A brief note on the format, in case you haven't listened to any of the In Our Time programmes - it's a BBC Radio 4 series where each week Melvyn Bragg invites 3 experts on a particular subject to come on the programme and they discuss that subject live on air for 45 minutes. The subjects cover all sorts of things - philosophy, history, the sciences, art etc. It's generally presented at a level where you don't need to know anything about the subject in advance, but it still feels like it gets into the details. Some programmes are very narrowly focused (someone's life & works, or a particular event in history, or a particular concept), some are more broad - like this one about the philosophical idea of Scepticism.
The experts this week were Peter Millican (Professor of Philosophy at Hertford College, Oxford), Melissa Lane (Professor of Politics at Princeton University) and Jill Kraye (Professor of the History of Renaissance Philosophy and Librarian at the Warburg Institute, University of London). They started the programme by discussing what the philosophical concept of Scepticism actually is - the idea that it isn't possible to be certain about anything, including whether or not the external world is real. They then moved on to discuss the origins of the philosophy in ancient Greece, and how it is opposed to more dogmatic movements that insist that some things can be assumed to be truth. The second half of the programme followed the rediscovery of this philosophy in medieval Europe & the impact that this had on the Renaissance & Enlightment eras (and on our own world). For instance Descartes philosophy (the man who decided "I think, therefore I am") came from an examination of Sceptic ideas. And modern science is heavily influenced by Scepticism - instead of dogmatically insisting one "knows" something, to come up with hypotheses that fit what's been observed & then keep asking questions, being sceptical.