Wednesday, 9 May 2012

Science of Morality

Hi guys, welcome to Orygyn!

A while ago, on my YouTube channel, I reviewed Sam Harris' book, "The Moral Landscape". To summarise the review, I thought it was a great introduction to the idea of a science of morality, and it lead me to look at morality differently. Another YouTuber I'm subscribed to was disappointed that the book didn't go far enough into the actual science. I would respond by saying that the book was never written for that purpose, but that is the point of this post. I have a degree in Maths, and a science of morality is likely to deal in Maths very heavily. I would like to share my thoughts on how a science of morality might work in practice.

It's important, first of all, to make 2 points. First, a science gets stronger with criticism. If you have criticisms, it is not necessary to throw out the idea entirely, unless those criticisms are made against the foundations of the science. People might bring up the Is-Ought problem, but this problem affects all ethical systems, and therefore is irrelevant to the science. The second point is that the ideas I will outline are not yet linked to brain states as Sam Harris outlines in his book, although there will be nothing to exclude the possibility of adapting the ideas to facts about the operation of the human brain in the future.

First off, we give people a utility value. Choosing the bounds of this value is important as it will affect the morality of any given action. After a lot of reflection, I've settled on 0 to 1, 0 representing minimum well-being, 1 representing maximum well-being. For example, someone with a utility value of 1 is in a situation where nothing could improve their subjective enjoyment of life or their objective health or general well-being. There are currently practicality problems when it comes to discovering any individual's utility value, but this is where Sam Harris' talk about brain states comes in. In the future, it will get progressively easier to assign that value to someone, given improvements in our understanding of neuroscience. The most important thing about choosing the bounds as 0 to 1 is that a dead or non-existent person has a utility value of 0. This means that killing any individual will always be a negative utility action (which I'll explain in detail later on) except when that individual's value is 0 for other reasons. In practice, a living human being's utility value will only be at 0 when they are in the womb, prior to the development of their brain and their mental capacity to feel pleasure or pain, or very near to 0 when in a coma.

Next, we need to look at moral actions. A moral action can affect many different people, and so is not subject to the same bounds as a person's own utility value. The upper and lower bounds on the utility increase or decrease caused by any action can be expressed mathematically as follows.

A = [-p, p]

AH! MATHS! Don't worry, I'll take you through it. A is any action which affects anyone's utility value. For example punching someone in the face will likely cause that person emotional and physical harm which will decrease their utility. This is therefore a negative utility action. The square brackets indicate a closed set which, in this case, means that the minimum possible effect on utility values is -p, and the maximum is p. p is used here to refer to the number of people affected by the moral action. The largest possible decrease in any one person's utility value is -1 (in practice, this would basically mean killing a perfectly content human being, which is unlikely as killing is not done by most people, and achieving a perfect utility is very unlikely as well). This largest possible decrease (-1) is then multiplied by the number of people affected (p) to give the maximum combined utility lost:

-1 x p = -p

Likewise, the largest possible increase in any one person's utility is 1 (this is pretty much impossible in practice, we're essentially talking about resurrection immediately followed by elevating the person to a state of perfect well-being). An action which increases utility is a positive utility action. The same maths is applied to this example as was to the previous and so the maximum combined utility gained is therefore:

1 x p = p

See, not so hard. But I like to be sure. Example time.


A serial killer has murdered 6 people. The utility values of this 6 people are 0.3, 0.4, 0.5, 0.55, 0.6 and 0.65. The murders give the serial killer a 0.01 increase in his own utility for each murder committed but don't freak out, moral actions are actions which affect others, and so this isn't included in the equation. What is the utility effect of the serial killer's actions?

This is kids' stuff when you know how. All you need to know is that murder makes a human being incapable of any kind of subjective experience and so it permanently decreases their utility values to 0. Let's take the 1st victim:

M = v2 - v1

where v1 is the victim's utility prior to the murder and v2 is the victim's utility after the murder. M is, of course, the murder itself. We know that v1 is 0.3 from the question and v2 is 0 because they die. Substituting those values into the equation we get:

M = 0 - 0.3 = -0.3

But it goes further. Since v2 will be 0 in all cases, we can simplify the equation to this:

M = -v1

All you need to do is put a "-" before the victim's utility prior to the murder. Now for the complete problem. This time we just work out M for each victim and add them together:

-0.3 - 0.4 - 0.5 - 0.55 - 0.6 - 0.65 = -3

So the serial killer's action result in a combined utility change of -3. As low a value as that might sound, this actually makes the action very wrong. You have to remember that a more minor negative utility action, for example punching someone in the face, will result in physical harm and anger which will probably result in a utility change of something like -0.05 if it's a relatively bad but non-fatal punch.The values chosen for the 6 people were completely arbitrary, so it's important not to take away from this that some lives are more valuable than others. Murder is ALWAYS a negative utility action, and so is always wrong. The fact that 1 individual has a lower utility value than another never means it is more OK to kill the person with the lower utility, it just means that that person loses less from their death. A negative utility action should always be treated as something you never do except when there are no positive or zero utility actions possible.


If people are unhappy enough with their lives, they may commit suicide. In the vast majority of cases, suicide will be a negative utility action. Why? As I've already said, the morality of the action depends on how much it affects other people. Killing yourself reduces your own utility to 0 but this isn't factored into the equation because you are not other people. However, suicide affects everyone that knows you, especially your family and friends. It will decrease their utility. Mathematically, this can be represented as:
S =  xi
       i = 1

S is the suicide, x is anyone whose utility is affected by the suicide with i being used to specify a certain individual (for example x1 could be the mother, x2 could be the father etc.) and n is the number of people affected. The ∑ means that all values of xi are added together from the number underneath (1) to the value above (n). Example:

A mother and father both lose utility 0.1 as a result of the suicide of their son. What is the total utility change caused by the son's suicide?

Well 2 people are affected, the mother (x1) and the father (x2). Both x1 and x2 are -0.1. We simply add them together.

-0.1 + (-0.1) = -0.1 - 0.1 = -0.2

The son's suicide has decreased utility by 0.2. This tells us that the son's suicide is wrong, although the son almost certainly knew the effect his death would have on his family and chose to kill himself anyway. This is simply maths telling you that people will miss you!

Before I go any further, some might look back at the murder scenario and look at it as overly simplistic in light of the fact that we are now including the effects the action has on relatives and friends in the equation. You'd be right. If this ever gets used in practice, these less direct effects must be included in the equations, I'm just introducing you to the science here.


Enough messing around. If the science can't advise us on the big issues, what's the point of it? By the simple fact that abortion remains a contentious issue, whatever I write here will be controversial. Let's get to it.

Conception is the creation of a moral agent, a life form with a utility value. How do we address the problem of the developing human being? Well, if morality is to be based on an organism's capacity for emotion, self-awareness and caring about its existence, none of this applies to a foetus until the neural architecture making this possible has developed. Until this point, the organism's utility value is 0 and so abortion at this stage is a zero utility action. It's neither wrong nor right. At this point, the pro-life side will make the following criticisms:

"What about the fetus' potential for life?"
"Isn't their any utility in the health of an organism?"

I'll deal with the second one first. The simple answer is no. At face value, an organism incapable of caring about its health has a utility of 0 as the organism is unable to care what you do to it. Does this necessarily mean that killing such an organism is never wrong? Not really, not if its actions still affect the utility values of others. For example, if a certain insect plays a crucial role in the conservation of the environment, killing enough of them will later on affect human beings.

The issue of a non-moral agent being able to perform moral actions is central to addressing the pro-lifers 1st criticism as well. An unborn human being has the potential to raise the utility of others on average, to lower it, or for the good and bad to cancel themselves out. Since the outcome is completely unpredictable, the 3 outcomes are treated as having equal probability. A fair criticism would be that the probability of an exact net zero change in the utility of others should be much lower, but what really matters is that the positive and negative utility outcomes have equal probability. This makes the expected utility change caused by that potential human's actions 0. In summary, because we never know whether that human being will be good overall or bad overall, the 2 equal probabilities cancel each other out and so both the developing human's own utility value and the change they are expected to cause in other people's utility values is 0. This makes the pro-lifers' first criticism irrelevant to the utility equations.

The pro-choice side will have a criticism of their own.

"Doesn't this mean that abortion after the fetus' brain is working is immoral?"

To some extent, yes. The fetus is capable of suffering and has a rudimentary awareness of its existence. Its utility value is therefore non-zero. The issue of abortion at this stage now reverts to the murder scenario outlined earlier: it will always be a negative utility action. At this stage, if you don't want the child, the more moral options are to remove it from the womb and have it grow further outside or to carry it to term and give it up for adoption. Ideally, the best thing to have done would have been to get the abortion early. I appreciate that the legality of abortion in any given country could make this impossible for some, but this is where the science comes in handy, as it shows that illegal early abortion is unjustified.

In cases where the mother's health is at risk, you just compare the outcomes of the following 2 scenarios.

1. The fetus is not aborted and the mother and fetus die.
2. The fetus is aborted so the fetus dies.

Mathematically, we can use the earlier murder equation to represent this:

m = mother's utility value
f = fetus' utility value

Case 1 = -m - f
Case 2 = -f

It's very straight forward. In either case, the fetus will die so no matter what stage of development the fetus is at, the higher utility option is always case 2. This is an example where both cases are negative utility actions. Neither are ideal, but since these are the only possibilities, you go with the option which decreases utility the least.

Remember, a science gets stronger with criticism. I WANT you to criticise this or ask questions about scenarios I may not have included here.


If we're all on the same page, you'll probably think it's not looking good for those who support euthanasia. Don't be too hasty though. When dealing with the issue of euthanasia, what we're asking in terms of the science is this: can it ever be positive utility to kill someone? If we're talking about killing someone against their will, no. It doesn't matter what the utility value of the murder victim is, it's always wrong. However, euthanasia deals with situations where the victim will die anyway. This makes it more analogous to the 2 scenarios in the abortion issue. Let's take the example of a patient on life support. This time the scenarios are as follows.

1. The patient will remain comatose/in agony until their death.
2. The patient is removed from life support and they die shortly after.

Case 1 depends very heavily on the condition of the patient. If they are in a coma and die while comatose, their utility is unlikely to vary much. Since the effects of the patient's death on the relatives and friends is unlikely to vary either, there is likely to be little difference in the utility change caused by the particular scenario chosen. What about when the patient is in agony?

First, let's assume they can communicate with us. We first need to establish a new principle for our science. I might rename it later, but for now I'll call it the Moral Responsibility Transfer principle:

MRT principle

"If an individual A freely wishes, without any manipulative influence upon them, to perform an action which lowers their own utility, but is unable to carry out the action his/herself, another individual B can carry out the action on behalf of A if A freely allows, without any manipulative influence upon them, to grant B this responsibility. B's actions are then treated in the utility equation as A's."

I've taken great care in the wording to exclude cases where someone is being manipulated into providing MRT, or is unable to consent, or cases where the MRT recipient decreases utility further than is requested. The application of the MRT principle in euthanasia is that, because the patient is unable to kill him/herself, another must do it for them, and since the patient wants to die, even though their utility is decreased to 0, because it is in accordance with the patient's wishes, it is not wrong. It can also be used by human beings long before an accident that puts them in that scenario occurs.

A simple way to sum up the action is to go back to what I was saying about a person decreasing their own utility not being immoral. This is exempt from the utility equation. The MRT principle simply treats the actions of the person assisting in the patient's suicide as the actions of the patient. I make this point to discourage possible criticisms that this is an arbitrary principle invented to justify my own views. Science is about modelling reality, and in reality, we don't punish people for carrying out the freely chosen wishes of another informed human being, even if those wishes are detrimental to that person. It's only when we doubt how free those wishes are or how informed they are that we take issue.

What does this mean for the 2 scenarios? Well, it depends on whether the patient wants to die. If they don't, case 2 would be treated in the same way as murder and the MRT principle doesn't apply. This would be a negative utility action for the person who makes the decision about life support. As for case 1, the decision to endure is the patient's and so morality isn't involved. If, however, the patient does want to die, the MRT principle applies to the person assisting in the death as it is the patient's informed choice. If the patient is not taken off of life support, despite the patient's wishes to the contrary, those who are able to do so are morally responsible for all of the patient's suffering prior to their death as they could've prevented it. How are all of these scenarios expressed mathematically?

Patient chooses not to die:

P = patient's utility value immediately prior to death
E = euthanasia action utility change on patient
\E = non-action utility change on patient
si = suffering event number i
di = decay constant of suffering event number i
t = time
                     n        -dit
Case 1: \E = sie          - P

Hieroglyphics? Don't worry, I'll explain it. What we're modelling here is not just the patient's death but their suffering up to the point of their death. The actual death is the -P part (the murder equation from earlier). The rest involves slightly more complicated mathematics. You may recognise ∑ from earlier, the function which adds together related variables. s refers to the change in utility caused when the patient experiences pain and i is simply used to describe how many times it's happened. For example, s3 means that the patient is experiencing a burst of pain for the third time. n refers to the number of times this burst of pain will occur prior to their death. However, the pain will decrease with time and their utility value will gradually rise again, most likely due, in this scenario, to the involvement of painkillers. This is where e, di and t come in. e is an irrational number like pi. Very roughly, it's value is close to 2.7. I'm not going to explain it in detail here, but it's standard practice to use this number for what I'm about to describe. As you can see, -dit is above e. We are raising e "to the power of -dit" which means we are multiplying e by 1 -dit times, or dividing e from 1 dit times, whichever way helps you understand it better. Because the logarithm (-dit in this case) is negative, e to the power of this logarithm will be between 0 and 1 and decreasing towards 0 as t increases. di was described in the equation key as the decay constant. This is just a number chosen to make the model accurate. You could describe it in this case as the effectiveness of the pain killers. The higher d is, the less time is required for e to the power of -dit to converge to 0. \E will always be less than 0 as the patient's utility decreases from a positive value to 0 as they die.

This equation is just a utility equation. Morality isn't relevant to it as the responsibility for the suffering and death involved was taken by the patient. In a morality relevant utility equation, e to the power of dit is not relevant as it describes the recovery of the suffering. People are not absolved of their actions simply because the suffering they cause will eventually subside.

Case 2: E = -P

This is a straight forward murder equation. The patient did not ask to be euthanised, so doing so is murder. This is a negative utility action for which the person doing the euthanising is culpable and that's all there is to it.

Patient chooses to die:

The utility equations for case 1 and case 2 are the same. However, since morality is relevant to case 1, and the decay rates aren't, we should describe this in a separate equation:

\Em = morally relevant utility change of no euthanasia

Case 1: \Em∑ si 

As you can see, e to the power of -dit has been taken out. As I described earlier, we don't absolve people of the suffering they cause simply because the suffering caused by the action diminishes over time. To get a value relevant to the morality of the action we have to remove this from the equation. -P, the death, is also absent from the equation as this is inevitable. The person who failed to respect the patient's wishes for euthanasia is not responsible for the patient's death simply because they are responsible for all of the patient's suffering prior to it. All we need to do then is add up the utility change of each sudden burst of pain, which will all be negative, and we get the morally relevant utility value of neglecting the patient's wishes. This will obviously always be negative as well.

Case 2 is as above, but the MRT principle applies, so the equation describes the wishes of the patient, and so is not morally relevant.

For now, I just want to look at 1 more scenario:


This issue describes the morality of having children. Natalists argue that there is positive utility in having children and antinatalists argue that there is negative utility in having children. What might this science of morality say?

We can model the scenario but we can't really say 1 side is right and the other is wrong as things currently stand. Let me explain.

We'll model what we know to start with. Conception doesn't immediately produce a non-zero utility human, but 1 develops in the womb. Conception with intention to carry the child could be seen as a positive utility action as, after the 9 month incubation period, a child is born with non-zero utility b (for birth). This could very simply be modelled as:

C = b

However, we also know for a fact that the child will eventually die. The parents bring a child into existence knowing it will die. If they are responsible for the positive utility of their birth, they are also responsible for the negative utility of their death, as we can't be selective about which events they are responsible for. However, it's unlikely that the utility after birth will be the same as the utility before death. We need a variable d for death, but we also need one to represent their lifetime utility change (l). Modifying the equation we get:

C = b + l + d = 0

The three variables will always add up to 0 as, because the human being created always dies, their final utility will always be 0. b is always positive, l could be positive, zero or negative, and d is always negative. The act of creating a new human being, then, is a zero utility action and so is neither right nor wrong.

One thing we've not considered is the utility change that the new human will bring about in others. However, as I said in the abortion scenario, this is completely unpredictable. Positive and negative utility change, therefore are treated as equal probability and so the expected change still adds up to 0. We will never be able to predict this change, so this is the fairest way of modelling the scenario.

Well, that's all for now. There are many more scenarios to consider, but this is just a taster of how we could use utility to quantify morality. Any questions or criticisms are encouraged and welcome.


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