Duration: 45 minutes
First broadcast: Thursday 24 September 2009

Melvyn Bragg discusses the epic feud between Sir Isaac Newton and Gottfried Leibniz over who invented an astonishingly powerful new mathematical tool – calculus. Both claimed to have conceived it independently, but the argument soon descended into a bitter battle over priority, plagiarism and philosophy.

Set against the backdrop of the Hanoverian succession to the English throne and the formation of the Royal Society, the fight pitted England against Europe, geometric notation against algebra. It was fundamental to the grounding of a mathematical system which is one of the keys to the modern world, allowing us to do everything from predicting the pressure building behind a dam to tracking the position of a space shuttle.

Melvyn is joined by Simon Schaffer, Professor of History of Science at the University of Cambridge and Fellow of Darwin College; Patricia Fara, Senior Tutor at Clare College, University of Cambridge; and Jackie Stedall, Departmental Lecturer in History of Mathematics at the University of Oxford.

http://www.bbc.co.uk/programmes/b00mrfwq

Duration: 45 minutes
First broadcast: Thursday 02 July 2009

Melvyn Bragg discusses Logical Positivism, the eye-wateringly radical early 20th century philosophical movement.

The Logical Positivists argued that much previous philosophy was built on very shaky foundations, and they wanted to go right back to the drawing board. They insisted that philosophy – and science – had to be much more rigorous before it started making grand claims about the world.

The movement began with the Vienna Circle, a group of philosophically-trained scientists and scientifically-trained philosophers, who met on Thursdays, in ‘Red Vienna’, in the years after the First World War. They were trying to remould philosophy in a world turned upside down not just by war, but by major advances in science. Their hero was not Descartes or Hegel but Albert Einstein.

The group’s new doctrine rejected great swathes of earlier philosophy, from meditations on the existence of God to declarations on the nature of History, as utterly meaningless. When the Nazis took power, they fled to England and America, where their ideas put down new roots, and went on to have a profound impact.

Melvyn is joined by Barry Smith, Professor of Philosophy at the University of London; Nancy Cartwright, Professor of Philosophy at the London School of Economics; and Thomas Uebel, Professor of Philosophy at Manchester University.

http://www.bbc.co.uk/programmes/b00lbsj3

Duration: 45 minutes
First broadcast: Thursday 02 April 2009

Patricia Fara, Stephen Pumfrey and Rhodri Lewis join Melvyn Bragg to discuss the Jacobean lawyer, political fixer and alleged founder of modern science Francis Bacon.

In the introduction to Thomas Spratt’s History of the Royal Society, there is a poem about man called Francis Bacon which declares ‘Bacon, like Moses, led us forth at last, The barren wilderness he past, Did on the very border stand Of the blest promis’d land, And from the mountain’s top of his exalted wit, Saw it himself, and shew’d us it’.

Francis Bacon was a lawyer and political schemer who climbed the greasy pole of Jacobean politics and then fell down it again. But he is most famous for developing an idea of how science should be done – a method that he hoped would slough off the husk of ancient thinking and usher in a new age. It is called Baconian Method and it has influenced and inspired scientists from Bacon’s own time to the present day.

http://www.bbc.co.uk/programmes/b00jdb6c