Hi Chandra, I am glad you have studied Kant and it is good that Russell has been helpful for you, but we have to remember that his history of western philosophy was not intended to be a scholarly history, and certainly this chapter on Kant is very limited.
Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic, spherical geometry is dual to hyperbolic geometry. Curvature or gravitation is dual. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought. Potential energy is dual to kinetic energy. Energy is dual to mass -- Einstein Dark energy is dual to dark matter. Energy is duality, duality is energy. Dark energy is repulsive gravity or negative curvature, hyperbolic geometry. Duality (energy) is being conserved -- the 5th law of thermodynamics! "Perpendicularity in hyperbolic geometry is measured in terms of duality" -- Professor Norman Wildberger.
My use of Rodin's Thinker as my icon is not to suggest I fancy myself as an intellectual, but rather a condemned man contemplating his fate at the gates of hell. As such I am in a quandary and looking for answers. I find the offerings of Will Durant far more helpful than anything from Bertrand Russel whom I feel wrote for other academics rather than the layman.
Maybe the alternative title "The Sphincter" suits your purpose better. At least it resonates with me. I found this lecture pretty impenetrable too. The others have been much easier to follow. All I got from this was that Kant was meticulously logical but tedious and wrong.
The good Lord created the laws of logic, the laws of nature and miscellaneous laws of behaviour etc. He ensured that some laws are very difficult to break indeed and to break them requires a miracle. If you, for example, try to walk on water or fly by flapping your arms, you will very rarely succeed. He did, however, create a great many weak laws, which are easy to break and doing so is called sin. For example, eating meat on Friday is a piece of cake. This, I think, was his downfall. The only way to deal with sin is by introducing a system of rewards and punishments. This solution is overly complicated and I beg the creator to reconsider making all laws strong. This amendment to the design would be very simple and make everyone happy. To implement this amendment, requires a simple command, "Let sin be impossible". You would still have free will, to select from a huge range of good options. It would never occur to anyone to steal, murder or harm another human being in any way. Admittedly, this is utopian, which is exactly what we and the good Lord want. I know he can do it and it's not too late as Jesus suggested in Matthew 19:26
