The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things, meaning simply that that which seems to each man assuredly is. If this is so, it follows that the same thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true, because often a particular thing appears beautiful to some and ugly to others, and that which appears to each man is the measure
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
The art of wealth-getting which consists in household management, on the one hand, has a limit; the unlimited acquisition of wealth is not its business. And therefore, in one point of view, all riches must have a limit; nevertheless, as a matter of fact, we find the opposite to be the case; for all getters of wealth increase their hard coin without limit.
There is only one condition in which we can imagine managers not needing subordinates, and masters not needing slaves. This condition would be that each (inanimate) instrument could do its own work.
It is the mark of an educated mind to expect that amount of exactness which the nature of the particular subject admits. It is equally unreasonable to accept merely probable conclusions from a mathematician and to demand strict demonstration from an orator.
Democracy is the form of government in which the free are rulers, and oligarchy in which the rich; it is only an accident that the free are the many and the rich are the few.
But since there is but one aim for the entire state, it follows that education must be one and the same for all, and that the responsibility for it must be a public one, not the private affair which it now is, each man looking after his own children and teaching them privately whatever private curriculum he thinks they ought to study.
Since we think we understand when we know the explanation, and there are four types of explanation (one, what it is to be a thing; one, that if certain things hold it is necessary that this does; another, what initiated the change; and fourth, the aim), all these are proved through the middle term.