Melvyn Bragg and guests discuss the consolation of Philosophy. In the 6th century AD, a successful and intelligent Roman politician called Boethius found himself unjustly accused of treason. Trapped in his prison cell, awaiting a brutal execution, he found solace in philosophical ideas - about the true nature of reality, about injustice and evil and the meaning of living a moral life. His thoughts did not save him from death, but his ideas lived on because he wrote them into a book. He called it The Consolation of Philosophy. The Consolation of Philosophy was read widely and a sense of consolation is woven into many philosophical ideas, but what for Boethius were the consolations of philosophy, what are they more generally and should philosophy lead us to consolation or lead us from it?With AC Grayling, Professor of Philosophy at Birkbeck College, University of London; Melissa Lane, Senior University Lecturer in History at the University of Cambridge and Roger Scruton, Research Professor at the Institute for the Psychological Sciences.

Melvyn Bragg and guests discuss one of the most important works of political philosophy ever written - Aristotle’s ‘Politics’. Looking out across the city states of 4th century Greece Aristotle asked what made a society good and developed a language of ‘oligarchies’, ‘democracies’ and ‘monarchies’ that we still use today. Having witnessed his home town of Stagira destroyed by Philip of Macedon, Aristotle tried to establish a way of preserving a good society in dangerous times. How should it be governed and who should be allowed to live in it? Thomas Hobbes, Jean-Jacques Rousseau, Thomas Aquinas and Niccolo Machiavelli, to name but a few, have all asked the same questions and come up with wildly differing answers.Aristotle’s conclusions range across the role of wealth and the law, across men, women and slaves, education and leisure. They are far reaching, influential and, at times, deeply unpalatable. But they are also answers to questions that have not and will not go away. With Angie Hobbs, Associate Professor of Philosophy at the University of Warwick; Paul Cartledge, AG Leventis Professor of Greek Culture at the University of Cambridge and Annabel Brett, Senior Lecturer in History at the University of Cambridge.

Melvyn Bragg and guests discuss an iconic piece of 20th century maths - Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

Melvyn Bragg and guests discuss one of the greatest intellectual projects in history - the mass translation of Greek ideas into Arabic from the 9th century onwards.One night in Baghdad, the 9th century Caliph Al-Mamun was visited by a dream. The philosopher Aristotle appeared to him, saying that the reason of the Greeks and the revelation of Islam were not opposed. On waking, the Caliph demanded that all of Aristotle’s works be translated into Arabic. And they were. And it wasn’t just Aristotle. Over the next 200 years Greek philosophy, medicine, engineering and maths were all poured and sometimes squeezed into Arabic. Centred on Baghdad, this translation movement introduced the Islamic world to the philosophy of Aristotle, the geometry of Euclid and the Medicine of Galen. It caused an intellectual ferment that demanded the creation of new words to explain new concepts and house new arguments. Over 600 years before the European renaissance the intellectual legacy of Greece was woven into the tapestry of Arabic thought and it was only through the Arabic versions that Europe go its hands on many Greek ideas. With Peter Adamson, Reader in Philosophy at King’s College London; Amira Bennison, Senior Lecturer in Middle Eastern and Islamic Studies at the University of Cambridge; and Peter Pormann, Wellcome Trust Assistant Professor in Classics and Ancient History at the University of Warwick

Melvyn Bragg and guests discuss the parting of the Red Sea, the feeding of the five thousand and the general subject of miracles. Miracles have been part of human culture for thousands of years. From St Augustine in the 4th century through the medieval cult of saints to David Hume in the 18th, miracles have captured the imaginations of believers and sceptics alike. The way they have been celebrated, interpreted, dissected and refuted is a whole history of arguments between philosophy, science and religion. They have also been used by the corrupt and the powerful to gain their perverse ends. Miracles have been derided and proved to be fraudulent and yet, for many, the miraculous maintain a grip on our imagination, our language and our belief to this day. With Martin Palmer, Director of the International Consultancy on Religion, Education and Culture;Janet Soskice, Reader in Philosophical Theology at Cambridge University; Justin Champion, Professor of the History of Early Modern Ideas at Royal Holloway, University of London.

Melvyn Bragg and guests discuss Materialism in Philosophy – the idea that matter and the interactions between matter account for all that exists and all that happens. We trace the descent of materialism from the ancient Greek philosophers Democritus and Epicurus, to its powerful and controversial flowering in the 17th, 18th and 19th centuries as an attack on religion. It’s provocative stuff even today and certainly was in 1770 when Baron D’Holbach published his book The System of Nature. He wrote: "If we go back to the beginning we shall find that ignorance and fear created the gods; that fancy, enthusiasm, or deceit adorned or disfigured them; that weakness worships them; that credulity preserves them, and that custom, respect and tyranny support them."Materialism was considered so dangerous that every copy of the Baron’s book was condemned to be burnt. Despite this, or perhaps because of it, materialism dominates much of our understanding of the world today. Associated with science and atheism, Materialism has influenced many forms of contemporary human thought from the process of history to the diagnosis of disease and boasts a cast list of devotees including Pierre Gassandi, Thomas Hobbes, the Marquis de Sade and Karl Marx. But what does materialism really mean, how has it developed over time and can we still have free will if we are living in a materialist world? With Anthony Grayling, Professor of Philosophy at Birkbeck College, University of London; Caroline Warman, Fellow of Jesus College, Oxford; Anthony O’Hear, Professor of Philosophy at the University of Buckingham

Melvyn Bragg and guests discuss the rich and radical ideas of Soren Kierkegaard, often called the father of Existentialism.In 1840 a young Danish girl called Regine Olsen got engaged to her sweetheart – a modish and clever young man called Søren Kierkegaard. The two were deeply in love but soon the husband to be began to have doubts. He worried that he couldn’t make Regine happy and stay true to himself and his dreams of philosophy. It was a terrible dilemma, but Kierkegaard broke off the engagement – a decision from which neither he nor his fiancée fully recovered. This unhappy episode has become emblematic of the life and thought of Søren Kierkegaard - a philosopher who confronted the painful choices in life and who understood the darker modes of human existence. Yet Kierkegaard is much more than the gloomy Dane of reputation. A thinker of wit and elegance, his ability to live with paradox and his desire to think about individuals as free have given him great purchase in the modern world and he is known as the father of Existentialism.With Jonathan Rée, Visiting Professor at Roehampton University and the Royal College of Art; Clare Carlisle, Lecturer in Philosophy at the University of Liverpool; John Lippitt, Professor of Ethics and Philosophy of Religion at the University of Hertfordshire.

Melvyn Bragg and guests discuss the Social Contract and ask a foundational question of political philosophy – by what authority does a government govern? “Man was born free and he is everywhere in chains”. So begins Jean Jacques Rousseau’s great work on the Social Contract. Rousseau was trying to understand why a man would give up his natural freedoms and bind himself to the rule of a prince or a government. But the idea of the social contract - that political authority is held through a contract with those to be ruled - began before Rousseau with the work of John Locke, Hugo Grotius and even Plato. We explore how an idea that burgeoned among the 17th century upheavals of the English civil war and then withered in the face of modern capitalist society still influences our attitude to government today. With Melissa Lane, Senior University Lecturer in History at Cambridge University; Susan James, Professor of Philosophy at Birkbeck College, University of London; Karen O’Brien, Professor of English Literature at the University of Warwick.

Melvyn Bragg and guests discuss the Algerian-French writer and Existentialist philosopher Albert Camus. Shortly after the new year of 1960, a powerful sports car crashed in the French town of Villeblevin in Burgundy, killing two of its occupants. One was the publisher Michel Gallimard; the other was the writer Albert Camus. In Camus’ pocket was an unused train ticket and in the boot of the car his unfinished autobiography The First Man. Camus was 46. Born in Algeria in 1913, Camus became a working class hero and icon of the French Resistance. His friendship with Sartre has been well documented, as has their falling out; and although Camus has been dubbed both an Absurdist and Existentialist philosopher, he denied he was even a philosopher at all, preferring to think of himself as a writer who expressed the realities of human existence. Awarded the Nobel Prize for Literature in 1957, Camus’ legacy is a rich one, as an author of plays, novels and essays, and as a political thinker who desperately sought a peaceful solution to the War for Independence in his native Algeria. With Peter Dunwoodie, Professor of French Literature at Goldsmiths, University of London; David Walker, Professor of French at the University of Sheffield; Christina Howells, Professor of French at Wadham College, University of Oxford.

Melvyn Bragg and guests discuss the Persian Islamic philosopher, Avicenna. In the city of Hamadan in Iran, right in the centre, there is a vast mausoleum dedicated to an Iranian national hero. Built in 1952, exactly 915 years after his death, it’s a great conical tower with twelve supporting columns. It’s dedicated not to a warrior or a king but to a philosopher and physician. His name is Ali Al Husayn Ibn-Sina, but he is also known as Avicenna and he is arguably the most important philosopher in the history of Islam.  In a colourful career Avicenna proved the existence of god, amalgamated all known medical knowledge into one big book and established a mind body dualism 600 years before Descartes and still found time to overindulge in wine and sex. With Peter Adamson, Reader in Philosophy at King's College London; Amira Bennison, Senior Lecturer in Middle Eastern and Islamic Studies at the University of Cambridge; Nader El-Bizri, Affiliated Lecturer in the History and Philosophy of Science at the University of Cambridge.