Melvyn Bragg and his guests discuss one of the most famous statements in philosophy: "Cogito ergo sum".In his Discourse on the Method, published in 1637, the French polymath Rene Descartes wrote a sentence which remains familiar today even to many people who have never heard of him. "I think", he wrote, "therefore I exist". Although the statement was made in French, it has become better known in its Latin translation; and philosophers ever since have referred to it as the Cogito Argument.In his first Meditation, published ten years after the Discourse, Descartes went even further. He asserted the need to demolish everything completely and start right again from the foundations, arguing, for instance, that information from the senses cannot be trusted. The only thing he could be sure of was this: because he was thinking, he must exist. This simple idea continues to stir up enormous interest and has attracted comment from thinkers from Hobbes to Nietzsche and Sartre. With:Susan JamesProfessor of Philosophy at Birkbeck College, University of LondonJohn CottinghamProfessor Emeritus of Philosophy at the University of Reading and Professorial Research Fellow at Heythrop College, University of LondonStephen MulhallProfessor of Philosophy at the University of Oxford.Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the Pelagian Controversy.In the late 4th century a British monk, Pelagius, travelled to Rome, where he became a theologian and teacher, revered for his learning and ascetic lifestyle. But he soon aroused the ire of some of the Church's leading figures, preaching a Christian doctrine which many regarded as heretical. Pelagius believed that mankind was not inherently depraved, and disputed the necessity of original sin. His opinions were highly controversial and led to fierce division. Pelagius's most prominent opponent was the African bishop St Augustine of Hippo. Their dispute resulted in the persecution and eventual condemnation of Pelagius and his followers, and was to be of long-lasting significance to the future of the Church.With:Martin PalmerDirector of the International Consultancy on Religion, Education, and CultureCaroline HumfressReader in History at Birkbeck College, University of LondonJohn MilbankProfessor in Religion, Politics and Ethics and the Director of the Centre for Theology and Philosophy at Nottingham UniversityProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the neutrino.In 1930 the physicist Wolfgang Pauli proposed the existence of an as-yet undiscovered subatomic particle. He also bet his colleagues a case of champagne that it would never be detected. He lost his bet when in 1956 the particle, now known as the neutrino, was first observed in an American nuclear reactor. Neutrinos are some of the most mysterious particles in the Universe. The Sun produces trillions of them every second, and they constantly bombard the Earth and everything on it. Neutrinos can pass through solid rock, and even stars, at almost the speed of light without being impeded, and are almost impossible to detect. Today, experiments involving neutrinos are providing insights into the nature of matter, the contents of the Universe and the processes deep inside stars.With:Frank CloseProfessor of Physics at Exeter College at the University of OxfordSusan CartwrightSenior Lecturer in Particle Physics and Astrophysics at the University of SheffieldDavid WarkProfessor of Particle Physics at Imperial College, London, and the Rutherford Appleton Laboratory. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the Victorian social reformer Octavia Hill.From the 1850s until her death in 1912, Octavia Hill was an energetic campaigner who did much to improve the lot of impoverished city dwellers. She was a pioneer of social housing who believed that there were better and more humane ways of arranging accommodation for the poor than through the state. Aided at first by her friend John Ruskin, the essayist and art critic, she bought houses and let them to the urban dispossessed. Octavia Hill provided an early model of social work, did much to preserve urban open spaces, and was the first to use the term 'green belt' to describe the rural areas around London. She was also one of the founders of the National Trust. Yet her vision of social reform, involving volunteers and private enterprise rather than central government, was often at odds with that of her contemporaries.With:Dinah BirchProfessor of English Literature and Pro-Vice Chancellor for Research at Liverpool UniversityLawrence GoldmanFellow in Modern History at St Peter's College, OxfordGillian DarleyHistorian and biographer of Octavia HillProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the Bhagavad Gita.The Bhagavad Gita, a 700-verse section of the Sanskrit epic the Mahabharata, is one of the most revered texts of Hinduism. Written in around 200 BC, it narrates a conversation between Krishna, an incarnation of the deity, and the Pandava prince Arjuna. It has been described as a concise summary of Hindu theology, a short work which offers advice on how to live one's life.The Gita is also a philosophical work of great richness and influence. First translated into English in the 18th century, it was quickly taken up in the West. Its many admirers have included Mahatma Gandhi, whose passion for the work is one reason that the Bhagavad Gita became a key text for followers of the Indian Independence movement in the first half of the twentieth century.With:Chakravarthi Ram-PrasadProfessor of Comparative Religion and Philosophy at Lancaster UniversityJulius LipnerProfessor of Hinduism and the Comparative Study of Religion and Fellow of Clare Hall at the University of CambridgeJessica FrazierResearch Fellow at the Oxford Centre for Hindu Studies and Lecturer in Religious Studies at Regent's College, LondonProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the dawn of the European Iron Age.In around 3000 BC European metalworkers started to make tools and weapons out of bronze. A complex trading network evolved to convey this valuable metal and other goods around the continent. But two millennia later, a new skill arrived from the Middle East: iron smelting. This harder, more versatile metal represented a huge technological breakthrough.The arrival of the European Iron Age, in around 1000 BC, was a time of huge social as well as technological change. New civilisations arose, the landscape was transformed, and societies developed new cultures and lifestyles. Whether this was the direct result of the arrival of iron is one of the most intriguing questions in archaeology.With:Sir Barry CunliffeEmeritus Professor of European Archaeology at the University of OxfordSue HamiltonProfessor of Prehistory at University College LondonTimothy ChampionProfessor of Archaeology at the University of SouthamptonProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the medieval universities.In the 11th and 12th centuries a new type of institution started to appear in the major cities of Europe. The first universities were those of Bologna and Paris; within a hundred years similar educational organisations were springing up all over the continent. The first universities based their studies on the liberal arts curriculum, a mix of seven separate disciplines derived from the educational theories of Ancient Greece. The universities provided training for those intending to embark on careers in the Church, the law and education. They provided a new focus for intellectual life in Europe, and exerted a significant influence on society around them. And the university model proved so robust that many of these institutions and their medieval innovations still exist today.With:Miri RubinProfessor of Medieval and Early Modern History at Queen Mary, University of LondonIan WeiSenior Lecturer in Medieval European History at the University of BristolPeter DenleyReader in History at Queen Mary, University of London.Producer: Thomas Morris.

In the 500th edition of the programme, Melvyn Bragg and his guests discuss the philosophical idea of free will.Free will - the extent to which we are free to choose our own actions - is one of the most absorbing philosophical problems, debated by almost every great thinker of the last two thousand years. In a universe apparently governed by physical laws, is it possible for individuals to be responsible for their own actions? Or are our lives simply proceeding along preordained paths? Determinism - the doctrine that every event is the inevitable consequence of what goes before - seems to suggest so.Many intellectuals have concluded that free will is logically impossible. The philosopher Baruch Spinoza regarded it as a delusion. Albert Einstein wrote: "Human beings, in their thinking, feeling and acting are not free agents but are as causally bound as the stars in their motion." But in the Enlightenment, philosophers including David Hume found ways in which free will and determinism could be reconciled. Recent scientific developments mean that this debate remains as lively today as it was in the ancient world.With: Simon BlackburnBertrand Russell Professor of Philosophy at the University of CambridgeHelen BeebeeProfessor of Philosophy at the University of BirminghamGalen StrawsonProfessor of Philosophy at the University of ReadingProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the age of the Universe.Since the 18th century, when scientists first realised that the Universe had existed for more than a few thousand years, cosmologists have debated its likely age. The discovery that the Universe was expanding allowed the first informed estimates of its age to be made by the great astronomer Edwin Hubble in the early decades of the twentieth century. Hubble's estimate of the rate at which the Universe is expanding, the so-called Hubble Constant, has been progressively improved. Today cosmologists have a variety of other methods for ageing the Universe, most recently the detailed measurements of cosmic microwave background radiation - the afterglow of the Big Bang - made in the last decade. And all these methods seem to agree on one thing: the Universe has existed for around 13.75 billion years.With:Martin ReesAstronomer Royal and Emeritus Professor of Cosmology and Astrophysics at the University of CambridgeCarolin CrawfordMember of the Institute of Astronomy and Fellow of Emmanuel College at the University of CambridgeCarlos FrenkDirector of the Institute for Computational Cosmology at the University of Durham.Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the Taiping Rebellion.In 1850 a Chinese Christian convert, Hong Xiuquan, proclaimed himself leader of a new dynasty, the Taiping Heavenly Kingdom. He and his followers marched against the ruling Qing dynasty, gathering huge support as they went. The ensuing civil war lasted fourteen years; around twenty million people lost their lives in a conflict which eventually involved European as well as Chinese soldiers. The Taiping Rebellion was arguably the most important event to befall China in the 19th century. Chinese nationalists and communists alike have been profoundly influenced by it, and historians believe it shaped modern China in the same way as the First World War shaped modern Europe.Rana MitterProfessor of the History and Politics of Modern China at the University of OxfordFrances WoodHead of the Chinese Section at the British LibraryJulia LovellLecturer in Chinese History at Birkbeck, University of London.Producer: Thomas Morris.