Reconstructing the central arguments of the text practice questions.

The argument of Plato's Republic IV that the soul has distinct parts rests on the principle that

• each part of a thing possesses a virtue that belongs to that part alone
• the same thing cannot undergo opposite states in the same respect at the same time
• every desire is in the last analysis a desire for what is genuinely good
• a city and an individual must always contain the very same number of functioning parts

Answer: the same thing cannot undergo opposite states in the same respect at the same time

Socrates needs a principle strong enough to force a division, and the case of the thirsty man who refuses to drink supplies opposite states in one soul; without the qualifications about respect and time the principle would be false and the division would collapse.

Plato's Republic first locates justice in the city and then transfers that definition to the individual soul. Which assumption must be granted for the transfer to go through?

• That the city came into existence before the individuals who now compose it
• That every citizen of the city belongs to exactly one of the three classes and to no other
• That the same form of justice is present in a city and in an individual alike
• That justice is easier to make out in a large object than in a small one

Answer: That the same form of justice is present in a city and in an individual alike

The claim about legibility in the large is the stated motive for looking at the city first, but it is the unstated assumption of a shared form that licenses the transfer of the result back to the soul, and that is the step critics of the analogy attack.

In the Sixth Meditation Descartes argues for a real distinction between mind and body. The premise that takes the argument from what he can conceive to a real distinction is that

• the mind is observed to continue functioning when parts of the body are removed, as surgeons had already observed
• whatever he can clearly and distinctly conceive as separate, God can bring about as separate
• the body is extended in space while the mind occupies no particular place
• the senses often deceive him about the properties of bodies

Answer: whatever he can clearly and distinctly conceive as separate, God can bring about as separate

The argument runs from conceivability to possibility by way of divine power, which is why it depends on the earlier proofs about God and about clear and distinct perception. Objectors press exactly there: conceiving two things apart may show only the limits of one's conception.

Mill argues that society may not interfere with conduct that concerns only the agent herself, even where others find that conduct distasteful. The argument depends on the assumption that

• no conduct whatever produces effects on other people
• displeasure at another's conduct does not count as the kind of harm that licenses interference
• everyone is an equally good judge of what will benefit her
• the state is generally incompetent to enforce any rule at all, so that any rule it makes will be applied badly

Answer: displeasure at another's conduct does not count as the kind of harm that licenses interference

Without that assumption the principle collapses, since almost any conduct distresses somebody and the distress would then license restraint. Mill defends it in chapter IV, saying there is no parity between a person's feeling for his own conduct and another's offence at it; critics reply that where harm ends and mere offence begins still needs argument.

In the second treatise of the Genealogy, Nietzsche argues that a practice such as punishment has accumulated many meanings in the course of its history and that none of them is fixed by how it began. The conclusion he draws is that

• punishment has no effects worth studying, since its meaning changes constantly, so that a history of it can teach us nothing
• the earliest use of a practice reveals its true and permanent function
• the present purpose of a practice cannot be inferred from its origin, since later forces impose new purposes on it
• practices with several meanings should be abolished as incoherent

Answer: the present purpose of a practice cannot be inferred from its origin, since later forces impose new purposes on it

The claim separates the emergence of a form from the uses to which it is later put, and it cuts both ways: it blocks any inference from origin to present function, including inferences a critic of morality might want to make.

At the start of the First Meditation the meditator says he will not examine his beliefs one by one. The strategy he adopts instead is to

• attack the principles on which his beliefs rest, so that the rest fall with them
• accept without further examination the beliefs most people share and doubt only those peculiar to himself
• sort his beliefs into those about mathematics and those about physical things
• keep every belief that has never in fact led him into a practical mistake

Answer: attack the principles on which his beliefs rest, so that the rest fall with them

The architectural image explains why the doubt proceeds by grounds of belief, senses, dreaming and a deceiving power, rather than by subject matter, and why one counterexample to a foundation is enough to unsettle everything built on it.