A moral argument is worth having only when it is stated in a form where someone can say exactly which line they reject.
Most are not. They arrive as a paragraph in which a case, a principle and a verdict are fused, and the person who disagrees can only repeat their own paragraph louder. The previous two lessons established that the question of what to do is not settled by opinion and not dissolved by metaethics, so it has to be argued. This lesson is the method, and it is the most immediately useful thing in the course. Everything after it is an application.
Put it in premises
The first move on any moral argument, including your own, is to write it as numbered lines with the conclusion at the bottom.
Take a real one. "Eating meat is wrong because it causes unnecessary suffering." Written out: (1) Factory farming causes severe suffering to animals. (2) Eating meat from factory farms is not necessary for human health or flourishing. (3) It is wrong to cause severe suffering for no necessary purpose. (4) Therefore eating meat from factory farms is wrong.
Now the argument has surfaces. Premise 1 is empirical and can be attacked with evidence about husbandry. Premise 2 is empirical and can be attacked with nutrition. Premise 3 is the moral premise, and it is where the real disagreement usually lives, though almost nobody attacks it, because as stated it looks unimpeachable. Notice also what has become visible: the conclusion is narrower than the slogan, since nothing in the argument touches meat from an animal that lived well and died painlessly, and an opponent who points that out has done something useful rather than merely obstructive.
Two habits go with this. State the argument in its strongest form, including repairs the other side has not thought of, because refuting a weak version teaches nobody anything. And identify the moral premise explicitly, since the previous lesson established that there is always at least one and it is always the load-bearing line.
Example. Put this in premises: "Voluntary euthanasia should be legal because people have the right to control their own bodies."
(1) Competent adults have a right to control what is done to their own bodies. (2) A right to control what is done to your own body includes the right to refuse or request medical interventions, including one that ends your life. (3) The law should protect the rights of competent adults where doing so does not seriously harm others. (4) Legalising voluntary euthanasia under safeguards does not seriously harm others. (5) Therefore voluntary euthanasia should be legal. Now look at where the argument is actually contested. Almost no opponent denies (1). Most attack (2), by holding that a right to refuse treatment does not extend to a right to be killed, which is the acts and omissions question of a later lesson. Serious opponents also attack (4) with an empirical claim about pressure on the vulnerable, which is a testable prediction rather than a principle. Two minutes of writing has relocated the disagreement from a slogan to two specific lines, one philosophical and one empirical.
Now you. Put in premises: "Capital punishment is wrong because the state should not kill."
Answer
(1) Killing a person is wrong unless it is necessary to prevent a comparable harm. (2) Executing a convicted prisoner is not necessary to prevent a comparable harm, since imprisonment already prevents further offending. (3) Therefore executing a convicted prisoner is wrong. (4) The state may not do what is wrong for a person to do. (5) Therefore capital punishment is wrong. Writing it out exposes two things the slogan hides. Premise 2 is empirical and hostage to the deterrence literature, so a retentionist who shows a large deterrent effect attacks it directly. Premise 4 is a substantial and often unnoticed assumption, since states are routinely permitted to do things individuals may not, such as imprison people and levy taxes, so it needs defending rather than assuming. And nothing in the argument mentions desert, which is where a retributivist actually stands, so the argument as written does not engage them at all.
One counterexample kills a universal principle
Moral principles are usually stated universally, and a universal claim is refuted by a single instance. This is the workhorse technique of the subject, and it is borrowed straight from logic.
Consider: "It is always wrong to break a promise." You promised to meet a friend for coffee at three. On the way you pass a child face down in a pond. Breaking the promise is obviously permissible, so the principle as stated is false. Note what has and has not been shown. The counterexample does not show that promises do not matter, and it does not establish any rival theory. It shows that this formulation is too strong, and it forces a repair.
The repairs are where the philosophy happens. You might weaken the principle to "it is wrong to break a promise unless doing so prevents a much greater harm", which concedes that promissory obligation can be outweighed and raises the question of by how much. Or you might restrict it: "it is wrong to break a promise for one's own convenience", which keeps absoluteness at the cost of covering much less ground. Or you might bite the bullet and insist the child should drown, which almost nobody does but which is at least a position. Each repair has consequences that can be tested with a further case, and the sequence of case, repair, case is what a philosophical literature actually consists of.
The same technique attacks the two halves of a criterion separately. If someone says an act is wrong if and only if it violates consent, you can attack sufficiency by finding a consent violation that is not wrong, such as a surgeon operating on an unconscious accident victim, and you can attack necessity by finding a wrong that violates nobody's consent, such as polluting an uninhabited river. Knowing which half you are attacking keeps an argument from going in circles.
Thought experiments, and what they cannot do
A thought experiment in ethics is a controlled comparison. Its purpose is to hold everything fixed except one feature and see whether the verdict moves, which is exactly what an experiment does and exactly why the cases are so artificial.
Take the two standard trolley cases, treated properly in a later lesson. In one, you divert a runaway trolley from five people onto one. In the other, you push a large man off a bridge to stop it, again saving five at the cost of one. The numbers are identical. If people's verdicts differ, and they do, something other than the numbers is doing the work, and the whole point of the pair is to isolate what. Objecting that no real trolley behaves like this misses the design, in the way that objecting to a frictionless plane misses the design.
The limits are real, though, and honesty requires stating them. First, intuitions about extreme cases may be unreliable precisely because they are extreme: a response system tuned by ordinary life may not have anything sensible to say about a bridge and a fat man. Second, they are sensitive to presentation. Lewis Petrinovich and Patricia O'Neill showed in 1996 that wording the same dilemma in terms of saving rather than killing moved judgements substantially, and that the order in which cases were presented changed the answers to later ones. Eric Schwitzgebel and Fiery Cushman reported in 2012 that professional philosophers with doctorates showed order effects of essentially the same size as everyone else, which undercuts the hope that expertise filters the noise out.
The reasonable conclusion is not to abandon the method but to treat a single intuition about a single case as weak evidence, and to look for the pattern that survives reframing. That is also what an experimentalist does with a noisy measurement.
Consistency and universalisability
The strongest lever in any moral argument is not a principle but an inconsistency in the other person's commitments, because it does not require them to accept anything new.
The general form runs: you judge case A one way and case B the other; name the difference between them that justifies the different verdicts; and then either the named difference survives testing, in which case you have learned something, or it does not, in which case one of the two verdicts has to go. This is the technique behind almost every famous argument in the subject. Rachels does it with two bathtubs, Singer with a pond and a cheque, the argument from marginal cases with a pig and an infant.
Universalisability is the same tool aimed at the agent. If it is permissible for you to do this, it is permissible for anyone relevantly similar, and "relevantly similar" cannot be filled in by naming yourself. The popular version, "what if everyone did that", is a blunt instrument that overreaches: if everyone became a doctor, nobody would grow food, yet becoming a doctor is fine. The repair is to ask not what would happen if everyone did it but whether you can coherently will that everyone in your circumstances be permitted to, which is Kant's test and gets its own lesson.
Example. A colleague argues that eating pigs is fine because they are not human. You want to test the principle rather than assert the opposite. What do you ask?
You ask what work "human" is doing, and then look for the property behind it. If the claim is that only humans have interests that matter, the test case is an anencephalic infant or a person in a permanent vegetative state, who lack the cognitive capacities a pig has, and whom the colleague presumably does not think may be farmed. If the reply is that the infant belongs to a species whose typical members have those capacities, that principle can be tested too: it implies that a hypothetical alien of high intelligence whose species were typically dull would be fair game. The point of the sequence is not to trap the colleague, which is a bad way to change anyone's mind, but to locate the property they actually rely on, so that the two of you are arguing about the same thing. Many people, pressed this way, end up defending a species-membership criterion openly, which is a real position with real defenders and can then be discussed on its merits.
Now you. Someone holds both that a fifty percent inheritance tax is theft and that a fifty percent income tax on a footballer is not. What do you ask them?
Answer
What morally relevant difference there is between the two transfers, given that both take half of an unearned or partly unearned gain from someone who currently holds a legal claim to it. Candidate answers exist and each is testable. They might say the inheritor did nothing to earn it, which cuts the wrong way for their view. They might say the deceased already paid tax on the money, which raises the question of why the same objection does not apply to spending it in a shop and generating sales tax. They might say the tax falls on a family unit rather than an individual, which is a real position about who owns what within a family and can be examined. The technique is neutral between political positions, and the same move works in reverse on someone who accepts inheritance tax and objects to a tax on wealth.
Reflective equilibrium
If principles are tested against cases and cases are tested against principles, what stops the whole thing being circular? The standard answer, from John Rawls in 1951 and again in A Theory of Justice in 1971, is that circularity is not the objection it looks like.
The method is called reflective equilibrium. You start with your considered judgements, meaning the ones you hold calmly, with the facts in front of you, and with no stake in the outcome. You look for principles that systematise them. Where a principle conflicts with a judgement you revise one or the other, choosing whichever you hold with more confidence and whichever is better supported by everything else you believe. You keep going until principles and judgements sit together without conflict. That state is the equilibrium, and it is the only standard of justification the subject has.
Two features stop it being empty. It is a coherence standard applied to a very large body of commitments, and coherence over a big enough set is hard to reach: most people's moral views, written out, are inconsistent in several places, and finding out where is genuinely informative. And in its wide form, the version Rawls and Norman Daniels defend, the equilibrium must also cohere with background theories of the person, of society and of how our judgements were formed, which is what lets a debunking explanation knock out a judgement. If your confident intuition that a caste is inferior is explained by the fact that you were raised in it, that explanation is part of the evidence and counts against the intuition.
The standard objection is that the method is conservative: it takes your existing judgements as data and can only tidy them, so a person who starts with monstrous views reaches a tidy monstrous equilibrium. The reply is that the wide version imports outside constraints, that consistency alone has historically had radical consequences, since almost every extension of moral concern was won by pointing out an inconsistency, and that no alternative method has been proposed that starts from nowhere. That is a real limitation honestly stated rather than a refutation.
Example. You are confident that torture is always wrong, and equally confident that if torturing one terrorist were the only way to find a bomb that would kill a city, it should be done. What does reflective equilibrium require here?
That you stop holding both, and it does not tell you which to drop. What it does tell you is how to decide. Ask which judgement you hold more firmly when calm and disinterested. Ask whether either has a debunking explanation: the second is the ticking bomb case, and it is worth knowing that it is a fictional scenario with no clear real instance, that it stipulates certainties no interrogator ever has, and that it was popularised partly through television, all of which is evidence about the reliability of the intuition it produces. Ask what each option costs elsewhere: dropping the absolute prohibition means accepting a threshold and then defending where it sits, while keeping it means accepting the city. Most people who work through this end up with a very high threshold rather than a true absolute, and the important thing is that they can say why.
Now you. What in this method distinguishes an intuition worth keeping from one worth discarding?
Answer
Nothing infallible, and three things that help. Stability under reframing: a judgement that reverses when the same case is described as saving rather than killing is measuring the words rather than the case. Independence from self-interest: a judgement that happens to favour the person holding it deserves suspicion, which is why the veil of ignorance in a later lesson is a device for stripping that out. And the absence of a debunking explanation: if there is a good account of why you would hold the judgement whether or not it were correct, from upbringing, from disgust, or from a cognitive quirk, it loses weight. Note that debunking is a double-edged tool. Joshua Greene has argued from brain imaging that our resistance to pushing the man off the bridge is an evolved alarm response rather than a perception of anything, and critics reply that the same style of argument would debunk the impartial arithmetic just as easily, since a preference for bigger numbers has its own causal history. A debunking argument is only as good as its account of why one side and not the other is compromised.
What good looks like
A moral argument has gone well when both parties can state the other's position in a form the other accepts, when the disagreement has been narrowed to one or two identifiable premises, and when each can say what would change their mind.
That last requirement is the sharpest test and it deserves to be applied first. If no possible fact and no possible case would move someone's position, they are not holding a view, they are announcing an allegiance. The same question asked of yourself is uncomfortable in a useful way, and the final lesson of this course is built around answering it.
With the method in place, the substance can start. The next lesson takes the most natural moral principle there is, the one almost everyone reaches for first, and states it precisely enough to be attacked: that the right thing to do is whatever makes things go best.