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 Professor of Philosophy at the University of St AndrewsPeter Millican Professor of Philosophy at the University of OxfordClare Carlisle Lecturer in Philosophy of Religion at King's College LondonProducer: 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 Professor of Philosophy at Hertford College, OxfordMelissa Lane Professor of Politics at Princeton UniversityJill Kraye Professor of the History of Renaissance Philosophy and Librarian at the Warburg Institute, University of London. 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 Professor of Arabic at SOAS, University of LondonJames Montgomery Sir Thomas Adams's Professor of Arabic Elect at the University of CambridgeAmira Bennison Senior Lecturer in Middle Eastern and Islamic Studies at the University of Cambridge.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.

Angie Hobbs, a philosophy associate professor, Peter Adamson, an expert in ancient thought, and James Warren, a classics lecturer, dive into Heraclitus's world. They discuss his enigmatic views on change, famously asserting that nothing remains the same. The trio explores the unity of opposites, where life and death intertwine. They also unpack his intricate philosophy of perception and the 'logos' that connects everything. Finally, an entertaining anecdote about Heraclitus's quirky death sheds light on his unique character, blending humor with philosophical insight.

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.

Melvyn Bragg and his guests discuss Malthusianism.In the eighteenth century, as expanding agriculture and industry resulted in a rapid increase in the European population, a number of writers began to consider the implications of this rise in numbers. Some argued it was a positive development, since a larger population meant more workers and thus more wealth. Others maintained that it placed an intolerable strain on natural resources.In 1798 a young Anglican priest, the Reverend Thomas Malthus, published An Essay on the Principle of Population. Malthus argued that the population was increasing exponentially, and that food production could not keep pace; eventually a crisis would ensue. He suggested that famine, disease and wars acted as a natural corrective to overpopulation, and also suggested a number of ways in which humans could regulate their own numbers. The work caused a furore and fuelled a public debate about the size and sustainability of the British population which raged for generations. It was a profoundly influential work: Charles Darwin credited Malthus with having inspired his Theory of Natural Selection.With:Karen O'BrienPro-Vice-Chancellor for Education at the University of BirminghamMark PhilpLecturer in Politics at the University of OxfordEmma GriffinSenior Lecturer in History at the University of East Anglia Producer: Thomas Morris.

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.