* How can we distinguish between right and wrong? This question was introduced by Socrates, but he professed himself unable to give a definitive answer, encouraging people to find the answer for themselves.
Philosophers who followed him showed no such modesty. Thrasymarchus the Sophist flatly denied that there are any absolute moral values. This was hotly disputed by Plato, who claimed that a select few (like himself) had the necessary training and intellect to achieve moral certainty, and therefore the moral right to tell everyone else what to do.
* What is the "good life"? Some ancient thinkers believed that happiness ought to be our main goal in life (hedonism). Others believed that doing well at things worth doing is more important (perfectionism). Aristippus of Cyrene was a no-nonsense hedonist. He taught that the supreme good is sensual pleasure, such as eating, drinking and sex. Unlike later hedonists, he didn't concern himself with maximising pleasure over a lifetime, foregoing some pleasures because of their injurious long-term effects. He was interested only in immediate gratification.
* How does change occur? Many ancient philosophers found the process of change puzzling. How do objects come into and go out of existence? How can one thing change into another? Heraclitus believed that change is fundamental: "Nothing ever is, everything is becoming." But Zeno denied that change occurs at all. His mentor (and, some say, lover), Parmenides, taught that the universe is one thing and changeless, dismissing sensory perceptions as mere illusion.
Zeno invented ingenious arguments (Zeno's Paradoxes) to support these views. One, the Racecourse, aims to show that motion is impossible. Imagine an athlete running a race. He must reach the halfway-line. He must then cover half of the remaining distance. And so on, ad infinitum. He must therefore cover an infinite number of distances, which he can never do in a finite amount of time.
* What kind of stuff is the world made from? Thales, the first philosopher, believed that everything is water. Some time later, Empedocles identified the basic constituents of matter as earth, air, fire and water, which combine in varying proportions to make up all physical objects. Top marks go to Democritus, who said that everything is made from tiny invisible atoms, the building blocks of the physical world. These are eternal and immutable, but can be arranged in many different ways, so there is a permanent, unchanging reality behind the changing forms we see in nature.
* Can we be certain about anything? Socrates believed that knowledge is possible, albeit difficult to attain. Plato believed that we can't be certain about anything in the changing world of the senses, but we can achieve knowledge of the intellectually perceived world of "Ideas". Pyrrho of Elis (c360-275 BC) claimed that we can never be certain of anything, and that it is impossible to provide a rational justification for one course of action rather than another. This led to his legendary indecisiveness. On one occasion he had to be rescued by his students because he refused to judge whether it would be advisable to move out of the way of oncoming chariots.