Plato's Philosophy

Discussed by Angie Hobbs, lecturer in philosophy at the University of Warwick

Plato believed that everyone wants to be a flourishing human being, and that philosophy is the way to find out how to achieve this, which in his day was a relatively new discipline. One of his most radical moves was to equate human flourishing and happiness with what he calls an inner harmony of our psyche. If you look at Homer and all the Greek poets who came before him, it was an external matter. Plato said that justice and virtue are really interior to you - they are about the inner state of your soul. This was later developed by the Christians into your 'conscience'. It was an enormously important move in the history of Western ethics and religion, and had a big impact on the development of Christianity.

Sun-centred (Copernican) Theory of the Universe

Discussed by Dr Robert Massey of the Royal Astronomical Society

Although Galileo Galilei wasn't the first person to suggest that the Earth went round the Sun (that wasn't even Copernicus - the record goes to a Greek astronomer Aristarchus who suggested it 2,000 years earlier) his discovery provided evidence and support of that theory. That was extremely influential. He discovered sunspots and was one of the first people to understand the moons of Jupiter, which indicated that the Earth was not the only centre of movement in the universe. He also understood that the Milky Way was not just a glow in the sky but made up of many stars. All these things are major discoveries in astronomy. The key thing Galileo did was to open up what we call the idea of the scientific investigation of the stars by using telescopes, by actually being able to see more than the eye could alone.

Cartesian Cogito

Discussed by John Cottingham, professor of philosophy at Reading University and contributor to The Cambridge Companion to Descartes

By declaring 'cogito ergo sum' (I think, therefore I am), Descartes put the thinking subject at the centre of his enquiry. Instead of starting with physics and the natural world, he started with this individual meditator. And he made a distinction between mind and matter, the province of science which dealt with the quantifiable and that part of reality which couldn't ever be reduced to science, namely consciousness and thought. Descartes is rightly called the father of modern philosophy. His perspective on thought and consciousness as lying outside the spheres of natural science was a really significant idea which we are still trying to come to terms with. His ideas opened up the possibility of a serious study of perception and psychological space.

Theory of Universal Gravitation

Discussed by Professor Martin Rees, professor of cosmology and astrophysics at Cambridge University

Newton's theory was the first demonstration that maths could be used to understand the natural world. We can predict eclipses a century ahead because the systems of the orbits of the planets are actually quite simple. Had Newton not existed it might have been a century or more before anyone else came up with the idea. The concept of the clockwork universe (that the universe was governed by mathematical laws) was very important in 18th-century culture. Newton's gravity is still the basis whereby programmes are made that send space probes to the the planets.

Adam Smith's Laissez-Faire Economics

Discussed by Joseph Stiglitz, winner of the 2001 Nobel Prize for Economics and chair of the Brooks World Poverty Institute at Manchester University

Adam Smith's major economic idea, or one strand of it, was that in pursuit of their self-interest, individuals would be led, as if by an invisible hand, to the common good. It was revolutionary because it said you don't need a benevolent despot to ensure that the general welfare is pursued; markets are all you need. The view underlies things like Thatcherism, the ideas that the World Bank exports to the developing world, and is also behind the rhetoric of some of Bush's policies. But there's a second strand to Smith's idea, less spoken about by the free marketeers, which is clear on the need for governments to intervene in some areas. Smith's Invisible Hand has now been discredited but it continues to have a lot of influence, good and bad. We learn from it the power of the market but taking away trade barriers has exposed developing countries to an onslaught of subsidised agricultural goods, destroying their capacities in agriculture and leading to famine.

Women's Liberation

Discussed by Lynne Segal, professor of psychology and gender studies at Birkbeck University

A Vindication of the Rights of Woman (1792) is incredibly important because it shows that women have always been there at moments of radical thinking and emancipatory and liberatory thoughts. Mary Wollstonecraft was critical of all the ways women are trapped within notions of femininity which she felt were belittling. At the end of the 19th century women were troubled by her radicalism (she thought they should choose free lives just like men). It's not until second-wave feminism in the 1960s that women returned to the voice of Wollstonecraft. It took quite a long while for the world in general to catch up, but if she hadn't been there I think somebody else would have been. She was very important, but I don't believe in this idea of single figures changing history.

Marxist Analysis of Capitalism

Discussed by Tony Benn, writer/politician

Marx's analysis is uniquely important because it studied the development of modern capitalism. He said the conflict in the world is not between genders and races, it's between the 95 per cent who create the world's wealth and the 5 per cent who own it. His analysis of where power lay explained it so clearly that the people who were being exploited realised this. He gave us the best explanation of what was going on at the time, and it's even more relevant today. Capitalism has got stronger but people are beginning to understand what it's about. He helps people to understand for example, that America invaded Iraq because they wanted the oil. And don't forget his moral judgment - anyone could have written a book about capitalism, but he said it was wrong. That's what gives strength to it. I think Marx's ideas are inextricable from the idea of democracy. Stalin distorted them to justify a dictatorship but you can't blame Marx for that. Stalin has nothing to do with Marx in the way the Spanish Inquisition have nothing to do with Jesus.

Theory of the Unconscious

Discussed by Professor Susie Orbach, psychoanalyst and visiting professor of sociology at the London School of Economics

Freud explored the way in which human behaviour is guided by the unconscious, which inclines one to do things which are not necessarily in one's conscious mind or felt to be in one's best interests. He was the first to say that if we let people talk in a particular kind of setting they will discover things, through dreams and slips of the tongue, that are much more complicated than the story they have about themselves. This opened up a notion that we could be curious in relation to ourselves; he made the human's relationship to its own mind and other minds a subject for study. Almost everything we understand about romance, art, culture, the movies, the problems between the sexes, refer to a kind of Freudian moment where we understand that we are more complex than we know. We're all post Freudian now. We believe that emotions are a critical part of what motivates people. The whole rationalist argument has been knocked on the head.

Theory of Relativity

Discussed by Professor Brian Cox, Royal Society University Research Fellow

Einstein's theory completely changed the world. It doesn't seem like it at first sight because it's a strange theory - it says things like there's no such thing as a universal time, so if you have a clock ticking in one place it ticks at a different speed to a clock ticking in another place, so it sounds very esoteric. Actually, it's the foundation of every modern theory we have of the way the world works, whether it's electricity and magnetism or silicon chips or transistors - all those theories are based on relativity. Without relativity we couldn't have the modern view of the world that we have today. For example, the GPS system, satellite navigation: it's bizarre because it works by measuring the time delay between your car and satellites in orbit.

World Wide Web

Discussed by Professor John Naughton of the Public Understanding of Technology, Open University

In less than two decades the web has gone from zero to hundreds of billions of pages (nobody knows how many), enabled everyone to become a publisher or broadcaster, brought the Louvre to your laptop and made it much, much harder to keep secrets. Tim Berners-Lee, who invented the World Wide Web more or less single-handedly in 1989-90, is our Gutenberg. Gutenberg invented printing by movable type in 1455, undermining the authority of the Catholic church, fuelling the Reformation, enabling the rise of modern science and shaping our world. The web is a technology of comparable reach and scope. Trying to assess the long-term significance of the web is like trying to forecast the impact of printing in 1475. Come back in 300 years and we'll know more.