Rationalism versus empiricism

Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene. Transcript Archimedes died mouthing back at an enemy soldier: “Don’t disturb my circles.” Or that’s how the story goes. Is this fact or fiction? We have third-hand ...  Show more

There is nothing counterintuitive about an infinite shape with finite volume, contrary to the common propaganda version of the calculus trope known as Torricelli’s trumpet. Nor was this result seen as counterintuitive at the time of its discovery in the 17th century, contrary to ...  Show more

Part 1 of a new short series where I am commenting on Karl Popper's lecture "On the sources of knowledge and of ignorance". This paper sets the scene for the link between objective knowledge and fallibilism - refuting, as it does so, the empiricism of the classic British traditio ...  Show more

Part 1.4. Outlines Galileo's revolutionary theories of astronomy and mechanical science and introduces Descartes' (the father of modern philosophy) ideas of philosophical scepticism. 

Here we delve more deeply into the ways our senses and our reason might go wrong in the creation of knowledge. There are no authoritative inerrant sources of knowledge and yet we can nonetheless come to knowledge...by creating it. Unusually for ToKCast we take a left turn into vi ...  Show more

The certainty of mathematics and its place in the supposed hierarchy of subjects (assumed to be above science which is itself above philosophy in turn). Some more remarks on Bayesianism and somehow ghosts and alien life.