Moral mathematics

[Celerity]

Subjecting the problems of ethics to the cool quantifications of logic and probability can help us to be better people

https://aeon.co/essays/how-to-solve-moral-problems-with-formal-logic-and-probability



The relationship between mathematics and morality is easy to think about but hard to understand. Suppose Jane sees five people drowning on one side of a lake and one person drowning on the other side. There are life-preservers on both sides of the lake. She can either save the five or the one, but not both; she clearly needs to save the five. This is a simple example of the use of mathematics to make a moral decision – five is greater than one, so Jane should save the five.

Moral mathematics is the application of mathematical methods, such as formal logic and probability, to moral problems. Morality involves moral concepts such as good and bad, right and wrong. But morality also involves quantitative concepts, such as harming more or fewer persons, and taking actions that have a higher or lower probability of creating benefit or causing harm. Mathematical tools are helpful for making such quantitative comparisons. They are also helpful in the innumerable contexts where we are unsure what the consequences of our actions will be. Such scenarios require us to engage in probabilistic thinking, and to evaluate the likelihood of particular outcomes. Intuitive reasoning is notoriously fallible in such cases, and, as we shall see, the use of mathematical tools brings precision to our reasoning and helps us eliminate error and confusion.

Moral mathematics employs numbers and equations to represent relations between human lives, obligations and constraints. Some might find this objectionable. The philosopher Bernard Williams once wrote that moral mathematics ‘will have something to say even on the difference between massacring 7 million, and massacring 7 million and one.’ Williams expresses the common sentiment that moral mathematics ignores what is truly important about morality: concern for human life, people’s characters, their actions, and their relationships with each other. However, this does not mean mathematical reasoning has no role in ethics. Ethical theories judge whether an act is morally better or worse than another act. But they also judge by how much one act is better or worse than another. Morality cannot be reduced to mere numbers, but, as we shall see, without moral mathematics, ethics is stunted.

In this essay, I will discuss various ways in which moral mathematics can be used to tackle questions and problems in ethics, concentrating primarily on the relationship between morality, probability and uncertainty. Moral mathematics has limitations, and I discuss decision-making concerning the very far future as a demonstrative case study for its circumscribed applicability.

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[delisen]

1. I think the first paragraph is in error..

Arbitrarily assigning a numerical value of 1 to each life may not be so clear cut as a moral decision.

[Celerity]

2. I disagree, it is simply the numbers of lives involved, you are adding more stipulations nt

[delisen]

3. I would agree if it were 6 identical objects.

[Bernardo de La Paz]

6. Under what circumstances would you choose one over five? ONLY if you have more information

... about them.

But that is NOT the scenario you are asked to deal with in the first paragraph. Manufacturing alternate scenarios can elucidate the first one, but they do not solve the first one.

You are asked to deal with ONLY the info given in the first paragraph, to solve the moral dilemma; the solution being "all else being equal, choose five over one". In the scenario given, not some scenario you can imagine, but the scenario given, you have five plus one people, equal people. You do not know their ages, sex, education, skin colour, tattoos, or how many children each has.

The point of the article (you should read it) is that people make mistakes about reasoning with probabilities.

[delisen]

8. Your assumption that I have not read the article is erroneous.

[Bernardo de La Paz]

9. It was based on your responses to the thread, which show a lack of understanding of fundamental

principles explained by the article.

But of course it is easier to question my assumptions about you than to actually address the issues being discussed and answer the questions posed of you.

Perhaps you don't want serious discussion? That's okay.

[Bernardo de La Paz]

4. No. There is no information to chose between those lives, so they MUST all get equal value

Since they must be assigned arbitrarily equal value, save the five and not the one.

Your quibble about "not so clear" is a big point of the full article and you'd do well to read it. The only way it becomes "not so clear" if there is more info about the scenario than set out in the paragraph. But there isn't, so they are assigned equal value. The scenario is applicable for example if someone arrives on the scene simply noting one person and five people and must make an instant decision. There is not time to inquire as to whether the fourth person in the group of five is a mass murderer or a school teacher.

The article has much discussion about the limitations, which are fundamentally limitations of prediction (from lack of probability information).

You are getting into issues of "utility" and "expected value", which is the meat of the article.



If we know nothing about the five people then we MUST assign them all equal value. But if we know something, then we can invoke expected value and utility, more or less to the degree that the information is reliable and complete. Read the article.

If the one is an accomplished brain surgeon entering prime of life and the 5 are retired ditch diggers, then there is a lot more information and that might make us wish to save the one because the utility to society will be higher.

[NNadir]

5. I'll try this later if I have a chance to read it. n/t.

[Bernardo de La Paz]

7. You won't miss much. It is wordy and doesn't give much insight for people used to mathematics

But it is very useful for people who think mathematics is abstract and doesn't apply to people or society.

[Tetrachloride]

10. A past friend of mine survived in the Mediterranean while 10+ drowned.

In most directions of the compass from me there is violence, starvation and high drama such as Iran.

These scenarios therefore aren’t so academic to me.

My father was infantry company commander in Korea, including against Chinese regular army. He said his main concern were the lives of his men and himself. Sometimes he had time and duty to think of the geopolitical connections, especially when away from his forward position.