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The Geometry of Desert: Moral Philosophy (Shelly Kagan)
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Welcome to the Deep Dive, your shortcut to being truly well -informed. Today we're tackling a concept that's, well, fundamental in ethics but often feels abstract. Desert. What you deserve. And we're not just talking about it, we're actually going to give it shape. Literally. I mean, this idea of desert, it shapes everything, right? Criminal justice, resource allocation. But philosophical discussions can get a bit murky. So our source material today... offers something pretty amazing, a philosophical framework that uses geometry, graphs, slopes, peaks, you name it, to model moral value itself. Our mission, to take these abstract gut feelings about fairness and turn them into something visible, something almost quantifiable. We want to understand what you deserve, not just intuitively, but maybe even mathematically, and see how these geometric models actually guide applied ethics in the real world.
It really is a fascinating approach. You know, growing graphs in moral philosophy isn't exactly common practice, but it's incredibly clarifying. By demanding this kind of rigorous structure for concepts like virtue or suffering, the geometry gives us a really perspicuous way, as the source puts it, to see the differences between moral viewpoints, differences that often get lost in just, well, It turns disagreements into something you can actually point to on a chart. Exactly. It makes the complex visible. So, yeah, let's dive into the structure. OK, first things first.
Let's get our terms straight. When we talk about moral desert for the next, say, half hour, what exactly are we zeroing in on? Right. So at its core, moral desert is tied directly to an individual's moral worth. Think of it as their overall level of virtue or vice. And that worth becomes the basis for determining the outcomes they should receive. Basically, the better someone is morally speeding, the more they deserve to be, well, better off. Better off, meaning like happier or... It could mean several things. Higher well -being is the most common one. Yeah, like happiness.
But it could also be things like praise, admiration, maybe even resources, depending on the context. Got it. So it's not just a feeling. It's a claim about... how things ought to be arranged for that person a moral claim precisely and that leads straight into the really fundamental value claim here the idea that it's an intrinsically good thing morally speaking when people actually get what they deserve intrinsically good meaning good in itself not just because it leads to something else exactly a world where desert is satisfied is just well better from this moral standpoint, even if nothing else changes. The value is in the matching of outcome to desert, period. That distinction is important. Intrinsic versus instrumental value. Okay, so where does this moral worth come from? Is it just adding up good deeds and bad deeds? Yeah. Or is there some kind of starting point? Yeah. Traditionally, it's heavily based on virtue and vice, your actions, your intentions, that sort of thing. That's the primary driver.
However, the framework we're exploring today highlights a really compelling alternative view, one that avoids starting everyone off at zero, morally speaking. What's wrong with starting at zero? Well, think about it. If you start at zero, you have to actively do good things just to become someone who deserves anything positive at all. Right. You'd have to earn your way into deservingness. Exactly. The alternative suggests that everyone starts with a sort of positive baseline of desert. You have some claim to well -being simply because you're a person. Ah, okay.
So personhood itself grants some level of desert. That's the idea. And it really shifts the moral calculus, you know? Virtue and vice still matter. They absolutely adjust that level up or down, but they don't define the entire basis of your desert. So even someone who acts quite badly. Even the least virtuous individual, according to this view, still retains some minimal positive claim to well -being just by virtue of being human. And that becomes really critical when we start talking about whether anyone deserves to suffer. Which brings up a practical point.
When we talk about someone's overall level of virtue, are we thinking about like last Tuesday or their whole life? Good question. For the kind of deep philosophical modeling we're doing here, especially with this geometry, it tends to look at the bigger picture. We're generally assessing desert based on the person's status overall across their entire lifetime. The holistic view. Right. It tries to capture their fundamental moral character, not just the snapshot in time. So, you know, a terrible person who has a change of heart late in life, their past wickedness is still factored in and vice versa for a good person who falls from grace. OK, so this idea of a potential.
baseline of desert, maybe even for the worst among us, seems to lead us right into a major fault line in moral philosophy, the clash between what the source calls moderates and retributivists. Absolutely. And this clash really centers on one key issue, suffering. How so? Well, the moderate view basically insists that no one deserves to suffer, period, no matter how terrible their actions or character might be. Even the absolute worst. Even them. Now, moderates aren't naive. They absolutely recognize different degrees of badness, of culpability. They might say the value of helping a very wicked person is heavily discounted.
Maybe the discount rate gets really close to 100%. But it never quite hits it. Never hits it. For the moderate, providing aid to anyone, even the most culpable person imaginable, still makes the world, from the standpoint of desert, a slightly better place. There's always some positive value in increasing well -being, rooted perhaps in that personhood baseline we talked about. So a moderate would say helping a serial killer feel a bit happier is still technically an intrinsically good thing, just maybe not a very good thing compared to helping a saint.
That's the logical conclusion of the moderate view, yes. It might be incredibly inefficient morally, but it's not intrinsically bad. Now contrast that sharply with a retributivist view. Retributivists do accept that some people can be so vicious, so culpable, that they genuinely do deserve to suffer. They often reject that universal positive baseline. So for them, suffering isn't always bad. From the perspective of desert, no. They believe that if someone is bad enough, providing them aid increasing their well -being actually has a bad aspect morally. Why? Because it means they're doing better than they deserve.
Wow. Okay, that's a huge difference. Yeah. The rich beauty of this isn't just saying helping the bad guy is a low priority. They're saying it can actively make the universe worse from a justice perspective. Precisely. It introduces a negative moral value. Helping them might increase overall happiness, maybe, but from the specific viewpoint of desert satisfaction, it's a minus. It implies that deserved suffering can actually be an intrinsic moral good. That's stark. It is. It's a fundamental disagreement about the structure of moral value. Now, it's important to add a qualifier here for our deep dive. Most retributivists are what philosophers call pluralists.
Meaning? Meaning they think there's more than one kind of fundamental value. So they might say well -being itself is good. So helping a vicious person is good in the sense that it increases well -being, but it's simultaneously bad in the sense that it violates desert. Okay, so it's a conflict of values for them. Exactly. But for the purpose of understanding this geometric framework, we're going to try and isolate just the value of desert alone. We'll set aside the overall what should we do, all things considered. Question for a moment. This focus lets us see the pure structure of desert claims laid bare by the geometry.
Right, let's get to the graphs. Yeah. We're taking these heavy moral claims and putting them onto an XY axis. What exactly are we plotting and why is this geometrical move so helpful? Well, the beauty of graphs really is that they force you to be precise. No more hand waving. You have to define your axis, define your slopes. It pushes vague intuitions into concrete shapes. It turns these moral puzzles into, well, geometry problems. Okay, so lay out the axis for us. Right. The x -axis, the horizontal one, is pretty straightforward. It represents the person's level of well -being.
Like happiness or suffering. Exactly. We can quantify it. Positive numbers mean lives that are, you know, worth living. Negative numbers represent lives not worth living states of suffering. The mirror might be a life that's neither good nor bad. OK, that makes sense. Well, being along the bottom. What about the vertical axis, the y -axis? That seems like the really novel part. It absolutely is. The y -axis represents goodness from the standpoint of desert. Think of it as intrinsic moral value specifically related to justice or desert. Whoa. So. Higher up on the graph means morally better. Morally better in terms of desert being satisfied, yes. The y -axis is our direct measure of how much moral good is achieved when people get what they're due, whether that's happiness for the virtuous or something else for the vicious, depending on your view. So we're literally plotting welfare against moral value. Okay, let's see the shape.
Now let's zoom in on the graph for a single individual. The characteristic shape the source uses is the mountain shape. Every person gets their own mountain. A mountain shape. What does that tell us right away? It tells us there's an optimal point. For every single person, there's one specific level of well -being that is best from the standpoint of desert. That's the peak of the mountain. Exactly. The x -coordinate of that peak marks the precise level of well -being that person absolutely deserves. That's their target. And the mountain shape itself means... If you're not at the peak, things are worse off, morally speaking. That's the key insight.
If you are below the peak level of well -being, say, a virtuous person who deserves happiness but is suffering, you're on the slope going down and to the left, the western slope. That's clearly a bad state of affairs. The why for you is lower than the peak. Okay, that makes sense. Suffering when you deserve well -being is bad. But what about the other side? Right. The mountain slopes down on the other side, too. If that same virtuous person gets more well -being than their absolute desert dictates, maybe they win the lottery twice when they only deserved one win. The graph goes down. And to the right, the eastern slope. So getting too much is also intrinsically bad from a desert perspective. According to this model, yes. There's a loss in moral value compared to the peak. Now, there's a subtle but important detail here about the steepness of those slopes.
The model generally suggests that the western slope, the suffering side, is typically stupor than the eastern slope, the side of getting too much. Why steeper on the suffering side? What's the moral idea there? It reflects a common intuition. It's generally seen as a worse moral offense, a bigger violation of desert, to let a deserving person suffer, a big drop down the steep western slope, than it is to give them a bit more than they strictly deserve, a smaller drop down the gentler eastern slope. Okay, so deprivation is morally... more urgent than excess in this view the steeper slope shows that faster drop in value exactly it builds that priority right into the geometry hashtag tag tag 2 .3 fault forfeits first fff and differential slopes okay this idea of slopes brings us back to that intuition we mentioned earlier fault forfeits first remember amos and boris amos is innocent boris caused the harm if you can only help one you help amos how does the graph show why this is where the slopes really shine The FFF intuition is captured perfectly by the difference in the slopes of Amos' and Boris' individual desert lines, specifically on the side where they need help, the western slope, typically. How does that work? Well, the slope represents the rate of change, how much moral value, y -axis gain, you get for each unit of well -being, x -axis increase, you provide.
Since Amos is innocent, his desert line will have a steeper slope. Let's say it's a slope of 1 .0. Meaning for every unit of well -being you give Amos, you get one full unit of moral value back on the y -axis. It's a one -to -one return. Okay. And Boris? Boris is culpable. Yeah. His fault means his claim is weaker. So his desert line will have a gentler slope, maybe only 0 .8. For every unit of well -being you give Boris, you only get 0 .8 units of moral value back. Wow, okay. So the geometry literally quantifies that intuition. We can see the better moral return on helping Amos. That's the power of it, yes.
You can see it precisely. Unit for unit, helping Amos does more good from the standpoint of desert than helping Boris. The slopes make that visually and mathematically clear. But life isn't always about giving equal units of help, right? What if you could help Boris a lot more than Amos? Excellent point. And the model handles this perfectly. Even though Boris' slope is gentler, a lower rate of return, if the amount of help you can give him is significantly larger if you can move him much further along the x -axis. Like saving his life versus just easing Amos' headache. Exactly.
If the total distance moved along the x -axis for Boris is large enough, the total gain in y, moral value, could still end up being greater than the smaller gain from helping Amos, even though Amos had the steeper slope. So it forces you to weigh the rate of return against the magnitude of the benefit. Precisely. It captures that complex tradeoff between the quality of the claim, slope steepness, and the quantity of the aid provided, x -axis movement. Okay, we've got the basic mountain shape for one person. But obviously, morality involves everyone. How do all these individual mountains fit together? How does the geometry handle differences between saints and sinners?
Hashtag, hashtag, trade price 3 .1 rotation and bell motion. We connect individual lines through two key concepts, rotation and what the source calls bell motion. These describe how the entire mountain shape changes based on a person's overall virtue or vice. Rotation? Like spinning the mountain? Sort of. Think about the slopes again. The core idea is that increasing culpability becoming more vicious reduces the value of the slopes. It makes the whole mountain, in effect, gentler, flatter. Conversely, increasing virtue rotates the line counterclockwise. This makes the slopes, especially the western slope leading up to the peak, steeper. More virtue means a higher moral return on aid. And more vice. More vice rotates the line clockwise. This makes the slopes gentler.
The moral return on aid gets smaller and smaller. And crucially, for some views, it can even become negative. Okay, walk me through reducing the value of the slope again, morally. It's about that return on investment. A highly virtuous person. Steep slope, counterclockwise rotation, helping them yields a big jump in moral value, y -axis for the well -being given, x -axis. A highly vicious person, gentle slope, clockwise rotation, helping them yields very little moral value or maybe even reduces it. And bill motion, what's that? Bell motion is just the name for the overall pattern of this rotation across the whole spectrum of people. Imagine lining up everyone's peaks from the most vicious person way over on the left, negative x value for their deserved well -being, to the most virtuous person way over on the right, positive x. Okay. As you move visually from left vicious to right virtuous, you'd see the individual desert lines systematically rotating counterclockwise. They start flat or even negatively sloped for the very vicious and become progressively steeper as you move towards the highly virtuous. It's like a wave or a bell shape if you consider the slopes themselves.
And this rotation, especially the clockwise rotation for the vicious, is how the retributivist view gets built into the geometry. The idea that helping the really bad guys is actually bad. Exactly. To make the retributivist view work geometrically, the claim that aiding the sufficiently vicious is intrinsically bad from a desert standpoint, their desert lines must be able to rotate so far clockwise that they acquire negative slope, at least on the eastern side, giving them more than they deserve. Explain that negative slope part again. Okay, imagine a truly terrible person who's... peak, their deserved level, is deep in suffering territory, say X -10. A retributivist might say moving them from negative 10 to 0, neutral well -being, is actually a bad thing from Desert's perspective. Because they're getting better than they deserve. Precisely. So on the graph, moving right along the X -axis, increasing well -being from net of 10 to 0, must cause the line to move down the Y -axis, decreasing moral value. That requires a negative slope, a negative multiplier. Maybe the slope is negative 0 .5 or even negative 1. Got it. So the geometry can actually map both views. Moderates, whose slopes never go negative, and retributivists, whose slopes must go negative for the extremely vicious.
That's the elegance of it. It provides a common framework to represent and compare these fundamentally opposed moral stances. Hashtag tag 3 .2, the skyline, the height of the peaks. Okay, we have all these individual mountains rotating based on virtue. What happens if we connect the dots, specifically the very top point, the peak of every single mountain? If you trace a line connecting all the peaks, you create the skyline. And the shape of the skyline represents perhaps the single most profound choice a moral theory based on desert has to make. Why is the skyline shape so important? Because it tells you how much intrinsic moral value is generated when anyone perfectly gets what they deserve. It reveals your core belief about whether satisfying desert for a saint is worth more than satisfying it for an average person. Okay, so what are the options for the skyline's shape? The source highlights three main possibilities. First, the standard skyline. This is just a flat, horizontal line.
Meaning all the peaks are at the same height. Exactly. All peaks have the same y -coordinate. This view embodies a kind of equal regard. It says, yes, people deserve vastly different levels of well -being. Their peaks are different places on the x -axis. But the amount of moral good achieved when any person hits their specific peak is exactly the same. So the universe gets the same moral goodness boost, whether a normal person gets their just desserts or Mother Teresa gets hers. the act of satisfaction is equally valuable. That's the core idea of the standard skyline. Now contrast that with the V -shaped skyline. V -shaped, meaning the peaks are higher at the extremes. Precisely. In this view, the peaks are higher, they have a greater y -coordinate the further they are from the moral center, x0.
So the peaks for the extremely virtuous and the extremely vicious are higher than the peaks for morally average people. What does that imply? It implies that it's intrinsically more important, it generates more moral value, to ensure that the morally significant individuals, the saints and the archvillains, get exactly what they deserve compared to moderately good or bad people. It prioritizes satisfying desert at the moral extremes. So if you hold this view, you might say, focus more societal resources on ensuring the saint is rewarded or the villain is punished appropriately because the moral stakes, the potential y -axis gain or loss, are higher there. That's a potential consequence, yes. It suggests the magnitude of the virtue, or vice, affects the importance of satisfying the corresponding desert. And then there's a third, quite radical option, the sea level skyline. Sea level, meaning flat on the bottom. Exactly. All the peaks lie directly on the x -axis. Their y -coordinate is zero. Why zero? But why is moral value? What does it mean if the peak, the best state, has zero moral value?
It means that satisfying desert doesn't actually create any positive intrinsic good. Instead, it merely eliminates the intrinsic bad associated with someone not getting what they deserve. Whoa. So justice, in this view, isn't about creating goodness. It's purely about preventing or fixing badness. The best you could do is reach zero, eliminate the injustice. That's the stark implication. The goal isn't positive moral achievement through desert. It's simply avoiding the negative value of injustice. So you see, the choice of skyline, flat, V -shaped, or sea level fundamentally defines the entire moral ambition of your desert -based system. Hashtag, hashtag, hashtag, 3 .3, dissecting types of desert beyond absolute. This whole geometric setup seems to allow for much finer distinctions than just saying someone deserves something.
The source mentions four specific types of desert that the geometry helps define. Yes. The precision of the graph lets us clearly distinguish between related but different concepts. First, absolute desert. We've talked about this one. It's simply the x -coordinate of the peak. It's the target, what level of well -being they absolutely deserve. The target level. Second, general desert. This refers to the entire character of the person's mountain, its specific shape, how steep its slopes are. rotation, where its peak is located. It's the overall profile of their deservingness across all possible outcomes. The whole picture for that person. Third, current desert. This is about the gap between where someone is and where their peak is. Specifically, it's measured by the Y gap, the vertical distance, the drop -off in moral value, between the height of their peak and the Y value of their current situation. So current desert measures how much moral value potential is currently unrealized for that person.
Exactly. It quantifies the extent of the current injustice or shortfall from the standpoint of desert. A large Y -gap means they are far below their peak in terms of moral value achieved. And fourth, immediate desert. This is all about the priority for helping right now. It's measured by the slope of the desert line at the person's actual current location on the graph. The slope right where they are. How does that give us priority? Think about it. If someone has a very steep slope at their current position, it means that even a small improvement in their well -being, a small move to the right on the x -axis, will produce a large increase in moral value. A big jump up the y -axis. Ah, the rate of return right now.
Precisely. So if you have limited resources and have to choose who gets the next small bit of aid, immediate desert says prioritize the person with the steepest slope at their current location, because that's where you'll get the biggest moral bang for your buck right now. Even if someone else has a larger overall wide gap, higher current desert, if their current slope is flat, immediate aid won't do much good from a desert perspective. OK, we've mapped the individual's desert landscape pretty thoroughly, but people don't exist in isolation. How does this geometry handle the complexities of comparing different people's deserts? Fairness between individuals. Hashtag hashtag 4 .1. Non -comparative versus comparative desert. Right. So far, we've mostly focused on what the source calls non -comparative desert.
That's the single mountain graph focusing on one person's relationship to their own deserved outcome. Getting their own peak. Exactly. But overall desert has another component. Comparative desert. This looks at the moral significance of how individuals stand relative to each other, considering what each deserves. It's about interpersonal fairness. If non -comparative is about hitting the ideal, comparative sounds like it's about fairness, when people inevitably miss their ideal. Hashtag, hashtag 4 .2, the Y -gap constraint and relative advantage. That's a very good way to put it. And the geometric framework offers a really elegant solution here, called the Y -gap view of comparative desert. The Y -gap again.
How does that work for comparison? The Y -gap view states that comparative desert is perfectly satisfied when the offense against non -comparative desert measured by that Y -gap, the drop from the peak is the same for everyone. Wait, so comparative fairness is achieved when everyone's Y -gap is equal, not when their well -being is equal or even proportional to their desert, but when the moral value shortfall is equal. Precisely. It doesn't matter if person A deserves 100 and is at 90 while person B deserves 10 and is at zero. If the vertical drop on the y -axis from their respective peaks is the same size for both A and B, then comparative desert is satisfied.
Why is that the measure? Because the wide gap represents the degree of moral offense, the amount of lost value, if the wide gaps are equal, it means no one is suffering a greater injustice relative to their own desert than anyone else. Neither person has a relative advantage over the other in terms of how far they fall short of their own deserved state, morally speaking. That's a really different way of thinking about fairness. It's not about equal outcomes, but equal moral shortfall. Exactly. It shifts the focus from comparing x -axis positions, well, being levels, to comparing y -axis drops, moral value losses. If someone has a smaller y -gap than you, they have a relative advantage because they are closer to achieving their deserved moral value than you are to achieving yours. Comparative Desert aims to eliminate those relative advantages by equalizing the y -gaps. Hashtag, hashtag, 4 .3, the problem with simple models, ratio view.
Okay, this y -gap approach seems quite sophisticated. It makes sense why simpler ideas about comparative justice might run into trouble. The source mentions the ratio view as an example. Yes, the ratio view is a historically appealing idea, maybe loosely connected to ancient concepts of proportional justice. It basically suggested that comparative desert is satisfied when the ratio of people's actual well -being matches the ratio of their deserved well -being, their peaks. So if A deserves 10 and B deserves 20, a 1 .2 ratio, their actual well -being should always be in a 1 .2 ratio.
That's the idea. Simple seems elegant until you hit zero or negative numbers, which, you know, happens all the time in ethics, people experiencing neutral lives or actual suffering. How does it break down? Catastrophically. Let's use that same example. A deserves 10, B deserves 20, 1 .2 ratio. Now, suppose something happens and A's actual well -being gets fixed at zero. Maybe they're in a coma, a life neither good nor bad. To maintain the 1 .2 ratio, what does B's well -being have to be? Two times zero. It has to be zero as well. Exactly. The ratio view demands B must also be at zero well -being, but that's morally absurd. B is the more virtuous person, deserving twice as much well -being as A. Surely comparative justice requires B to be better off than A, not equally neutral. Yeah, that's clearly wrong. And it gets even worse with negative numbers.
Suppose A deserves zero and B deserves negative. Deserves to suffer. If A happens to be doing well, say at plus five actual well -being, what does the ratio view demand for B? The math just breaks down completely or gives nonsensical results. So the ratio view fails because it's stuck comparing x -axis values directly. Yes, it tries to make the levels of well -being proportional without considering the moral value represented on the y -axis. The y -gap view solves this by focusing on the equality of the moral offense, the drop in y, which works perfectly well across positive, negative, and zero values on the x -axis. It shows that the geometry isn't just complexity for its own sake. It solves real problems that simpler models can't handle. Okay, so we have these two parts of desert. Non -comparative.
Hitting your peak. Yeah. And comparative equalizing the Y gaps. But surely they sometimes conflict, right? Like maybe helping person A gets them closer to their peak, but it makes the Y gaps between A and B much less equal. Absolutely. That's a core tension in applied ethics. Improving one aspect of desert might worsen the other. This forces a crucial question. How do we weigh these two values against each other? Is one vastly more important? Does non -comparative always trump comparative or vice versa? The position taken in this framework is actually quite nuanced.
It argues that the two partial values, non -comparative and comparative desert, are of roughly the same order of significance. Roughly the same. What does that mean in practice? It means neither one completely swamps the other. While in a specific situation, one might outweigh the other, maybe. Non -comparative desert is 10 times more important in this particular choice. It's not likely to be a million times more important. They're in the same ballpark of significance. Why is that rough comparability so important? Because it keeps the moral dilemmas real. If, say, comparative desert equalizing Y -gaps was overwhelmingly more important, we'd basically ignore individual peaks and just try to make everyone equally far from their ideal, morally speaking. We'd aim for equal injustice, essentially. Right. And if non -comparative hitting the peak was all that mattered, we'd just focus on getting one person to their peak, even if it created massive unfairness relative to others. By saying they're roughly comparable, the model ensures we always have to consider both. We have to weigh the benefit of moving someone closer to their absolute deserved level against the benefit of reducing relative inequality between people. It forces a constant balancing act, reflecting the complexity of real moral choices. Hashtag 4 .5 relevance to applied ethics, deontology and improvement. So we've gone deep into the geometry peaks, slopes, rotations, skylines, y -gaps. Bringing it back out, how does all this intricate mapping actually help us think about real world ethics like laws or policies? Is it more than just a philosopher's diagram? Oh, absolutely. The claim is that these geometric distinctions aren't just theoretical curiosities. They map directly onto real substantive disagreements in ethics and political philosophy.
Think about any ethical theory that includes a duty to give people what they deserve. That's a cornerstone of many justice theories, especially the analogical ones. Like Kantian ethics, perhaps, or just basic fairness principles? Exactly. But what does giving people what they deserve actually mean in complex cases? The geometry provides the necessary toolkit to figure that out. Do we mean satisfy their absolute desert, match their peak? Or prioritize immediate desert, get the best moral return right now? Or focus on comparative desert, equalize the Y gaps. A legal system, for example, would need to decide which of those is the primary goal of, say, sentencing or resource distribution. Precisely. Are we trying to... perfectly match the punishment to the initial crime, absolute desert? Or are we trying to allocate rehab resources where they'll have the biggest immediate impact on reducing future harm related to maximizing value game like immediate desert?
These geometric concepts correspond to different policy goals. And it's not just about hitting perfection, right? Most systems are imperfect. That's the other key application. We rarely, if ever, achieve perfect desert satisfaction for everyone. So we desperately need a way to judge whether one imperfect situation is better or worse than another imperfect situation. We need to measure moral progress. Exactly. And the geometry, specifically the y -axis representing moral goodness, gives us that measure. We can analyze a policy change. Does it tend to move people closer to their peaks overall? Does it tend to reduce the average y -gap? Does it increase the total sum of y -values across the population?
The framework allows us to compare different imperfect states and determine which one constitutes a genuine moral improvement from the standpoint of desert. Hashtag outro. So we started with this seemingly fuzzy idea what people deserve, and we've ended up with a surprisingly concrete visual language. Mountains representing individual desert, slopes showing moral return, rotation reflecting virtue and vice, and skylines revealing fundamental commitments about equality versus significance. Yeah, it's quite a journey. We've seen how deep philosophical battles, like the one between moderates and retributivists, can be understood as disagreements about the basic geometry. Should slopes be allowed to go negative?
Should the overall pattern exhibit bell motion? And as you said, the choice of a skyline really crystallizes a core moral commitment. The standard skyline prioritizes equal value in the act of satisfaction itself. The V -shaped skyline prioritizes maximizing value by focusing on the morally significant individuals at the extremes. It forces you to decide what matters more, equal regard or rewarding moral magnitude. Which leads us, and you, with a final thought directly from this geometric structure. If you lean towards that V -shaped skyline, if you think the moral value of satisfying desert should be higher for the very good or the very bad, well, the geometry demands an answer.
How much higher? Right. How much taller should the saint's peak be on the y -axis compared to the average person's peak? What's the justification for that specific difference in moral value? Is the ultimate aim of a just society to ensure equal value flows from satisfying anyone's desert, standard skyline, or is it to maximize the total moral good by differentially rewarding significance? v -shaped skyline. That's the choice that geometry lays bare for us to consider.