Melvyn Bragg and his guests discuss the influential British philosopher Bertrand Russell. Born in 1872 into an aristocratic family, Russell is widely regarded as one of the founders of Analytic philosophy, which is today the dominant philosophical tradition in the English-speaking world. In his important book The Principles of Mathematics, he sought to reduce mathematics to logic. Its revolutionary ideas include Russell's Paradox, a problem which inspired Ludwig Wittgenstein to pursue philosophy. Russell's most significant and famous idea, the theory of descriptions, had profound consequences for the discipline.

In addition to his academic work, Russell played an active role in many social and political campaigns. He supported women's suffrage, was imprisoned for his pacifism during World War I and was a founder of the Campaign for Nuclear Disarmament. He wrote a number of books aimed at the general public, including The History of Western Philosophy which became enormously popular, and in 1950 he was awarded the Nobel Prize in Literature. Russell's many appearances on the BBC also helped to promote the public understanding of ideas.

With:

AC Grayling

Mike Beaney

Hilary Greaves

Producer: Victoria Brignell.

Melvyn Bragg and his guests discuss the French philosopher and social activist Simone Weil. Born in Paris in 1909 into a wealthy, agnostic Jewish family, Weil was a precocious child and attended the prestigious Ecole Normale Superieure in Paris, achieving the top marks in her class (Simone de Beauvoir came second).

Weil rejected her comfortable background and chose to work in fields and factories to experience the life of the working classes at first hand. She was acutely sensitive to human suffering and devoted her life to helping those less fortunate than herself. Despite her belief in pacifism she volunteered on the Republican side during the Spanish Civil War and later joined the French Resistance movement in England.

Her philosophy was both complex and intense. She argued that the presence of evil and suffering in the world was evidence of God's love and that Man has no right to ask anything of God or of anyone whom they love. Love which expects reward was not love at all in Weil's eyes.

Weil died of TB in Kent at the age of only 34. Her strict lifestyle and self-denial may have contributed to her early death. T.S Eliot said "she was not just a woman of genius, but was a genius akin to that of a saint"; Albert Camus believed she was "the only great spirit of our time."

With:

Beatrice Han-Pile

Stephen Plant

David Levy

Producer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the Ontological Argument. In the eleventh century St Anselm of Canterbury proposed that it was possible to prove the existence of God using reason alone. His argument was ridiculed by some of his contemporaries, but was analysed and improved by later thinkers including Descartes, Spinoza and Leibniz. Other philosophers have been less kind, with the Enlightenment thinker David Hume offering one possible refutation. But the debate continued, fuelled by interventions from such heavyweights as Immanuel Kant and Kurt Gödel; and it remains one of the most discussed problems in philosophy.

With:

John Haldane

Peter Millican

Clare Carlisle

Producer: Thomas Morris.

Melvyn Bragg and his guests discuss Scepticism, the idea that it may be impossible to know anything with complete certainty. Scepticism was first outlined by ancient Greek philosophers: Socrates is reported to have said that the only thing he knew for certain was that he knew nothing. Later, Scepticism was taught at the Academy founded by Plato, and learnt by students who included the Roman statesman Cicero. The central ideas of Scepticism were taken up by later philosophers and came to the fore during the Renaissance, when thinkers including Rene Descartes and Michel de Montaigne took up its challenge. A central plank of the philosophical system of David Hume, Scepticism had a powerful influence on the religious and scientific debates of the Enlightenment.

With:

Peter Millican

Melissa Lane

Jill Kraye

Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the life and work of the Arab philosopher al-Kindi. Born in the early ninth century, al-Kindi was heavily influenced by Greek philosophy and supervised the translation of many works by Aristotle and others into Arabic. The author of more than 250 works, he wrote on many different subjects, from optics to mathematics, music and astrology. He was the first significant thinker to argue that philosophy and Islam had much to offer each other and need not be kept apart. Today al-Kindi is regarded as one of the greatest scholars of the medieval Islamic world.

With:

Hugh Kennedy

James Montgomery

Amira Bennison

Producer: Thomas Morris.

Melvyn Bragg and his guests discuss Neoplatonism, the school of thought founded in the 3rd century AD by the philosopher Plotinus. Born in Egypt, Plotinus was brought up in the Platonic tradition, studying and reinterpreting the works of the Greek thinker Plato. After he moved to Rome Plotinus became the most influential member of a group of thinkers dedicated to Platonic scholarship. The Neoplatonists - a term only coined in the nineteenth century - brought a new religious sensibility to bear on Plato's thought. They outlined a complex cosmology which linked the human with the divine, headed by a mysterious power which they called the One. Neoplatonism shaped early Christian, Jewish and Muslim religious scholarship, and remained a dominant force in European thought until the Renaissance. With:Angie HobbsAssociate Professor of Philosophy and Senior Fellow in the Public Understanding of Philosophy at the University of WarwickPeter AdamsonProfessor of Ancient and Medieval Philosophy at King's College LondonAnne SheppardProfessor of Ancient Philosophy at Royal Holloway, University of LondonProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the work and influence of the eighteenth-century philosopher Moses Mendelssohn. A prominent figure at the court of Frederick the Great, Mendelssohn was one of the most significant thinkers of his age. He came from a humble, but culturally rich background and his obvious intelligence was recognised from a young age and nurtured by the local rabbi where he lived in the town of Dessau in Prussia. Moses's learning earned him the sobriquet of the 'German Socrates' and he is considered to be one of the principal architects of the Haskala, the Jewish Enlightenment, and widely regarded as having helped bring Judaism into the mainstream of European culture. Mendelssohn is perhaps best remembered today for his efforts to bring Jewish and German culture closer together and for his plea for religious toleration.With:Christopher ClarkProfessor of Modern European History at the University of CambridgeAbigail GreenTutor and Fellow in History at the University of OxfordAdam SutcliffeSenior Lecturer in European History at King's College, London Producer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the ancient Greek philosopher Heraclitus. Writing in the 5th century BC, Heraclitus believed that everything is constantly changing or, as he put it, in flux. He expressed this thought in a famous epigram: "No man ever steps into the same river twice." Heraclitus is often considered an enigmatic thinker, and much of his work is complex and puzzling. He was critical of the poets Homer and Hesiod, whom he considered to be ignorant, and accused the mathematician Pythagoras (who may have been his contemporary) of making things up. Heraclitus despaired of men's folly, and in his work constantly strove to encourage people to consider matters from alternative perspectives. Donkeys prefer rubbish to gold, he observed, pointing out that the same thing can have different meanings to different people.Unlike most of his contemporaries he was not associated with a particular school or disciplinary approach, although he did have his followers. At times a rationalist, at others a mystic, Heraclitus is an intriguing figure who influenced major later philosophers and movements such as Plato and the Stoics.With:Angie HobbsAssociate Professor of Philosophy and Senior Fellow in the Public Understanding of Philosophy at the University of WarwickPeter AdamsonProfessor of Ancient and Medieval Philosophy at King's College LondonJames WarrenSenior Lecturer in Classics and a Fellow of Corpus Christi College, University of CambridgeProducer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the Continental-Analytic split in Western philosophy. Around the beginning of the last century, philosophy began to go down two separate paths, as thinkers from Continental Europe explored the legacy of figures including Friedrich Nietzsche and Martin Heidegger, while those educated in the English-speaking world tended to look to more analytically-inclined philosophers like Bertrand Russell and Gottlob Frege. But the divide between these two schools of thought is not clear cut, and many philosophers even question whether the term 'Continental' is accurate or useful.The Analytic school favours a logical, scientific approach, in contrast to the Continental emphasis on the importance of time and place. But what are the origins of this split and is it possible that contemporary philosophers can bridge the gap between the two? With:Stephen MulhallProfessor of Philosophy at New College, University of OxfordBeatrice Han-PileProfessor of Philosophy at the University of EssexHans Johann-Glock Professor of Philosophy at the University of ZurichProducer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the work of the philosopher David Hume. A key figure in the Scottish Enlightenment of the eighteenth century, Hume was an empiricist who believed that humans can only have knowledge of things they have themselves experienced. Hume made a number of significant contributions to philosophy. He saw human nature as a manifestation of the natural world, rather than something above and beyond it. He gave a sceptical account of religion, which caused many to suspect him of atheism. He was also the author of a bestselling History of England. His works, beginning in 1740 with A Treatise of Human Nature, have influenced thinkers from Adam Smith to Immanuel Kant and Charles Darwin, and today he is regarded by some scholars as the most important philosopher ever to write in English.With:Peter MillicanProfessor of Philosophy at the University of OxfordHelen BeebeeProfessor of Philosophy at the University of BirminghamJames HarrisSenior Lecturer in Philosophy at the University of St AndrewsProducer: Thomas Morris.