to some extent. In order to make any statement about anything, we have to have some idea what we're talking about. Specifically, we have to know what that person did, and whatever facts we take to be relevant to a moral assessment of actions of that kind. For instance, I think that it is OK to steal food to feed one's starving children if there are no other ways of getting food, and if the person one steals from is not herself starving. In order to say that someone who stole food acted wrongly, I would have to know that she did not do so for this reason.

In some cases, things that I cannot understand seem to me clearly relevant to moral judgment. This is especially true when one considers people who have survived torture, concentration camps, or some other form of hell: I think that in order to judge actions performed in these situations I would have to understand fairly clearly what the experience of systematic and sustained brutality is like, and since I do not, I hesitate to judge. But in other cases I do not feel that my inability to understand another person does not prevent me from judging, since I do not think that what I do not understand is relevant to my judgment.

For instance, I do not understand the motives of those who rape children. Presumably, some child rapists are insane, and I do not judge them. But since people are various and human nature is multiform, there is probably at least one sane person somewhere who has raped a child; and I do not feel that my inability to understand that person's motives prevents me from saying that his actions are wrong, and that he is a horrible person. I said above that I need to understand only those facts about a person's motives which are relevant to moral assessment; in the case of sane child rapists, I do not think that there are any such facts, or that anything the rapist could tell me about his motives or decision would alter my opinion of him and his actions.

(Here I am concerned only with the question: what is the minimum level of understanding which we must have in order to judge another person? For reasons given earlier, I think that we should always try to understand others as fully as possible; and that the fact that we have achieved this minimum is no reason not to try to understand them more fully.)

Can we ever understand what someone else does if we have not been in the same situation ourselves?

Yes. First of all, notice that no one has ever been in exactly the same situation as anyone else. This weekend, I was tempted to put off some work I needed to do. You might have experienced a similar temptation at some point. But I'll bet that no one reading this blog has been in an exactly similar situation, with my precise background, temperament, childhood experiences, etc. You may think that these differences aren't important; but since you haven't experienced them for yourself, and therefore (if you can't understand what you haven't experienced) can't understand them, how would you know? If we cannot understand what we haven't experienced ourselves, then we cannot understand anyone except ourselves at all.

Notice also that this assumption would make the study of history and other cultures pointless, psychology a lost cause, and the existence of non-autobiographical novels which seem to depict people accurately inexplicable.

It is hard to understand other people, and the difficulty increases as their experiences become more remote from one's own. And it is easy to wander around blithely passing judgment on people whom one has not made the slightest effort to understand. Such judgments are usually glib, shallow, and disrespectful. But this shows only that we should try to understand other people, to develop the capacities of empathy and imagination which this requires, to realize that understanding other people takes effort and hard work, and to be aware of the possibility that our views about other people are not always right. To throw up one's hands and decide that understanding other people is just impossible is, I think, just a way of avoiding this task. It also lets people who don't bother to try to understand others off the hook, by taking their failures to be inevitable, not the result of insufficient effort or imagination.

But you're ignoring the elephant in the room: moral claims can't be true or false, so it makes no sense to talk about them.

In this post I will not consider the question whether moral judgments can be true or false in any detail. (If anyone wants, I can do that later.) For now, I'll just say two things, and then consider a few bad reasons for thinking that moral claims can't be true or false, arguments that I think need to be gotten out of the way before serious consideration of this question can begin.

The two things: first, there are a lot of terms we feel quite comfortable using that are not found in science. We say, for instance, that some poems or paintings are beautiful and some are not, that some jokes are funny while others fall flat, and so forth. We have long arguments about why this is so: about questions like: why is this painting so dreadful? We may even develop whole theories to answer these questions. And in so doing, we are often quite untroubled by the fact that neither beauty nor funniness are terms found in science. Anyone who finds arguments about beauty or humor unproblematic should ask him- or herself why morality is different.

Second, one possible answer to the question whether moral judgments can be true or false is to say: some of them have determinate answers, and others do not. One might think, for instance, that Gandhi is a better person than Jeffrey Dahmer, or that torture is wrong, but also that there is no determinate answer to the question whether Gandhi or Nelson Mandela was right about the legitimacy of armed resistance to a profoundly unjust regime. It's worth bearing in mind that the fact (if it is one) that some moral questions do not have determinate answers does not imply that no moral questions do.

(Literary criticism is like this. There are some interpretations of, say, Hamlet that are plainly wrong: for instance, the view that everything turns on its sixth act, or that the key to understanding Hamlet is to count the frequency of various punctuation marks in each scene. But it's not at all clear that any particular interpretation is right, or that different interpretations should be assessed based on how closely they approximate to the One True Interpretation. Likewise, it's clear that Middlemarch is a better novel than a Harlequin romance, but that doesn't commit you to thinking that there is one absolutely best novel that Middlemarch approximates more closely than the Harlequin romance, or even that there is a determinate answer to questions like: is Middlemarch better than The Brothers Karamazov?)

The bad arguments:

a) Different people hold different moral views. This disagreement shows that there are no objective moral truths.

-- No it doesn't. There are lots of cases in which the existence of disagreement shows only that some people are wrong. If one of those depressing surveys of people's geographical knowledge showed that 25% of Americans believed that Botswana was in South America, this would not imply that there was no objective truth about which continent Botswana was in, or that its location depends on one's point of view. It would show that those 25% are mistaken. If one wants to argue from the existence of disagreement about moral claims to the conclusion that no moral claim can be true, one must explain how that disagreement differs from (for instance) disagreement about the location of Botswana, and why the existence of that difference implies that there are no objective moral truths.

b) Objective truths are true because they report or reflect our observations of the world. If you go to the right part of Africa you will in fact find Botswana; you could spend your life combing South America and never find it there. We can check the answer to the question about Botswana; if we do, we will all find the same thing; and therefore we have a way of resolving that disagreement. But moral claims do not reflect our observations, and we cannot use our observations to check them. Therefore they are not objectively true.

-- Not all objective truths report observations. The justification of mathematical claims, for example, involves proof, not observation.

To say that some claim is objectively true is to say that there is some justification of that claim which no one could rationally reject. (The fact that people can irrationally reject any claim at all does not count against the truth of those claims. I could, if I wanted to, insist that President Bush is twenty feet tall. Maybe I am insane; maybe I just like watching you try to convince me that he isn't when I know that I have made up my mind to reject any evidence to the contrary. But that doesn't show that there is no objective truth about his height, or that claims about how tall he is cannot be objectively justified.) The argument under consideration only implies that moral claims cannot be objectively true if all such justifications appeal to observable facts; and the existence of truths like 2+2=4, which do not depend on observation, seems to show that this assumption is false.

c) Moral claims are neither dependent on observation nor mathematical, nor do they follow from pure logic. There are no other valid forms of objective justification. Therefore moral claims cannot be objectively justified.

-- The key sentence in this argument is "There are no other valid forms of objective justification." This claim needs to be argued for. And it is very hard to prove that something doesn't exist, especially when that something is as hard to pin down as a form of objective justification. One can show that something cannot exist if it would be self-contradictory. This is how we know that there are no five-sided squares or ninety year old infants. If any of you can show that the idea of a non-mathematical, non-logical, observation-independent objective justification is self-contradictory in this way, publish your arguments immediately and you will become a famous philosopher.

Another reason for thinking that something doesn't exist is that numerous attempts to find it have failed. This failure does not prove that the thing in question doesn't exist -- people might not have looked hard enough, or they might have looked in the wrong places. It is not clear to me that philosophers have failed in their attempts to justify moral principles. Should you wish to evaluate their attempts yourselves, contact me and I'll give you a reading list. Heh heh heh.

***

That's all I can think of at the moment. Hope it's helpful to someone.

* UPDATE: I thought more about the date; on reflection, I think it was the early 90s.

Comments

[bob mcmanus]

"...in the case of sane child rapists, I do not think that there are any such facts, or that anything the rapist could tell me about his motives or decision would alter my opinion of him and his actions."

I watched The Woodsman just the other night. A little pat and predictable, but the great performances, especially Bacon's, elicited compassion for all the characters. Recommended for any who like challenging movies.

[kenB]

I think I'd understand where you're coming from better if you could explain exactly what you mean by a "moral truth". How do you know when you've got one?

Personally, I think the burden of proof is on the one asserting the existence of moral "truths", since simple observation would lead one to believe that our "truths" are ultimately based on social consensus (since there's no official, universally-agreed-upon rulebook). Your argument at the end sounds a bit like how some believers argue for the existence of God -- just because you can't see Her doesn't mean She doesn't exist. OK, but absent any evidence that She does exist, Occam's Razor leads me to the godless conclusion.

I'm not sure you've made your case for the utility of making moral judgments either, but there again I may just be misunderstanding what you mean by the term. It's of course a good thing for me to work out for myself which standards I should hold myself to; and it's useful to consider the actions of others and see how they fit or don't fit into my moral scheme. But when you write about "moral judgment" or cast someone as "evil", I understand from that that you're asserting that there's some universal standard that the other "should" hold to, that you are not simply giving your opinion but stating a fact. That's a perfectly natural, human reaction, but where is the utility in it? How does it do anything but foster a sense of self-righteousness?

If one has strongly-held beliefs and wishes to force them on others (and all of us do), I believe it's actually better to be honest with oneself and admit that there's no external basis for that judgment -- it's an imposition of will for which one should accept full responsibility and not deflect onto an unobservable "Moral Truth".

[Sebastian Holsclaw]

"since simple observation would lead one to believe that our "truths" are ultimately based on social consensus (since there's no official, universally-agreed-upon rulebook)."

Why should the second clause suggest anything about the first?

[Frank]

This seems a good place for me to admit a secret shame. I do not always read all of hilzoy's longer posts. This one I did and enjoyed. Stuff like this is why I took all the philosophy classes I could in college. I've always used to think that morality, like mathmatics, depends on the axioms that you use. For the last several years I've had a sense that there is a system of morality which would best fit the circumstances humans now face, but I don't think anyone really knows what it is. (myself included)

[Katherine]

"But moral claims do not reflect our observations, and we cannot use our observations to check them."

Do you accept this premise? I don't, at all.

[Slartibartfast]

Um...Katherine, that's one of her cases in point of a bad argument.

Me, I echo ken's question about the difference between moral truth and the more conventional kind.

[Sebastian Holsclaw]

"I've always used to think that morality, like mathmatics, depends on the axioms that you use."

Even in math, there are true things that are not provable. Morality may be a true thing which is unprovable by science.

[liberaljaponicus]

When I was an undergraduate, I was absorbed with reading Albert Camus and after reading him like only an undergraduate convinced he has found the one truth-teller in the world can, I had an opportunity to hear a lecture by A. J. Ayer. In it he made an aside that that Camus couldn't be considered a philosopher because he said that the first question of any philosophy was whether or not we should commit suicide and that philosophy couldn't tell people how to live. That got my dander up, so in the question period, I said that if the task of philosophy is to determine what is real with what is not, isn't it implicitly telling us how to live. He said that was a very good point and he'd have to consider it (I think, this is over 25 years ago. Anyway, I don't remember being humiliated). I guess I wasn't cut out for Logical Positivism...

Going to Wikipedia, there is this anecdote about Ayer

At a party that same year held by fashion designer Fernando Sanchez, Ayer, then 77, confronted Mike Tyson harassing Naomi Campbell. When Ayer demanded that Tyson stop, the boxer said: "Do you know who the f**k I am? I'm the heavyweight champion of the world," to which Ayer replied: "And I am the former Wykeham Professor of Logic. We are both pre-eminent in our field. I suggest that we talk about this like rational men" (Rogers 1999:344).

[Sebastian Holsclaw]

"But moral claims do not reflect our observations, and we cannot use our observations to check them."

Here is an interesting question: Without agreeing to what the exact moral code is, is it nevertheless possible to observe that in certain situations morality is implicated?

Example 1: The ticking bomb/torture hypothetical

Example 2: Using sanctions which hurt a lower class population in order to try to destabilize a regime

Example 3: Child Rape

[hilzoy]

Seb: it may be, but that remains to be seen. Myself, I think there are good arguments in support of moral claims.

Ken: I wasn't trying to show that there are moral truths in the part at the end; just that some common arguments for the claim that there aren't don't work. This of course leaves open the possibility that other arguments do show this; and in fact there have been lots of much better attempts than the ones I put up here.

And Katherine: a lot depends on how you think observation plays in. Suppose you think e.g. that it's important to be kind: you need to notice what matters to a given person, and what she's like, in order to know what kindness to her would be. Likewise, if you think that the consequences of actions matter for whether they are right or wrong, then you;d have to pay attention to the kinds of consequences that certain types of action normally have.

But when it comes to justifying the more basic claim in these cases -- that people should be kind, for instance -- I'm not at all sure how this could be established on the basis of observation -- unless it depended on some even more basic moral claim, about which I;d raise the same question.

[Slartibartfast]

By dividing ways of thinking about morality into "the right way" and "the wrong way", are you exploring a sort of meta-morality?

[Sebastian Holsclaw]

"Seb: it may be, but that remains to be seen. Myself, I think there are good arguments in support of moral claims."

I think so too, but I was trying to take a step back even from that.

[ral]

hilzoy, thanks for starting this conversation.

A long time ago I had a discussion with a rabbi about moral judgments of people. At that time, I took the position that the value in such judgments was that it would help predict what people's future behavior might be.

Nowadays, I am not so sure. I have learned through experience how likely I am to make errors, and how limited my life experience is. And, of course, people can change, although they often do not.

Even taking your example of "2+2=4" (something I deeply believe is true) -- how do I know? I haven't read Principia Mathematica and even if I did and devoted enough effort to convince myself I comprehended it, I could still make a mistake.

So what is the practical value of making these moral judgments and (as I imagine you are suggesting) applying them to politics? I share Katherine's view, for example, of the mendacity of the Bush administration, but what use is it? I find Shrillblog amusing and apt, but will it convince anyone else?

I believe I share many if not all of your (hilzoy's) definitions of "good" (devotion to truth, for example). But I don't see how to apply them other than faithfully pursuing them myself.

-----

By the way, here is an interesting example that just happened to pop up: Paul Krassner on Michael Scanlon. Is it true? It fits with my prejudices but I don't trust that as an indicator.

[hilzoy]

ral: I think that it has to start with faithfully pursuing them yourself. Other applications will presumably pop up without notice. For instance, in the Mississippi thread, I say that the politicians in charge of this should be ashamed. Lo! an unanticipated use of moral language -- and one that I feel perfectly comfortable making.

The use I was thinking of when I wrote this, though, was just: making it clear, presumably in one's own conduct and conversation, that one is comfortable with moral assessment, primarily of oneself. There are enough people out there who have the peculiar view that liberalism is somehow opposed to this that serving as a counterexample would be a service all by itself. (As the Book of Common Prayer says: shewing forth the Gospel not only with our lips, but in our lives.)

[Katherine]

We observe that when other people behave immorally towards us, it sucks. This is most obvious in extreme cases, where the actions run across basic biological imperatives to survive, avoid pain, see your children survive you: "there is no man under the canopy of heaven who does not know that slavery is wrong for him." It sucks so badly that we almost universally decide it is not merely unpleasant to experience these things; it is immoral for others to do them. (Even those who claim not to believe in morality in the abstract, find it hard to shake specific moral beliefs).

We observe that other people seem to be, well, people, independent beings with the same senses and emotions and basic humanity as we have.

If it is immoral for them to do something to us, and they are human beings too, it logically follows that it is immoral for us to do it to them.

So observations aren't enough in themselves, by any means, but they are HIGHLY relevant. (Kant says not so much, right? But from the little I know of Kant I'm not the biggest fan.) And this is why the most immoral acts often occur in cases where people literally don't observe the effects of their actions on other people, or where there's some breakdown in the observation that these people are human beings too.

[hilzoy]

Katherine: I'm with you there. (And Kant would be too, I think. Insofar as I can channel someone who's been dead for a while.) The only problem would be using observation to justify some claim like: I should treat people as I would like to be treated; or: if someone is a person like me, I should treat her as I would want to be treated. That's all I meant.

That said, though, I agree about people who seem not to notice the effects of their actions on others. Morality, it seems to me, requires that one try to become perceptive about such things; avoidable obtuseness is not OK.

[Anderson]

Excellent post. Almost makes me wish I'd stayed in philosophy.

The comments to the "Evil" post were depressing; no wonder Hilzoy wrote this new one. If you're comfortable with the idea of goodness and benevolence, then I don't see how you can be against using their opposites as concepts.

In what different ways people are wicked, how it feels to them, how it's possible to be evil, are interesting questions, but they are not advanced by pretending that there's no such thing as "evil."

Nor is it valid to argue that it's too religious- or metaphysical- sounding. The same applies to "good."

[st]

slart -
a utilitarian meta-morality at that - note that hilzoy's "right way" is, quite simply, the way that accomplishes more, produces more and varied effects, and generates "results" - more self-knowledge, an evolving primer for reacting to future situations, etc.

The "wrong way," OTOH, simply ossifies, and accomplishes nothing except to increase the likelihood that the next situation will be reacted to in exactly the same way as before, out of an unhealthy pleasure principle - certainty is more comfortable than doubt. Less useful, thus less good.

However, this is not an objective judgment that Hilzoy is making - if one wanted to make an argument for tribal self-preservation as the font and basis of morality, then mindless repetition and reinforcement of received social mores may well be a higher good than a moral sense that seeks to "understand," humanize, and thus, in an undeniable way, justify the actions of those that destabilize society by violence, disease, and other destructive traits.

To put it another way, just because Hilzoy has reserved the right to make moral judgments, that does not mean that she has stated their basis. Hilzoy reserves the right to judge the man lecturing the accident victim, but offers no basis for this judgment other than the fact that the lecturer is "heartless."

Hilzoy's ultimate moral arbiter seems to be a gut instinct she follows to make moral judgments. This may be superficially comparable to other non-scientifically testable propositions like "what is beautiful," but in effect, this may be simply throwing the whole question over to the complex web of experience and learned reflex that informs our instincts. As none here can say whether this set of inputs is a more akin to the Jungian vision of a lovely mass synchronistic consciousness or the elemental fears of a crouching cave lizard, it seems to me that the central question - what are we doing when we make moral judgments - remains unanswered.

That said, to the degree we have to pick one or the other, I'm with Hilzoy. The former is as right a way as we're likely to get. Like everything else though, people wind up in the middle, curious and receptive in some contexts; in others, locked in amber.

[hilzoy]

st: I can't really see why you think that I have a 'utilitarian meta-morality', or that my "ultimate moral arbiter seems to be a gut instinct". I don't see that I said anything one way or the other about what my, or the, ultimate moral arbiter is; I was trying, apparently unsuccessfully, to avoid metaethics.

Just for you and Ken (and anyone else who's interested), I have put a .pdf of an article up on my .mac page. In it, I try to justify a substantive moral conclusion. It is not utilitarian, and it's not based on my gut instinct. Enjoy.

[DaveC]

If there are two competing views of morality and one of those decides to fight to win preeminence, and the other decides that it is wrong to fight at all, then the fighter will win. And if fighting is immoral then only the immoral will dictate morality. So in that case, are we obligated to perform immoral acts to preserve our notion of morality, or should we submit and allow others to dictate what morality is at large?

Our own failings, not those of others, should always be our primary concern.

This is probably best for personal morality, but does not work on a larger scale. Leaders of society should in fact reflect on their own failings, but they in fact could not ever change anything if their
personal failings were always their primary concern.

[ral]

hilzoy, you might want to fix the file name (right now it's "A_w_o_C_pdf.pdf.pdf-zip.zip", which isn't really right -- in fact it's a .pdf, not a .zip).

[rilkefan]

"Anyone who finds arguments about beauty or humor unproblematic should ask him- or herself why morality is different."

One difference is that we don't currently put people in jail for having a really bad sense of humor or an unspeakable way with a tercet (sadly in the latter case). We also tend not to run into people claiming there is a correct way to write iambic pentameter or tell a punch line and who make it their business to enlighten us.

[Anarch]

Don't have time to read through the thread (or, hell, the post) in its entirety, but two things jump out at me:

Sebastian: Example 3: Child Rape

I'd be very interested to know historical attitudes towards this -- that is, child rape as opposed to regular rape -- in particular moral systems "uncontaminated" by Victorian adulation of childhood innocence.

ral: Even taking your example of "2+2=4" (something I deeply believe is true) -- how do I know? I haven't read Principia Mathematica and even if I did and devoted enough effort to convince myself I comprehended it, I could still make a mistake.

1) I can prove it to you if you like, from any of a variety of axiom systems (ZFC, PA, Q, whatever).

2) I actually wrote a 3 hour talk entitled "Why does 2+2=4?" [It was supposed to be an hour, but they scheduled another speaker before I edited it down.] Short answer: *shrug* But mine is a most educated kind of ignorance.

[liberaljaponicus]

. And if fighting is immoral then only the immoral will dictate morality

I think you are confusing fighting with resisting. If I say that I won't spend any of my money at this store and convince everyone else to do the same, is that fighting? If I refuse to move from the lobby of a building, am I fighting?

There's a notion embodied in the martial art I do, which is aikido, and I've put up a placeholder post at HoCB that I'll try to write up after, appropriately enough, my aikido class tonite.

[Harald Korneliussen]

Frank wrote: "Stuff like this is why I took all the philosophy classes I could in college."

The scarcity of stuff like this is why I didn't. Thank you, hilzoy, you've convinced me that it's possible to talk sense with philosophers.

Dave C: What happens when a set of moral principles are followed, is not necessarily relevant for saying whether those principles are true. Outcomes depend on many things which are out of our hands - most importantly the moral choices of others.

[Donald Johnson]

The more partisan part of me was hoping people would comment on the conservative "ownership" of moral values. But the discussion here has been very good, a very nice change from the usual partisan bickering.

That said, I'll start with the partisan bickering. In the human rights arena it seems to me that it's the lefties who are, on average, the real believers in absolute moral standards, while the conservatives (again, on average) are the ones who talk about moral absolutes but have a purely tribal morality in mind. When they say we need to distinguish between Good and Evil, they mean we should condemn our enemies and not our friends--if we condemn the crimes of both, we're guilty of the heinous sin of "moral equivalence". There are exceptions to this pattern--lefties who romanticize or excuse the crimes of our enemies and conservatives who are morally consistent, but it's not an accident that Amnesty International and Human Rights Watch are perceived as leftist organizations in the US. (And presumably as reactionary tools of capitalism in communist countries, the ones that still exist.) I think some (not all) of the allergic reaction lefties have to the use of the word "evil" comes from hearing too many rightwingers use the term about the crimes of America's enemies and never about our own actions. Us Christian lefties don't necessarily have a problem with the word. I thought Reagan's use of the term "Evil Empire" for the USSR was apt, though coming from a death squad enabler like St. Ron, it smacked of that hypocrisy I was just complaining about. It's correct to describe a vicious antisemitic crime by Arabs as "evil", but we should also use it about some of Israel's policies. And so on. So if one is going to use the word, in the interests of fairness and accuracy it should be used in ways that will shock or irritate people across the political spectrum.

[st]

hilzoy: I can't really see why you think that I have a 'utilitarian meta-morality'

Well, because you evaluate two proposed purposes for moral reasoning purely in terms of what appears to be their utility, and declare one to be objectively right and the other to be wrong. The right way gives us guidance, helps us avoid unhappiness in our lives and work, gives us a library of "alarm signals" to help us spot potentially dangerous behavior in others, etc., while the wrong way is wrong because it is selfish, a "sneaky . . . self-congratulation," and serves no purpose but to feed a purely internal hunger for validation. Nothing is improved, nothing is learned, there is no utility.

And considering that the first half of your post was not about moral judgments themselves, but rather about preferred perspectives on the making of moral judgments, it seemed to me that the post was specifically about metaethics, rather than an attempt to avoid them.

Honestly, I am punching way above my weight class here, so if the above is nonsense, please disregard. I haven't had a chance yet to read the article you linked above regarding the source of moral judgments, but I will, and thanks for the reference.

[hilzoy]

st: ah. I see.

I was not really trying to argue for the 'right view', above (hence my saying it was tendentious of me to call it 'the right view' -- mild, and no doubt unsuccessful, attempt at humor.) I thought that if people assumed that what I called 'the wrong view' was in fact the only reason why anyone ever engaged in moral reasoning, it would seem pretty awful, and so I wanted to propose an alternative.

Any such view will involve some reference to what, exactly, you are trying to do when you engage in moral reasoning, and thus to the consequences you're trying to achieve. (Similarly: what are you trying to do when you talk to someone? Impart information; pass the time; make friends -- all of these refer to consequences.)

But actually deciding which view is best might or might not involve just looking at the consequences. If I were to actually try to argue for the two views -- as opposed to just laying them out -- I would probably focus more on the fact that only what I called the 'right view' makes sense, while the 'wrong view' seems to have an internal contradiction in it.

The 'wrong view' is not, I'm assuming, just a cynical ploy -- someone who just talks about morality while knowing full well that s/he doesn't care about it at all, and is just pretending in order to pull one over on other people does not hold the view I describe. Someone holds the wrong view if she seems to herself to care about morality, but in fact uses it primarily to demonize others, and to emphasize to herself how different she is from them.

But if morality is worth caring about at all, then what matters, surely, is how virtuous I really am, not how virtuous I think I am. (I suppose one could design a hokey example in which how virtuous I really am is just a function of how virtuous I think I am, but let's not bother with that -- it would in any case not be a counterexample to my claim.) Someone who holds the wrong view, however, seems to be committed to the idea that her own virtue is what really matters, but she's not acting on that view consistently. (Just as someone who thinks that succeeding in her job really matters, but in practice tries not to actually succeed, but only to convince herself that she is succeeding, isn't consistent.)

Does that help?

[Slartibartfast]

I took the wrong view as meaning roughly this: that way-of-looking-at-things that does more to diminish understanding and distinction and encourage an ossified, we're-right-by-definition, positional way of being.

So, wrong in the sense that it tends to run counter to philosophy, i.e. that it works to shut down inquiry.

Have I landed in the same quadrant as the intended meaning?

[Slartibartfast]

Shorter me: "wrong" roughly equates to that which runs counter to the aim of philosophy.

[hilzoy]

Slarti: yes, but I'd add: it also runs counter to the aim of morality itself. (Lots of things run counter to the aim of philosophy without being problematic. Rock-climbing, for instance, works to shut down inquiry, at least while you're actually scaling the cliff face. But caring more about whether you can convince yourself that you're en route to the top while all those other suckers are lost than about whether you actually are en route to the top runs counter to the aim of rock-climbing itself.)

[Slartibartfast]

Rock-climbing, for instance, works to shut down inquiry, at least while you're actually scaling the cliff face.

Oh, I disagree most enthusiastically. Rock-climbing tends to shut down inquiry outside of the immediate interest of scaling the rock in question without killing oneself. The inquiry of how to accomplish the climb is engaged in most rigorously. At least for me it is; maybe that's one of the multitude of things that separates me from the talented climbers.

[hilzoy]

Slarti: true enough. I was thinking of philosophical inquiry, but should have said so.

Trying to do almost anything right involves inquiry of some sort. Trying to convince yourself that you are doing things right, unlike all those other idiots, shuts it down. In so doing it works against inquiry, but also, I would argue, against one's ostensible goal (the goal of whatever it is that one is trying to convince oneself one is doing right.)

[Slartibartfast]

I find that generally agreeable, although I don't see that there's all that much difference between inquiry-into-being and inquiry-into-doing (I'm really sadly lacking in terminology, here). I think both of these, to be done effectively, need to involve an examination of the interaction between self, thoughts, and actions. Probably overly terse, but that's the extent of my thinking. Certainly to navigate from belief in any endeavor is to effectively shut one's eyes to the world.

I've experienced a personal change along these lines. When I first began involving myself in the wonderful world of online discussion, I tended to gravitate to those places where disagreement was actively discouraged, and of course those of us who agreed were Right. I'm not going to tell you where, because you're probably all too familiar with this sort of site. Sometime in the last couple of years, though, I've started to realize that none of this self-congratulatory laying claim to Truth really accomplishes anything aside from making the participants feel all comfortable and cozy in their agreement and righteousness. Which is why I've gravitated here. The mutual-ridicule technique of debating didn't seem to ever result in anyone's thinking being changed, and I was just never any good at it to begin with. Certainly I wasn't persuading anyone, nor was anyone persuading me. In effect, it was just exactly like not discussing anything, only there was more anger and agitation involved.

Even more recently, I've realized that being right has limited utility. I've recently been spot-on in my analysis of an issue related to my work, and in the process of working through it I realized that just being right isn't anywhere near sufficient to the task. Being right and making the case for it to others, that's where things begin to happen. Prior to this I'd been fairly heedless of the value of persuasion; now I'm beginning to think that there's something to that whole public-speaking and presenting thing that's useful and vital.

All of this is coming rather dismayingly late in life to me. Better late than never, I suppose.

Still, I am only an egg. Just when I think I've thoroughly mapped out the extent of my personal ignorance, I discover how ignorant I am about that as well.

[ral]

Slarti, I'm very glad you're here.

[hilzoy]

Slarti: "Just when I think I've thoroughly mapped out the extent of my personal ignorance, I discover how ignorant I am about that as well."

-- You're in good company.

[Frank]

hilzoy- I'm reading your piece, and not that I'm disagreeing with you but you seem to be rejecting the "Forgive them Father, for they no not what they do defence."

Sorry I just felt moved to share that.

[Kent]

A terrific article. Thanks.

I used to teach ethics and religion myself, back in the day. My Ph.D. advisor used to have a way of talking about ethics that made it seem like the most important thing in the world. He would say that the study of ethics is the study of the kind of life that is worth living.

Although you didn't use the same terminology, hilzoy, I got the same feeling all through the first half or so of this article. The "right way" to think about ethics is the way that leads us to think about the kind of life that is worth living, the kind of person that is worth being -- and so to actually lead that kind of life and be that kind of person. The "wrong way" does not point us in that direction at all.

So I was surprised by the interpretation of these remarks as being "utilitarian." On the contrary!

....

The basic point, that liberals need to not abandon moral language to the conservatives, is well taken. It is of course similar to the ever-recurring point made by Ms. Goodman that religion must not be abandoned to the conservatives. Both are true, and worth talking about.

Some people in comments have wondered about the utility of moral language. I would respond as follows.

First, there is a political utility. If liberals never talk about morality, and if when other people talk about morality they feel the need to change the subject, they are going to continue to lose elections.

Second, there is an intellectual utility to having these discussions. No matter how intelligent you are, and how clear you are that morality is "not real" or "not objective" or "just a cover for power" -- it's worth knowing that some very, very intelligent people believe that morality is real and objective. Hilzoy is one of them, obviously, and she has a lot of support in the philosophical literature. It's possible to take the position that morality is not real, but (IMHO) one should do so with the understanding that it is very possible that one is wrong about that. It is a philosophically contentious subject, and rightly so. Belief in objective morality is like belief in dark matter, say, but unlike belief in "intelligent design": it may be wrong, but it's not obviously wrong.

OK, enough babbling. Thanks again for the post, hilzoy!

[susabelle]

Would you mind if I used this in an intro to healthcare ethics course? I taught this to nursing students for the first time last quarter and was stunned when students refused to make moral judgments. They had difficulty saying that there was something wrong with the syphilis experiments at Tuskegee. I'm not kidding.

[kenB]

hilzoy, thanks for the link. I'd certainly agree with the general thrust of the article; but I'm not convinced by your example of an "objective moral claim" at the end. This is mainly because I don't see your statement as being a "moral claim" at all, at least as I understand that phrase -- it's more of an observation about morality. Your claim is that if a person wishes to lead a moral life (however she wishes to define morality), she should actively make choices in a situation of moral conflict. This is hard to argue with, and I have no problem accepting it as being objectively valid, but of course it doesn't speak at all to what moral framework she or we should use when making those decisions, and that's what I think of when I hear the term "moral claim".

Going back to the original point of your post, I think maybe you should expand more on why and how it's useful to pass judgment on others based on your own standards. I don't think anyone would argue against the utility of moral reasoning as applied to one's own life, but passing moral judgment on others would seem to have a lot to more to do with self-righteousness than self-improvement.

To be clear, I don't have a problem with forcing others to follow certain standards of our own -- what I'm questioning is making a categorical judgment. IOW, the difference between "That action horribly offends my moral sense and I'm willing to do anything in my power to prevent you from doing it" vs. "That action is evil and you should not do it". The latter IMO leads to vindictiveness, intolerance, withholding of sympathy & understanding, and lots of other bad stuff, without AFAICT offering any good stuff in return.

[st]

Hilzoy - yes, that did help, as did your back and forth with Slarti, above. At the risk of pissing you off, though, I note that your description of the contradiction within the wrong view is that adopting that view runs counter to the "aims of morality;" in other words, it is not a useful moral perspective as it tends to hamper the expressed goal. Choosing away from that sounds like a utilitarian choice to me. Okay, I'll shut up about it now.

And OT re: Forgive them Father, for they know not what they do
That passage (Luke 23:34) has always bugged me - after the Romans nailed Jesus to the cross and hauled him up, Jesus looked at them and said "Father, forgive them; for they know not what they do." Doesn't this mean that Jesus generally approved of crucifying people? Or, at least, did not believe it was a sin? I mean, the thing that the Romans "knew not" was that he was the son of god. Presumably they were aware that they were crucifying a human being (and political agitator). So Jesus was saying that they should not be blamed for what they did not know, and "forgiven." But they still were nailing people to crosses and leaving them to die horribly of exposure and dehydration. Pretty harsh, if you ask me.

[Urinated State of America]

Hilzoy,

Following on your excellent post, any recommendations on a good introductory text on ethics?

"Prior to this I'd been fairly heedless of the value of persuasion; now I'm beginning to think that there's something to that whole public-speaking and presenting thing that's useful and vital."

Well, remember your education as an engineer: all that you need to do to find the answer is identify the necessary simplifying assumptions and crunch the math. Is it any wonder that we engineer work-units avoid dealing with unpredictable, unreliable meatware?

[ScottM]

As I was reading through, I had the immediate reaction that this should also be related to your discussion about CS Lewis's observations about wanting things blacker. If I could introduce a link, it would be to link: because morality requires generosity to http://obsidianwings.blogs.com/obsidian_wings/2005/02/hatred_is_a_poi.html

Sorry that my comment isn't more substantive. Thanks for a post that has me thinking.

[Slartibartfast]

Is it any wonder that we engineer work-units avoid dealing with unpredictable, unreliable meatware?

Right. But I've realized that other engineer work-units are controlled by mid-level meatware of the sort that don't instantly recognize my solution for the right and perfect thing that it obviously (to other engineer work-units in the same class as myself) is, and take appropriate action in engaging still other work-units in working toward a solution.

Once I got my mental meat-hooks around that the analytical solution doesn't actually solve the problem until implemented, and isn't going to get implemented until someone's convinced that we need to spend the money to implement it, the necessity of honing persuasion skills was kind of a no-brainer.

[Kyle Hasselbacher]

Sebastian Holsclaw: Even in math, there are true things that are not provable.

I'm not sure I believe this. In math, true statements are either proven or axiomatic. There may be things that you believe are true that you can't prove mathematically, but I don't take that to mean that they are true "in math."

hilzoy: The justification of mathematical claims, for example, involves proof, not observation.

Mathematical "truths" are only "true" within their systems. More to the point, math can "prove" things that are absolutely senseless in the "real world." This is not to say I think mathematical claims are not true, but it's a definition of truth that is not universally useful.

A joke that might make my point:

1/2 = 0 (for sufficiently large values of '2')

The "for sufficiently large values of 2" system isn't any more or less true than any other mathematical system--as far as math is concerned.

[mason]

-- Sebastian Holsclaw: Even in math, there are true things that are not provable.

I'm not sure I believe this. In math, true statements are either proven or axiomatic. There may be things that you believe are true that you can't prove mathematically, but I don't take that to mean that they are true "in math." --

Without meaning to be snarky, it sounds as if you should read up on some Gödel. Or, if you are aware of Gödel, I'd be interested in hearing more about what you mean, i.e., why Gödel doesn't provide a counterexample to your claim.

[Kyle Hasselbacher]

I'd be interested in hearing more about what you mean

My understanding of the Incompleteness Theorem (which admittedly is old and frail by now) is that it shows that every one of a certain type of mathematical system can express certain true statements that it can't prove. However, those statements are considered "true" only insomuch as they can be proven in another system. This is a far cry from saying (as Sebastian did) that they are "not provable."

So, I'm still left with: in math, there is no truth without proof (or axiom).

[mason]

However, those statements are considered "true" only insomuch as they can be proven in another system.

My understanding of it is that those statements are simply seen to be true through an understanding of their self-referentialness, not through the possibility of providing a formal derivation of them in some other system. The notion of 'truth' here is indeed that of 'truth-within-a-system,' but those statements are seen to be true within the system in which they are not provable.

However, perhaps an expert will step in here.

[Sebastian Holsclaw]

"However, those statements are considered "true" only insomuch as they can be proven in another system. This is a far cry from saying (as Sebastian did) that they are "not provable.""

Not quite, because even when you expand your system to include other systems there are still true things that can't be proven. That was the really nasty thing (from a completist point of view) about the Incompleteness Theorem.

[mason]

Not quite, because even when you expand your system to include other systems there are still true things that can't be proven.

This doesn't quite address Kyle's claim, though, because including other systems results in different true-but-unprovable sentences.

Kyle was claiming (I think) that the true-but-unprovable sentence in system X is true by virtue of its being provable in some other system Y. The fact that Y then generates its own Gödel sentence doesn't quite answer Kyle, because he can just keep saying, yes, but that sentence is again true because it is provable in some further system Z. (Iterate as desired.)

I think the key is to see that the truth of the true-but-unprovable sentence is not tied to its being provable in some other system. One of the effects of the theorem is to disconnect truth from provability in this way within a single system.

again with the caveat that I'm not a pro at this, though I did have some graduate work in it.

[Slartibartfast]

I gathered that it wasn't so much that there would remaing a particular true-but-unprovable statement, but that even if you could prove the statement in a different system, that system itself would have at least one true-but-unprovable statement.

I'd stay out of this entirely, being fully aware that my above-average knowledge of mathematics is as nothing compared with, say, anyone who's a Senior and a math major. Maybe a Junior; I like to puff myself up from time to time.

[kenB]

In any case, given that the theorem depends on a system having a defined method for distinguishing true and false propositions, it's hard to see the relevance to a discussion of morality (at least until we all sit down together and agree on a set of axioms and operations for answering moral questions).

[Kyle Hasselbacher]

Not quite, because even when you expand your system to include other systems there are still true things that can't be proven.

In what way are they regarded as "true"? What does "true" mean in math, if not proven? (And if we're not sticking to the "in math" context, I'm not sure what we're talking about anymore.)

I don't disagree with what you wrote. When you expand the system to prove the previously unprovable, you still have true things you can't prove. That said, they're still "true" only in the sense that they're provable elsewhere. The fact that we can't (or won't) find the proof doesn't make them unprovable.

[mason]

I gathered that it wasn't so much that there would remaing a particular true-but-unprovable statement, but that even if you could prove the statement in a different system, that system itself would have at least one true-but-unprovable statement.

I agree, and that's part of what I tried to say at 3:29.

In any case, the fundamental nugget of the point is that Gödel showed that, within a given system, truth and provability aren't the same thing. The true-but-unprovable sentence may be formally derivable (= provable) in some other system, but its truth in the system under consideration is not determined by any provability it may have elsewhere.

ok, I'm done, sorry for the threadjack.

[mason]

That said, they're still "true" only in the sense that they're provable elsewhere.

One last time: I think this is where your mistake is. They are seen to be true via an understanding of their semantic property of self-reference, not via any syntactic derivability. I'm pretty sure that's part of the standard understanding of Gödel.

What does "true" mean in math, if not proven?

The theorem raises this question in a deep philosophical way, which is a big reason why it is so important.

[Sebastian Holsclaw]

The thing about the Theorm is that it proves that in ANY system (no matter how comprehensive) there will be truths that are not proveable within the system (no matter how comprehensive you make it). That means that there are true propositions (even in rigorous areas like math) that cannot be systematically proven.

[Frank]

st- Since you were intrigued enough to comment I suppose I'd better clarify my point. Hilzoy in her 01:13 AM comment links to a short article (long blog item) in pdf format. I hesitate to try to sum it up, but what I'm getting from it is that she has an philisophical argument that any reasonable moral system calls for those that practice it to develop a virtue I think of as illumination, a mindfulness or awareness that allows one to chose to do what one does.

She tends to use the example of the Milgram experiments, and I decided to throw one in from religeon. I was implying that I think Jesus felt that the fact that those nailing him to the cross were under orders was a mitigating factor in their sin. I think they probably didn't think of themselves as choosing to drive the nails in but felt it was something they had to do, much as the participants in Milgram's experiments didn't think of themselves as having chosen to electrocute someone as they did it. (or thought they had.)

Obviously if Jesus thought they needed forgiveness for crucifying him, then they were sinning, but possibly he (in his role as intercessor) thought their lack of mindfullness was their best bet for a plea bargan. After all humans aren't equiped to always be paying full attention to everything and be always making thoughtful decisions to boot. That kind of hypervigilance will wear you out mighty fast.

[kenB]

The thing about the Theorm is that it proves that in ANY system (no matter how comprehensive) there will be truths that are not proveable within the system

Actually, no -- check out this section from the wikipedia link given above.

[st]

Frank - that's an interesting reading to the passage, but I wonder if being under orders is expressed by Jesus' statement that they "know not" what they do. People under orders to do something onerous know they are doing evil, but cannot avoid taking the action without (presumably) ceding their own life. Alternatively, you have the good burghers outside Treblinka who would sweep the fine ash off their doorsteps, without wondering why the "work camp" down the road produced so much of it; they "knew not" what they did, but nor were they manning the ovens; in the Luke story, the only piece of information the Roman soldiers didn't have was the fact that Jesus was divine. That, to me, is what they "knew not."

[Anarch]

An expert was called for; I guess I'll have to do.

[Added in proof: ken's link has rendered this largely obsolete, I think, but the hell with it. I ain't throwin' this all away now!]

mason: One last time: I think this is where your mistake is. They are seen to be true via an understanding of their semantic property of self-reference, not via any syntactic derivability. I'm pretty sure that's part of the standard understanding of Gödel.

That's it in a nutshell: we know they're true metatheoretically, not within the theory proper, precisely by "their semantic property of self-reference".

Specifically, G (the Godel sentence) asserts -- and I can make this more precise if anyone's interested -- that "G is not provable". Assuming our derivational calculus is sound, i.e. we can't prove false theorems, G cannot be provable because if it were then G would be false. Therefore, via this metatheoretic understanding of G, it must be true... but not provable.

Of course, then we get into "But what does truth mean?" and immediately fall over Tarski's Undefinability of Truth, but them's the breaks.

Sebastian: The thing about the Theorm is that it proves that in ANY system (no matter how comprehensive) there will be truths that are not proveable within the system (no matter how comprehensive you make it).

I'd normally let this ride, but if we're pushing the littoral regions of the Incompleteness Theorem it's worth mentioning the actual statement of the First Incompleteness Theorem:

First Incompleteness Theorem [Godel, 1931]: There is no (first-order) consistent, complete, axiomatizable extension of PA.

[This is usually rendered in English as: 'Any sufficiently strong theory cannot be complete', where "sufficiently strong" == "extends PA".]

Technical Note #1: This isn't actually what Godel proved but it's the version we're now familiar with and generally what people call the First Incompleteness Theorem.

Technical Note #2: Robinson weakened PA to Q in the 1960s. Kripke's actually shown that Q can be weakened still further to a system he calls SCHOOL, the set of all quantifier-free truths in arithmetic, which represents the ultimate "natural" weakening of the ground system.

Technical Note #3: One can also strengthen the notion of "extension" rather considerably; it suffices that our Godelizing theory can "definably encode" PA (or Q, or SCHOOL), rather than simply extending it outright.

Going over these one at a time, in reverse order:

* PA = Peano Arithmetic, the (first-order) axiomatization of arithmetic. It consists of the usual rules of arithmetic (axioms for addition, multiplication, etc.) as well as the (first-order) induction scheme.

* An extension of a theory T consists of T plus other stuff. And I should warn you, also: in mathematical logic, we use "theory" synonymously with "collection of sentences" without any further restriction. So, for example, {'2+2=4', '3+1=7'} is a theory in this sense of the word (and one which happens to not be consistent with PA).

* Axiomatizable is a little tricky to describe, but in brief: a theory T is axiomatizable iff there is a subtheory T' such that i) every sentence in T is provable from the sentences in T' (so T' is an axiom system for T) and ii) T' is "computable", i.e., there is an algorithm that can effectively decide all the sentences of T'. If the collection T' is finite, we call the theory finitely axiomatizable. It turns out that Q is finitely axiomatizable, but both PA (= arithmetic) and ZFC (= set theory) are only axiomatizable, not finitely so.

[This latter, incidentally, is quite tricky to prove. I could do the ZFC proof off the top of my head, but I'd probably have to look up the proof for PA.]

* Complete means: Given any sentence S, either S or -S (= not-S) lies within the theory.

* Consistent means: no contradiction can be proven from the theory. To use the example I gave above, {'2+2=4', '3+1=7'} is, by itself, a consistent theory. [Try to derive a contradiction just from those sentences!] If we union this theory with PA, however, we do get an inconsistent theory, since it's provable in PA that i) 3+1=4 and ii) 4 != 7.

* First-order is the specific kind of logic being employed here, what most people think of as "real" logic. Key features for these purposes: i) it allows quantification over elements but not subsets of the universe; ii) it admits only of binary truth values (i.e. everything is either True or False); iii) it usually comes equipped with a notion of "proof", aka "deductive" or "derivational calculus", that allows you to infer/deduce/derive sentences given a set of hypotheses.

Whew!

The key point here is that you can have any subcollection of those words strung together; the Theorem only kicks in when you have all of them. Thus, you can have complete, consistent, axiomatizable theories -- even finitely axiomatizable ones!; or complete axiomatizable extensions of Q; or complete, consistent extensions of Q; or consistent, axiomatizable extensions of Q (throw in the Godel sentence G as an additional axiom) and so forth. You can even sort of change the logic -- e.g. first-order to second-order, that sort of thing -- without breaking Godel there... but IME changing the logic ends up breaking something else.*

So what does all this mean? Ummm... I dunno, really. It largely depends on your application. If you're interested in doing the vast majority of mathematics proper -- and I'm including all of applied and computational math here -- there's no real import, since no-one's ever encountered a Godel sentence in the wild, so to speak, and there are massive physical limitations on our computational abilities that kick in long before any Incompleteness. If you're interested in pushing the limits of math, again, it's not particularly useful because, again, you generally don't run into Godel sentences outside of the Incompleteness Theorem itself. [It's useful in the sense that knowing there are undecidable sentences can broaden one's vision when encountering statements that have resisted proof, e.g. there's a small but increasingly vocal contingent who believe that P=NP is undecidable.] Even in set theory, the First Incompleteness Theorem is more of a Cool Result than it is a Useful one; there the Second Incompleteness Theorem rules the day, since it provides a more Useful impossibility. It's potentially useful as tool in undecidability results -- for example, one of my friends showed that a particular lattice-theoretic question was undecidable by essentially encoding arithmetic into the lattices in question -- but there are oftentimes more tractable theories at hand.

It's only in philosophy, or when looking at the Really Big Picture, that the First Incompleteness shines, IMO. And what's amazing about it, to me, is how robust it is: no amount of twisting and turning seems to work. Kripke used to describe it as "the Godel Barrier", the ultimate boundary beyond which our understanding simply can't pass. I don't know if I'd go that far, but it's certainly got the Cool Factor up the wazoo :)

* For example, there is a canonical, decidable sound proof calculus for first-order logic. There isn't a (canonical) decidable sound proof calculus for second-order logic... because if there were, you could essentially use it to break the Incompleteness Theorem by porting everything first-order up to second-order and exploiting the vastly greater power of the second-order proof calculus.

[Frank]

st- I think that the soldiers didn't know that they had a choice. If you had asked them why they chose to put Jesus to death they would have said they didn't. They weren't thinking about what they were doing. The "good burghers" knew more than you give them credit for. They knew that the air smelled like burned meat, and they knew that far more people went into Treblinka than ever came out. In some cases, I'm sure they didn't put those facts together in the obvious way because they weren't that bright, but I'm also sure that in some cases they didn't want to think about the matter because they sensed it would lead in an unpleasant direction. You should read hilzoy's article, you will probably get more out of her more profesional look at the topic.

[Frank]

st- I don't agree with your conclusion here. If killing Jesus was only a sin because Jesus is divine then God is a creep.

[Frank]

I suppose Jesus could have just been asking God not to break out the 'special wrath' but I don't find that an appealing explanation.

[mason]

Anarch: thanks for the expert perspective.

[Anderson]

Interesting if predictable diversion into math, the bane of philosophy IMHO.

I see Plato as so intoxicated by the promise of geometry that he thought that the same degree of certainty and agreement could be generalized to morals etc.

We are just in the past 120 years starting to recover from this misconception.

[st]

Frank - I dunno - maybe not a jerk, per se, but Jesus himself is perhaps a fatalist; realizing that people live in the world into which they are born, and that instead of the soldiers not knowing they had a choice, perhaps they simply didn't know that nailing jews to crosses was wrong; they had lived their whole lives, after all, in a violent, dangerous world where people were killed every day. What they "know not" perhaps is the kingdom of heaven.

But on the other hand, Jesus clearly felt himself to be deserving of exceptions, whether in moral culpability or in smaller things - recall Matthew 26:11, wherein a woman anoints him with expensive oil, and the apostles criticize her for wasting money on finery that could be given to the poor. Jesus rebukes the apostles, and says that their calculation of value is wrong: "For ye have the poor always with you; but me ye have not always."

[Slartibartfast]

Thanks, Anarch, for showing yet again how humble my math skills truly are.

But the bit about useful vs. neato results: bang on. Not that I even so much as consider employing, for example, variational calculus on the job, but I can say that for any purpose such as integrating equations of motion, evaluating the suitability of a given numerical method, etc: this sort of thing rarely ever gets to the point where one has to engage in proofs, never mind proofs of whether proofs are even sufficient.

Further caveat: I still stand in slack-jawed awe of guys like Gauss, so Godel is hopelessly esoteric, to my way of thinking.

[Frank]

st- Good point, I did overlook that.

When Jesus made that remark about the oil he was also making reference to the fact that he was going to die soon. Annointing with oil was something people did back then to prepare a body for burial.

Jesus seems very often to have said things that were true on more than one level.

[rilkefan]

"When Jesus made that remark about the oil he was also making reference to the fact that he was going to die soon. Annointing with oil was something people did back then to prepare a body for burial."

I had not realized that, and it's quite beautiful. Thanks for the heads-up.

[Anarch]

On a vaguely unrelated note -- related only in the sense that I'm watching it right now -- hilzoy, have you seen I Heart Huckabees? And if so, what did you think?

[Winston Smith]

Good job, Hilzoy.

Moral skepticism and relativism on the left is a big problem. It originates in part, I think, b/c the religious right has tried to make the term 'moral' mean something like *puritanical*. So when Smith hears Jones urging us to be more moral, Smith automatically thinks that Jones is urging him to adopt an irrational puritanism. Since liberals generally (and rightly, of course) reject puritanism, they mistakenly think they're rejecting morality.

The discussion of math/logic is telling. This is the way discussions of meta-ethics often go in these informal contexts. If we can draw a lesson from this discussion it's something like this: one common way of rejecting the objectivity of morality entails the rejection of any standards of rationality at all. That is, a common kind of skepticism about moral proof is really just skepticism about proof in general. Now, we might not have an answer to global skepticism, but it's important to show people that they can't pick and choose their skepticisms as easily as they think--that is, that if they're going to profess skepticism about morality, then they may have to profess skepticism about science and math, too. One big error many folks make: thinking that morality is wishy-washy and non-objective but scientific proof is unproblematic. Not so.

Finally: the most important mistake to avoid is KenB's. Casual observation most decidedly does NOT suggest that "our [moral] 'truths' are based on social consensus." First, observation doesn't suggest this about moral truths any more than about non-moral truths. Second, KenB underestimates the overwhelming uniformity in moral belief across societies. The trivial, complicated, probably-merely-conventional stuff like marriage and sexual practices differs alot, but not the central stuff (e.g. beliefs about murder and cruelty). Finally: *truths* can't be based on merely consensus (except, of course, truths *about* consensus). That's a misleading way of saying that there are no truths. Re: moral truths, that's moral nihilism. Now, some want to defend that position, but they should at least be clear about what they are defending. They're defending the claim that there's no (real, objective, non-fictional, non-imaginary) difference between, say, Hitler and Churchill.

[Matt McIrvin]

Part of this may be about words. Many of the liberals I know seem to shy away from saying they have a definite concept of morality, but in fact are perfectly willing to make strong moral judgments (they may call them "ethical" instead). I think they may associate words like "morality" and "evil" with conservative concepts of morality: with divine command theory, an emphasis on punishment and traditional father-led family structure, and the regulation of sex.

[Matt McIrvin]

Also, a trap I keep falling into lately is to let the "right view" of morality devolve into a kind of guilt-driven masochistic parody, in which one seeks out loud, self-righteous critics and lets oneself be bullied by them. It's done in the name of moral improvement but doesn't actually engender anything but fatalistic depression. I suspect that a lot of so-called moral relativism among educated liberals might really be this sort of thing: openness to moral criticism taken to an unproductive extreme.

[Winston Smith]

I think that's exactly right, Matt.

People confuse 'morality is relative' with 'my moral judgments are fallible.' The latter's true, the former's false.

[kenB]

if they're going to profess skepticism about morality, then they may have to profess skepticism about science and math, too.

Why? A given mathematical system has a set of assumptions and a defined process for generating new true statements from those assumptions. The truth of those statements is entirely contained within the system.

You could define such a system for morality as well, if you wish. List your fundamental principles and your method for moral reasoning, and then you can generate moral truths. Except that you'll have shown only that they're true within your system, so only the people who agree to work within that system will consent to be bound by them.

the most important mistake to avoid is KenB's.

Yay, I'm the most important!!

First, observation doesn't suggest this about moral truths any more than about non-moral truths

Note the quotes around "truth" in my statement. Truth exists only within a system that has a definition for truth.

KenB underestimates the overwhelming uniformity in moral belief across societies

On the contrary, that's exactly what I meant -- when people want to identify a given moral precept as an objective moral truth, the first thing they do is point to uniformity across societies. I was working with a broad definition of the term "social".

*truths* can't be based on merely consensus

OK, so then what are they based on, apart from consensus?

Re: moral truths, that's moral nihilism

Not at all, it's moral realism. Absent a universally-accepted moral framework, there's no universal moral truth.

My question to you is, why do you think that the idea that there are no objective moral truths means that we are therefore unable to enforce moral standards? My whole point is that acknowledging the absence of a universal standard forces us to be more honest with ourselves about what we're doing when we impose our standards on unwilling others. After all, if you can't give me any way to prove that a given moral precept is "true", then simply asserting it to be true is no justification for imposing it on those who don't agree with it.

In other words, even if I allow the possibility that there is such a thing as an objective moral truth, pragmatically it makes no difference as long as we have no way to prove that any given precept is true.

[Winston Smith]

Dunno where to start, Ken...

Well, how about here:

"Not at all, it's moral realism. Absent a universally-accepted moral framework, there's no universal moral truth."

Um, no it's not. 'Moral realism' is a problematic term, but the one thing it clearly doesn't mean is what you said. If morality is a fiction (e.g. has no binding rational force), then moral nihilism is true.

You seem to be using the term 'moral realism' as one might if one were to say e.g. "look, let's be realistic: there's no such thing as morality." So I think I understand what you're saying, but that's not what the term 'moral realism' means.

Next:

"My question to you is, why do you think that the idea that there are no objective moral truths means that we are therefore unable to enforce moral standards?"

I don't think I said that, but I might agree with it, depending on what you mean. Of course we COULD impose such standards, but it would be mere bullying if there were no objectively good moral reasons for imposing them. But, of course if nihilism were true then there's nothing wrong with bullying (or murder or anything else for that matter), so such behavior would not be impermissible...though it wouldn't be permissible, either, presumbably, since the nihilist seems to think that nothing is either permissible or impermissible...whatever that means.

Gotta run to class, but finally and perhaps most importantly:

"[me:] *truths* can't be based on merely consensus

[you:] OK, so then what are they based on, apart from consensus?"

Well, your question is confused. Just because consensus can't ground such truths doesn't mean that something else can. indeed if nihilism is true then NOTHING can. I'm not committing myself here to the claim that anything can...I'm just pointing out that consensus can't. Lots of people saying '2+2=5' does not make 2+2=5', even if nothing else can make it true either. That's probably the fundamental relativist confusion.

[hilzoy]

Ken: "Absent a universally-accepted moral framework, there's no universal moral truth."

Is this true in any other field? Does the absence of a generally accepted view of, say, George Bush's exact IQ, or the truth or falsity of string theory, or the exact number of galaxies in the universe, mean that there is no right answer to these questions?

If not, what makes morality different? And why, in particular, wouldn't a convincing argument for some moral theory -- even if it's not generally known, let alone 'recognized', show that that theory was true?

[mason]

KenB said
You could define such a system for morality as well, if you wish. List your fundamental principles and your method for moral reasoning, and then you can generate moral truths. Except that you'll have shown only that they're true within your system, so only the people who agree to work within that system will consent to be bound by them.

Isn't this in fact a big part of what moral philosophers try to do? They try to find elements of a basic framework everyone will accept, typically by using thought experiments or real-world scenarios to generate 'intuitions' -- meaning (as I think Hilzoy recently put it) not hunches, but things we are all prepared to accept. Those then serve as axioms, or are traced back to axioms that imply them, and then it is (hopefully) possible to proceed deductively.

I know that's not all moral philosophers do (well, maybe it was all Spinoza did), but that's a fundamental part of the enterprise, no?

The 'only within your system' line applies, but as I understand it the hope is to find intuitions that are so universal that any system based on competing or incompatible intuitions would be absurd/unacceptable/have no appeal. So the hope is to find a system that will be universal, meaning, inter alia, not tied to a particular culture or ideology, but applicable to us all. ("Qua rational beings," was Kant's version, I think.)

Whether that has a hope of succeeding is not something I wish to take a stand on.

[Anarch]

Just to be annoying:

Lots of people saying '2+2=5' does not make 2+2=5', even if nothing else can make it true either.

Sure they can: simply relabel '4' and '5'. (:

[Slartibartfast]

Just as a completely out-of-my-buttocks stab at the "moral truth" bit, I'd say that as a minimum a moral truth would have to involve no contradictions in any of the underlying arguments. Just as a necessary condition.

Probably lame, but lame is my middle name.

[kenB]

Winston:

'Moral realism' is a problematic term

OK, forget I used it then, I didn't realize it was a term of art.

but it would be mere bullying if there were no objectively good moral reasons for imposing them

I wouldn't call it "bullying" because that has negative connotations. But you didn't address my main point -- if you can't give a method to determine whether a given moral precept is objectively good or not, then how is your imposition of a "moral truth" anything other than bullying? Pragmatically there's no difference, except in the attitude of the imposer -- justifying your "bullying" by calling it a moral truth is simply deflecting responsibility. Why not just give all the reasons people usually use as evidence of a moral "truth" as the justification? Why insist that the precept is either somehow written into the fabric of the universe or it's not valid at all?

Hilzoy:

Does the absence of a generally accepted view of, say, George Bush's exact IQ, or the truth or falsity of string theory, or the exact number of galaxies in the universe, mean that there is no right answer to these questions?

As far as I know, one's IQ is determined by the results of a specific sort of test. A person has an "exact IQ" to the extent that s/he always gets the same score on such a test. If George scores differently on different valid IQ tests, then no, I don't think there is an answer to the question -- it's not an essential attribute of a person. Binet himself said "my test measures what my test measures".

The term "galaxy" refers to a particular set of characteristics, and so perfect observation could determine how many things with that set of characteristics exist. As long as there's consensus on how one defines the term and the definition isn't ambiguous, there's a right answer.

I'm not sure what you mean by the "truth or falsity of string theory" -- to the extent that it's meant to describe the physical world, the question is how well it models observable phenomena, not whether it's "true". The theory of gravity isn't "true", it's just the best model of a class of phenomena that science has come up with at the moment.

And morality is different from these because it's addressing what "should" be, rather than what is. You can make all sorts of observations about commonalities of different moral systems, their different assumptions and consequences, but observation will not get you to what "should" be except with prior agreement about how to evaluate them.

And why, in particular, wouldn't a convincing argument for some moral theory -- even if it's not generally known, let alone 'recognized', show that that theory was true

What do you mean by "convincing" -- who's being convinced? As long as X number of people accept your fundamental assumptions and your chain of reasoning, your theory is true for that X number of people.

[Winston Smith]

Ken,

I think we may be agreeing on a major point; tell me whether I'm right.

I think we agree that forcing someone to act in a certain way without good reason is unjustified (roughly: bullying). So, if there are no such things as good (moral)reasons, then when we force people to be (note scare quotes) "moral", we're really just dignifying our bullying.

Is that right? I.e., do we agree about that?

In addition to that I think that you think that we have no methods for separating good reasons from bad reasons in the moral sphere. I think you're saying that in the absence of such methods it doesn't make sense to say that what we do in any given case is moral.

I'm sort of inclined to agree--but not really sure about it--that without some method for identifying moral truths AS moral truths, we'd have no right to call some things moral truths. (Without such methods our getting it right would just be luck. Though I'm reading Kant's third Critique right now, so I may want to take that back if I ever understand this beast. He seems to think there are some judgments we can be justified in making even if we don't know the rule that warrants the judgment.)

However, *I* think (FWIW) that we have some criteria for distinguishing truths from non-truths in this realm. For example, moral truths seem to be universalizable--that is, if you are obligated to x because and only because you are F, and I am F as well, then I'm obligated to x as well. This is, of course, where things get tricky, but morality seems to demand something like a respect for humanity, or for persons as ends in themselves, or whatever. But it at least requires universalizability--i.e. treating like cases alike.

Now, you might respond that that's kinda sketchy, or that there's disagreement about it, or that we're not sure about it, or whatever. I'd agree that it's sketchy (though not that there's much disagreement about it...but whatever.)

But that's where I'd point out that the math discussion earlier is relevant. With regard to the philosophical foundations of logic, or of science, we're every bit as much in the dark as we are about the philosophical foundations of morality. Maybe more, actually. When we start, e.g., trying to explain why it's rational to believe that the external world exists, or why it's rational to reason inductively, we end up giving accounts that are uncertain, subject to dispute, etc. Most of them are disasters, actually.

I'm inclined to think that certainty isn't required in order to have good reasons, but I have great sympathy with those who think otherwise. I just want to point out that if uncertainty (esp. about foundational matters) entails skepticism, then it does so both places--i.e. in the case of morality as well as in the case of science.

Not to be too long-winded here but I do briefly want to emphasize the point in which I have the most interest: that once we've begun to discuss THESE points--which are genuinely interesting and important--we've left far behind the view that consensus could be enough to ground truth.

Anarch points out jokingly that we could just start using the numeral '4' to mean five...and, of course we could start using the words 'morally right' to mean *agreed upon.* But that wouldn't make 4=5, nor would it make *morally right* the same as *agreed upon*. It would just change the meanings of the words. Everybody agrees that we could do that for anything...but calling lead 'gold' and turning lead into gold are completely different things.

Well, anyway.

[Winston Smith]

Ken,

After a quick glance at your reply to Hilzoy, I think I may have identified the source of our disagreement.

You seem to be a verificationist or something. If that's true, then we'll probably have to go farther back to find principles we'd both agree on in order to make progress on these points.

Though at the end of that reply you again assert something that seems to entail that truth and agreement are the same thing...so maybe not.

Could you explain how you think that my believing something makes it true (for me, or whatever)? Presumably you aren't just using 'true for me' to mean *believed by me*, right?

[rilkefan]

"I think we agree that forcing someone to act in a certain way without good reason is unjustified (roughly: bullying)."

What if that good reason is we want to, it gives us great pleasure, it relieves our suffering?

I still think there's a relatively easy disproof of morality as anything other than arbitrary by describing a morality as a map from the set of behaviors to the reals and noting that claiming there exists a privileged ordering of the maps from the set of moralities to the reals is silly.

[Anarch]

Winston Smith: Anarch points out jokingly that we could just start using the numeral '4' to mean five...and, of course we could start using the words 'morally right' to mean *agreed upon.* But that wouldn't make 4=5, nor would it make *morally right* the same as *agreed upon*. It would just change the meanings of the words.

That's true, but on reflection I think I was making a deeper point than I realized. Essentially, the reason we can argue that relabelling the numerals doesn't change the underlying fact that 2+2=4 is that there's an objective semantic dereferencing that's built in to the very concepts themselves. Specifically: whatever we call the gadget '4', it's fixed into its relative position by the rest of the theory; hence the theory (indeed, the model) remains isomorphic on changing the labels, i.e. the semantics remain invariant under the switch.

To illustrate with a little more precision: in PA, '4' doesn't exist as a numeral, it's a circumlocution we use in the metatheory for the actual term 'SSSS0'. The essential character of this term, it's "4-ness" if you will, is governed by the interaction of this term with other terms as moderated by the axioms of the theory. That "4-ness", in turn, will exist in any system where the ambient axioms applied to the given term -- which could be 'SSSS0' or '4' or 'Xenon' or whatever -- cause it to interact with the other terms in the "4-ness" way.* Technically, this is semantically encapsulated by notions of "isomorphism" and syntactically encapsulated by "atomic diagram" (or "elementary diagram" if you need a bit more firepower).

The catch is that when speaking of morality, we don't a priori have this kind of semantic dereferencing built into the system. If I say something is "good" and you want to know whether or not it really is good, there's no objective way to dereference the predicate and check to see whether the object indeed has "goodness". Such a dereferencing may indeed exist, but the mere fact that you're still hacking through Kant in search of it suggests to me that its immediacy is woefully lacking.

[Not to say that there's anything wrong with hacking through Kant. I pride myself in understanding at least 2 of every 3 words he uses, at least in my own special way.]

* This is a particularly category-theoretic way of looking at the matter, now that I think about it: nothing exists in itself in any meaningful way, they're purely characterized by the nature of their interactions with other objects. Ultimately, I'd say that's true of arithmetic; nothing exists in vacuo, only in their relationship with other numbers. In fact, that's explicitly how non-zero numbers are defined in most foundational systems; '1' is the number that follows '0', '2' follows '1', and from this all the rest follows.

rilkefan: I still think there's a relatively easy disproof of morality as anything other than arbitrary by describing a morality as a map from the set of behaviors to the reals...

How do you know that morality implies linear ordering? Isn't that an awfully big assumption to make?

[Winston Smith]

Rilkefan,

You and your zany "map of behaviors to the reals." Why to the reals? Because you think that the number of human actions is non-denumerably infinite? Or what?

If this is the kind of thing you're thinking then (since you're not here to ask) I'm going to guess that it's because you think that (roughly) every human action has to be given a unique place in a "ranking" of more justified to less justified actions.

But my line on justification, in case anybody's interested (note: they're not): to refute nihilism we don't have to show that there's an objective ranking for everything in the given domain. Rather we have to show that there's a ranking of *something* (which probably means at least two things) in that domain. Of course we think (and hope) we can evaluate ("rank") more than just two actions, but two is all it takes for nihilism/skepticism to be false, strictly speaking.

That is, so long as there is at least one action that is really better than at least one other action, then nihilism is false.

This is actually more interesting than you might think (I'll have you know) because many relativist/nihilist/skeptical arguments take the form of some arguments we've seen here: that is, they point out that some things apparently can't be "ranked", and conclude from that that morality is crap. But the non-nihilist non-skeptic need not say that. He need only say that SOME things can be "ranked."

In fact, nobody--not even Pat Robertson--thinks that everything can be moraly "ranked", since lots of things fall into the same evaluative category. Most actions are, for example, neither obligatory nor forbidden...they're just permissible.

Anarch,

I don't exactly understand your point, but in part because I'm not familiar with the terminology "semantic dereferencing"... I guess it goes without saying that I agree that 4 = SSSS0...though (not to be picky here) I'm not sure I'd agree that '4' is a circumlocution for 'SSSS0'...they're just co-referential terms. They both denote the number 4 (if you believe in that sort of thing).

So that's where I have to stop until I find out what it means to dereference a predicate (or expression generally). Is this something akin to disquotation or something? Inquiring minds wanna know.

[rilkefan]

"How do you know that morality implies linear ordering? Isn't that an awfully big assumption to make?"

I don't think my "argument" rests on using R, or Rn, or some infinite Hilbert space.

WS, I didn't claim that the map had to be onto. I think you're saying that there are b_g, b_b in the set of behaviors such that for any m, m(b_g)>m(b_b). I assume you're thinking there are b_n such that for good/bad pairs above, m(b_g) > m(b_n) > m(b_b). Ok, you already lost me at bad and good, but I now have a set of m that meets your criteria: is any a priori ordering of the m possible? I can't imagine any.

[Anarch]

I guess it goes without saying that I agree that 4 = SSSS0...though (not to be picky here) I'm not sure I'd agree that '4' is a circumlocution for 'SSSS0'...they're just co-referential terms.

They're not, though, at least in mathematical logic. 'SSSS0' is a term in the language of PA and, as such, is part of the theory proper; '4' is a metatheoretic abbreviation for 'SSSS0', used because writing 'SSSS0' is a pain in the ass. Upon interpretation -- the formal term in mathematical logic for what I'm more loosely calling "semantic dereferencing" -- they both refer to the same object (which, if your model is at all sane, is what we'd call the number 4) but they do so because one is an abbreviation for the other, not because they're both independently evaluated to the same object.

To be even more precise, and forgive me if you already know this stuff: an intepretation of (the language of) PA is a map from the symbols of the language of PA to the model in question, matching constants with elements, function symbols with functions, and so forth. The key point here is that because PA doesn't have '4' as a constant, '4' never gets interpreted; instead, we designate some c in our model as (the referent of) '0' and then interpret the unary function symbol 'S' as a "successor function" f. The reference of 'SSSS0' is thus consequentially defined as the result of applying f to c four times, i.e. 'SSSS0' -> f(f(f(f(c)))). At no point do we ever jump the gun and give '4' a notion independent of 0 or S (or c or f); it's purely an abbreviation in the metatheory for the actual nuts-and-bolts of the construction.

[It would be possible to construct a variant PA in which you had constant names for all the (finite) integers... but then you'd have to throw in a crapload of new axioms related these new names to the existing structure of PA (e.g. "4 = 1 + 1 + 1 + 1") in order to make it cohere with the old one, which it will to no useful effect. This is unsurprisingly known as augmenting by defined symbols (sometimes augmenting by definitions) and it's a useful technique pedagogically, if worthless mathematically. Of course, when you start adding constant symbols for integers not expressible as 'SSS...SS0'... well, that's when things start getting interesting.]

I don't exactly understand your point, but in part because I'm not familiar with the terminology "semantic dereferencing".

That would probably be because I made it up on the spot :) Hopefully the above makes it clearer.

If not, I'm sort of sneakily invoking the Platonist view that numbers really "exist" in some objective sense, either as concrete abstract objects -- whatever that means -- or via a formalist/category-theoretic belief that whether or not there's an actual gadget that is the number four, the quality "4-ness" is completely encapsulated by the relationship that '4' (really, 'SSSS0') has to the other numbers. IOW, there's an actual semantic content to "4-ness" that means we can dereference the symbol '4' (blah di blah 'SSSS0') in an objective fashion.

[If you're comfortable with technical terminology, '4' (whibble SSsss) can either be dereferenced i) semantically within ZFC as the set {0, 1, 2, 3} (von Neumann ordinals) or {0, 1, 2, 3 | } (Conway games); ii) syntactically within PA as 'SSSS0'; iii) syntactically and semantically as an isolated type, in some sense, over PA. {It's a doofus type since '4' is actually definable, but whatever.} And of course, iv) as our understanding of iv. Once you've decided how you want to "understand" '4', you can be as precise and objective as you like, if not necessarily useful.]

Now obviously, at some point this will have to degenerate into turtles all the way down; everything foundational does. My point is that I don't see morality having the same immediacy of dereferencing, a way of canonically -- definitionally -- mapping behaviors/attitudes/beliefs to notions like "good" or "evil". I'm not saying that such notions don't exist -- I don't really know what I believe about this, actually -- merely that there's no way to do so in any a priori meaningfully objective fashion. It may ultimately devolve into the other bugbear of foundationalism, namely, we all tend to agree on what "four" should mean, and we all tend to have profound disagreements about what "evil" should mean, so "objectivity" in this case might be a code for "hardwired into our psyches" or something; but it says something, though I don't know what, that we don't generally get disagreements about "4-ness" and we do about "evil". And it says something, though I don't know what, that I can produce a definition -- a number of them, actually -- that most everyone who's studied the matter would agree is a valid definition of '4' (although perhaps not the "correct" one), but the same doesn't appear to be true in notions of morality.

[Anarch]

I don't think my "argument" rests on using R, or Rn, or some infinite Hilbert space.

I'm sorry, I sort of assumed that by mapping everything to the reals you were implicitly assuming that "gooder" behavior corresponded to larger numbers. Not sure why you'd want a general Hilbert space -- is there an algebra of moralities? -- although I can certainly see an attraction in having infinitely many "dimensions" of morality along which each different behaviors can be ranked.

That said, I've always been attracted to the topos way of looking at things, where truth values aren't chosen as merely "True" or "False" but rather open sets in some topological space.* It gives not just a notion of intermediacy of truth values -- something which a lot of alternate logics, e.g. fuzzy logics and continuous logics, possess -- but also a notion of localization, of being true "over there" but not "over there". Or something like that. I could certainly see morality being formalized in something of the same way; the "morality" of an act would the open set here, where the entirety of the space would count as "perfect good" and the empty set would count as "perfect evil".

Your Mileage, Can, Will, and bloody well Ought To Vary here.

* OK, so that's not quite the same thing, but it's close enough.

[rilkefan]

It's a bit hard for me to speculate on the exact setup given that I don't think there is a sensible coherent description of morality. I would guess WS is talking about disjoint sets which can be ordered - there are neutral acts (scratching an itch), good acts (petting a kitten), bad acts (eating a puppy), and presumably eating two puppies or petting two kittens are either the same sort (ordinality?) as the single-pet equivalents or not, in which case he's talking about something along a range of R or the whole thing, I think.

I think D&D had a scheme where actions fell on the good/bad chaotic/order plane, and one might think chaotic good and lawful evil are equivalently immoral, or not.

[Winston Smith]

Anarch,

Whew. Lots of stuff here, but to start with:

You write:

"They're not, though, at least in mathematical logic. 'SSSS0' is a term in the language of PA and, as such, is part of the theory proper; '4' is a metatheoretic abbreviation for 'SSSS0', used because writing 'SSSS0' is a pain in the ass."

I've never, ever, ever heard this before. I'm not saying it's not right, but I've never heard it. 'SSSS0' IS a term in PA, but '4' is a term in the language of mathematics. So in PA '4' is introduced to abbreviate 'SSSS0'...but that's just *from the perspective of PA*. 'SSS0' isn't even defined outside of PA to the best of my knowledge...so, though we could speak both ways, it's less contrived to just say that '4' and 'SSSS0' are co-referential. They are the translations of each other in their respective languages.

You write:

"Upon interpretation -- the formal term in mathematical logic for what I'm more loosely calling "semantic dereferencing" -- they both refer to the same object (which, if your model is at all sane, is what we'd call the number 4) but they do so because one is an abbreviation for the other, not because they're both independently evaluated to the same object."

O.k., I know what an interpretation of a formal language is...but 'semantic dereferencing' doesn't seem like a perspicuous phrase for capturing that idea. I'm not complaining, I'm just saying. Anyway, it just isn't true that they co-refer primarily because '4' is an abbreviation of 'SSSS0' in PA. Rather, they co-refer because they refer to the same object, or because they are translations of each other in their respective languages. '4', after all, wasn't chosen arbitrarily as an abbreviation of 'SSSS0' in PA. Rather, in fact, '4' came first, and 'SSSS0' was later introduced as part of a formal theory that was supposed to say something interesting about 4 &co.

I understand interpretations of formal languages fairly well, though I have to confess that (*ahem*) I've never got around to learning category theory...but I don't really see how any of this helps us here.

Anway, I know we're not even getting to the important stuff here yet...and actually I don't think any of what I've discussed so far really helps... we haven't really touched morality. I think your big point may be that the foundations of math are more secure than the foundations of morality. But that's not all that clear. None of this stuff matters if, say (and speaking of Tortoises) the tortoise is right and Achilles is wrong. Skepticism about *modus ponens* is possible, too.

In fact, I'm inclined to agree with Perice who thinks that mathematics is fundamental and logic derivative...so logic doesn't really make math any more certain or well-grounded than it was already.

Anyway: I really think we're off base here.

But I've recently resolved to spend less time on the internet... So I gotta to do something else. Maybe more later in case it matters, which it probably doesn't.

[Anarch]

I think your big point may be that the foundations of math are more secure than the foundations of morality.

Not exactly; I'm saying that it's more immediately clear that the concepts are well-defined in foundational math then they are in foundational morality. And also that "objectivity" is better-defined in foundational math than in foundational morality, too, although I'm not entirely sure what I mean by that.

IOW, I'm still pondering whether your claim that Lots of people saying '2+2=5' does not make 2+2=5', even if nothing else can make it true either. -- which I more or less believe -- actually relates to the issue of morality, at least in any immediate way. And that's partly because there's a notion of truth (or maybe objectivity?) in foundational math that, to me at least, is more immediately accessible than in foundational morality.

IOW, I'm not disputing that there's no such thing as an objective (extrinsic?) morality. I tend to doubt there is, but I don't really feel well-enough informed to say. I am, however, claiming that the valuations such a system would possess are significantly unlike the valuations on sentences like "2+2=4" or "2+2=5" in arithmetic; and that the differences are accounted for in large part by our ability to map the numeral '4' to the number "4" (etc, etc) in a much more profound way than our ability to map the word 'evil' to the concept it supposedly names.

Or at least, trying to claim. I haven't exactly been the model of clarity here in large part because not even I am exactly sure what I'm trying to say.

O.k., I know what an interpretation of a formal language is.

Oops, sorry. I was afraid that was going to happen; half the philosophers I know do and half of them don't, and I always seem to guess wrong.

In fact, I'm inclined to agree with Perice who thinks that mathematics is fundamental and logic derivative...so logic doesn't really make math any more certain or well-grounded than it was already.

As Achilles might say, it's Tortoises all the way down :)

[I'll forebear any more mathy stuff unless someone other than me is interested...]

[Sebastian Holsclaw]

"I am, however, claiming that the valuations such a system would possess are significantly unlike the valuations on sentences like "2+2=4" or "2+2=5" in arithmetic; and that the differences are accounted for in large part by our ability to map the numeral '4' to the number "4" (etc, etc) in a much more profound way than our ability to map the word 'evil' to the concept it supposedly names."

This is interesting. I suspect that most people would feel they can map 'evil' to the concept it supposedly names much more easily than most people could map i or e (the mathematical constants) to the concepts they supposedly name. People can get a kind of intuitive understanding of pi at least, but lots of people really never get the other two. I think the idea of evil is a lot like pi--just because I can't give you the exact decimal value doesn't mean I can't get a very useful working approximation.

[Russell]

I understand that, in the context of a philosophical discipline, it's desirable to formalize an understanding of morality. My sense is that that is where the analogies to mathematics and logic presented upthread come in.

I think that's wrong headed. The quanta of value -- the valuable things -- in moral thinking, vs logical, systematic thinking, are not commensurable.

Morality exists in relationships between persons. A moral relationship is one in which each party recognizes that the other is a person just as they are, and acts accordingly.

For those inclined to include God in this equation I'd say the result of doing so is to make seeing others as being "just like ourselves" that much easier, because in the context of an immanent divinity differences between humans, even at the extremes, become minimal.

On the topic of the moral basis of liberal political thought, here's how I make it out.

Liberals believe that people who participate in a political community bear, by virtue of that participation, a responsibility for each other, and also believe that public, civic institutions -- government -- are a perfectly good vehicle for fulfilling that responsibility. Conservatives tend to reject either the first or second clauses of that statement.

I think that liberal vs conservative opinion on the latter issue -- whether government is a good vehicle for members of a community to carry out their responsibilities toward each other -- is informed by whether you see government as an integrated part of society (a more liberal view) as opposed to being separate from, and in some ways hostile toward, society (a more conservative view).

Thanks -

[hilzoy]

Anarch: "Lots of people saying '2+2=5' does not make 2+2=5', even if nothing else can make it true either.

Sure they can: simply relabel '4' and '5'. (:"

-- Oddly enough, I had something about this in the first draft, but cut it out, thinking: surely no one will say that... ;)

ken: "As far as I know, one's IQ is determined by the results of a specific sort of test. A person has an "exact IQ" to the extent that s/he always gets the same score on such a test. ...

The term "galaxy" refers to a particular set of characteristics, and so perfect observation could determine how many things with that set of characteristics exist. As long as there's consensus on how one defines the term and the definition isn't ambiguous, there's a right answer...."

-- Here you seem to have moved from the claim (a) that there needs to be consensus on the answer to a question to (b) that there needs to be a consensus on how to answer it. I agree. But note: there are recognized ways of moving from one claim to another so as to preserve the truth of the original assumptions. They are called 'logic'. Suppose a valid argument from some premise that your interlocutor accepts to a moral conclusion: would that not count as showing that your interlocutor ought to accept that conclusion? And wouldn't that be a recognized method of justifying claims?

If so, then we're back where I said we were: at the claim that whether or not moral claims can be justified depends on whether there are good arguments for them. This, I think, remains to be seen.

[kenB]

Suppose a valid argument from some premise that your interlocutor accepts to a moral conclusion: would that not count as showing that your interlocutor ought to accept that conclusion? And wouldn't that be a recognized method of justifying claims?

Sure, but only for people who accepted those assumptions. In practice, there may be a decent-sized set of assumptions that would satisfy most people living today and that would allow you to reach some non-trivial conclusions. To the extent that people are open to moral reason, this may well be a useful exercise. But your conclusions still couldn't be called objective or absolute, in the ordinary sense of those terms.

Perhaps, as mason suggested, if you came up with a set of assumptions that was a minimum set for anyone doing any sort of sensible moral reasoning across all time and all societies, you could conceivably call any conclusions you reached "objective" moral truths (with an asterisk), but I'm skeptical that there exists such a set that generates any interesting claims.

[hilzoy]

kenB: Now we're making progress: we've moved from needing a consensus about ethics as a whole to an agreed-on method of deciding moral questions; we've agreed that logic (and reason generally?) is such a means; and we're now asking whether there would be any premisses for such an argument to start from that wouldn't be mere assumptions about which people could disagree.

At this point I'll bring up the article I linked to. Its main argument (sec. 3) proceeds from premisses that I think are not mere assumptions. Namely:

(a) Suppose you have some view about how you should live your life. It need not be highly articulate, or in any normal sense "moral", nor need you think it is justified. It just needs to involve the idea that some sort of life is better (according to you) than some other.

(b) Whoever wills an end wills any means necessary for realizing that end.

(implicit premiss c: having a view about how you should live your life is setting yourself the end of living that way.)

From a, b, and c: (d) If you have some view about how you should live your life, and you need to do something (call it X) in order to live that way, then you should do X.

Example: suppose you think that you should try to become a world-class swimmer. Practicing swimming is a necessary means to this end. So if you want to be a world-class swimmer, then you should practice swimming. -- Not too controversial.

But suppose that there is something -- call it Y -- that is a means not to living in some particular way, but to living whatever sort of life you think you should lead. Then it would follow from (d) that if you think you should live any (specific) sort of life at all, then you should do Y.

(The argument then proceeds to identify a value of Y.)

Now: is "I have some idea of how I want to live my life" just an assumption that someone could choose to reject? Suppose I try: I decide to live completely at random, by throwing dice. Oops: that's a way of living, and I'm deciding to live that way. I decide to drift along like a little twig on the stream of life, but oops: I'm doing that deliberately, not really drifting at all. I decide to kill myself: oops! yet another deliberate action. Is this really rejectable?

[Frank]

hilzoy- "Is this really rejectable?"

I didn't think so, although I used to argue about logicaly contradictory things with my Phil profs.

Just because you can't imagine a five sided square doesn't mean there isn't one. Perhaps seeing one is like seeing Cthulhu, how would you know?

[Anarch]

Sebastian: I think the idea of evil is a lot like pi--just because I can't give you the exact decimal value doesn't mean I can't get a very useful working approximation.

You absolutely can, as can most everyone else. The trouble is, where virtually everyone will agree on "4-ness" -- quibbling only over which version we should take as the "official definition" and which ones are consequences -- I don't think you're going to get anything like the same agreement when speaking of "evil". What's more, if forced to justify one's notion of "4-ness" as versus one's notion of "evil", you're far more likely to have the numerical notion considered objective and secure (?) than with "evil".

I completely agree that e, pi and i don't have this same universality -- sci.math used to, and for all I know still does, erupt in periodic flamewars involving the definition of pi -- although I'd argue again that in some way there's a distinction between their definitions and moral ones. I'm not sure how to express this, though, without descending into far greater mathwankery than anyone (least of all myself) wants to see... and even then, I'd probably be wrong.

hilzoy: -- Oddly enough, I had something about this in the first draft, but cut it out, thinking: surely no one will say that... ;)

You underestimate my enormous tracts of... pedantry. (:

[mason]

Anarch, if you are still reading down here, here's a somewhat tangential question for you that occurred to me tonight:

I was thinking about completeness and consistency, and it occurred to me that consistency is considered important in formal systems because: inconsistency means there's a contradiction somewhere in the system, and that in turn means you can prove anything in the system (thus rendering it useless).

But that depends on the formal feature of implication/modus ponens whereby a contradiction lets you construct an argument for absolutely anything, because (p & -p) --> q for all values, because (p & -p) is always taken to be false, and the conditional as a whole is thus always true, no matter what q is.

My (probably stupid) question is this:

In a system that contains/implies a contradiction, why is (p & -p) to be evaluated as false? If the system supports them both, why not evaluate (p & -p) as true? (Since they are both provable in the system.) In that case you wouldn't be able to just automatically run [(p & -p) --> q] as true no matter what.

I know that it's standard to simply regard (p & -p) as false by definition, but trying to see it as I've just described strikes me as no weirder than imaginary numbers, or denying the parallel postulate in geometry.

I'm vaguely reminded here also of Wittgenstein asking "Contradiction? Why just this bugbear?" (or whatever charming locution he used.)

(-- the idea there being, perhaps, that just because the contradiction lets you in some formal sense derive whatever you like doesn't mean you have to actually do it. The actual practice of deriving particular consequences is finite, comes to an end somewhere, and is pursued only relative to concrete, practical ends.)

I suspect I'm making some elementary mistake here, but I'm going to post this anyway.