1
Show where an argument needs a moral premise
Find the counterexample row for an argument from facts to a duty, write the bridging premise that closes it, and say what accepting that premise commits the arguer to.
Course · Philosophy
Ethics and the Arithmetic of Welfare
Put a number on a moral view and see what it commits you to. Add up welfare and find who the sum ignores, count the people needed to beat a flourishing life, weigh the worse off, forbid an act and watch a recommendation flip, and test a duty by asking what happens when everyone does it.
facts alone never entail an ought
a definition fails: too broad, too narrow
total welfare cannot see who gets what
n·ε > total(A): the crowd that beats A
priority: a gain counts more the lower down
a side constraint deletes an act first
double effect: is the harm the means?
What this course is about
- Subject
- Philosophy
- Lessons
- 12
- Format
- Interactive
Overview
What you will be able to do
By the end you can state a moral position as something with a checkable structure, compute what it recommends on a case, and say which premise a critic would reject.
2
Test a definition against cases
Evaluate a proposed definition of “good” on a table of cases, classify each failure as too broad or too narrow, and see which definitions survive the verdicts you accept.
3
Compare distributions of welfare
Rank two outcomes by total, average, priority-weighted score and Gini coefficient, and compute the population at a tiny welfare level that beats a flourishing one.
4
Apply a side constraint to a decision matrix
Lay a trolley case out as acts against outcomes, apply total welfare, forbid an act, and name the case in which the recommendation changes.
5
Model the structure behind a deontic claim
Test a universalisation, a means-or-side-effect distinction and an omission in a small model, and write a dilemma as a set of principles that cannot all hold.
6
Mark where a method breaks down
Formalise a function argument and a slippery slope, find the premise each one needs, and say what each of four treatments of vagueness does to the slope.
Lessons
12 lessons
The course runs from the logic of moral argument, through the theories that add welfare up, to the theories that forbid acts whatever the sum, and ends with two methods that cut across the divide.
Is and OughtWhy facts alone never deliver a duty, and what the missing premise costs.Not marked
Defining “Good” and the Open QuestionTesting “good = pleasant” and “good = desired” against cases, and classifying how each fails.Not marked
Utilitarianism and the Sum of WelfareRanking outcomes by total welfare, and what the total cannot see.Not marked
Total, Average and the Repugnant ConclusionWhat happens to the sum when the number of people changes.Not marked
Priority, Equality and Levelling DownWeighting the worse off, measuring inequality, and the case that separates them.Not marked
The Trolley Problem as a Decision MatrixTwo cases with the same numbers, and the constraint that separates them.Not marked
Kant and the Universalisability TestTreating a maxim as the defecting choice in a many-player game, and asking whether its point survives everyone adopting it.Not marked
Double Effect, Means and Side EffectsReading “the harm is the means” as a dependence, and testing it by flipping the harm in a causal model.Not marked
Doing, Allowing and Omissions as CausesModelling a rescue not performed as a variable, and testing whether the omission makes a difference to the death.Not marked
Moral Dilemmas and Deontic ConsistencyWriting a dilemma as a set of sentences that cannot all hold, and naming the principle each way out gives up.Not marked
Virtue Ethics and the Function ArgumentFormalising Aristotle’s argument from function, finding the premise it needs, and saying where the lab’s reach ends.Not marked
Slippery Slopes and Small DifferencesWriting a slippery slope as a chain of conditionals, and watching four treatments of vagueness give four verdicts on it.Not marked
Recommended background
Decision matrices and expected value from Decision and Rationality, the n-player dilemma from Games and the Social Contract, and the causal models of Science, Induction and Causation.
Practice suggestions
Work forward. The consequentialist lessons assume the earlier ones: “Total, Average and the Repugnant Conclusion” leans on the totals computed in “Utilitarianism and the Sum of Welfare”, and “The Trolley Problem as a Decision Matrix” needs the decision matrix from Decision and Rationality.
Change the numbers. Every lab accepts a distribution, a payoff table or a set of sentences typed by you, and every verdict is recomputed exactly. The quickest way to see what a position commits you to is to make the case a little worse for it and watch where it gives way.
Separate the arithmetic from the premise. The labs compute what follows from the welfare numbers, the forbidden acts or the sentences a lesson states. They do not say whether a number is the right measure of a life, whether an act belongs on the forbidden list, or whether a principle is true. Each lesson says where its own stipulation sits.
Expect questions left open on purpose. A lesson shows an argument is valid and says what accepting its conclusion or rejecting a premise would cost. Choosing is yours.
What it does not cover
Metaethics beyond is and ought and the open question. Expressivism, error theory and the arguments for moral realism are not here; none of them has a verdict a lab can compute without misrepresenting it. The Frege–Geach problem, which asks whether arguments with embedded moral terms stay valid, can be posed as a validity check, and is a candidate for a later lesson.
Virtue ethics beyond the function argument. The doctrine of the mean, practical wisdom and moral education have no structure a lab can test, and the lesson on the function argument says so rather than invent one.
Welfare itself. Every lab takes welfare as a number supplied by the example. How lives are measured, whether they can be compared between people, and what makes a life go well are open questions the numbers assume away.
Applied ethics. No lesson tells you what to think about a particular policy, profession or practice. The cases are chosen because their structure is clear, not because they settle anything outside the course.
The history of ethics as history. Arguments are taught as arguments; dates, schools and influence are not computable and are not here.