Key concepts and their function in the text practice questions.

In Plato's Republic the allegory of the cave is introduced in Book VII. Within the argument of that book its main function is to

• prove by argument that the Forms exist quite independently of their particulars
• record the actual training given to guardians in a city Plato had visited
• picture education as a turning of the whole soul, and ground the return to rule
• show that the senses can never deliver even the beliefs we ordinarily rely on

Answer: picture education as a turning of the whole soul, and ground the return to rule

The cave carries the claim that education redirects an already existing capacity rather than putting sight into blind eyes, and it is what makes the philosopher's obligation to go back down intelligible. It is not itself an argument for the Forms; that argument is made in Book V against the lovers of sights and sounds, while Book VI's sun and line describe what the Good does for knowing and how knowing is graded.

In Meditation II Descartes turns to the piece of wax after establishing the cogito and that he is a thinking thing. Within the argument of that Meditation the example is there to

• settle whether any body exists outside the meditator's own mind
• support the closing claim that the mind is better known than the body
• restore the standing of the senses once the deceiving demon has been set aside
• show that the essence of a body is exhausted by what it presents to the senses

Answer: support the closing claim that the mind is better known than the body

Meditation II ends by claiming that the mind is better known than any body, and the wax is the test case: even where a body seems best known, what survives the change is reached by the intellect. The passage is not an argument that bodies exist, which Descartes only attempts in Meditation VI.

Mill opens On Liberty by warning about the tyranny of the majority. The function of that idea in his opening chapter is to

• argue that majority rule ought to be replaced by the rule of a trained elite of experts
• show that a democratic government cannot be legitimate unless its decisions are unanimous
• identify the machinery of the state as the only thing that can genuinely restrict liberty
• widen the question of liberty from acts of government to the pressure of opinion

Answer: widen the question of liberty from acts of government to the pressure of opinion

Mill's target is social tyranny, the enforcement of custom by opinion, which he says penetrates further into private life than any magistrate. Reading the phrase as a complaint about voting rules misses why the essay goes on to discuss discussion and individuality rather than constitutions.

In the third essay of Nietzsche's Genealogy of Morality, the ascetic ideal takes hold, on his account, because it

• offered the sick an effective cure for the physical causes of their suffering
• gave suffering a meaning, so that the will had something left to will
• was imposed from outside on a weaker people by the priestly caste of a rival one
• expressed the confident self-affirmation of the noble mode of valuation

Answer: gave suffering a meaning, so that the will had something left to will

For Nietzsche what was unbearable was not suffering but its meaninglessness, and the ascetic ideal supplied an interpretation of it. This is a different mechanism from the slave revolt of the first essay, which explains the inversion of good and bad rather than the management of suffering.

In the Republic Socrates proposes that philosophers should rule. Within the argument of the work, the function of that proposal is to

• answer the question whether the city that has been described could actually come into being
• introduce a new definition of justice that replaces the one reached in Book IV
• provide a historical account of how existing Greek cities were in fact governed
• concede that the city described so far has been shown to be internally inconsistent at several points

Answer: answer the question whether the city that has been described could actually come into being

The proposal is presented as the smallest change that would make the city possible, which is why it comes after the definition rather than before it, and why the discussion of knowledge and the Forms follows: the case for the rule of philosophers depends on there being something they know that others do not.

Mill devotes the third chapter of On Liberty to individuality as one of the elements of well-being. The function of this chapter in the work as a whole is to

• restrict the principle defended in chapter one to matters of opinion alone, so that conduct falls outside it
• supply the positive case that liberty produces goods, complementing the earlier defensive argument
• abandon the argument from utility in favour of an appeal to natural rights
• concede that customs supported by long tradition should not be questioned

Answer: supply the positive case that liberty produces goods, complementing the earlier defensive argument

Chapters one and two say what may not be interfered with and why suppression fails; chapter three says what liberty is for. Missing that division is what produces the common misreading of On Liberty as a purely negative doctrine.