Samsara

In order to answer the question of what logic may be like in this twenty-first century we examine the history of logic. One thing that we see is a recurrence of ideas but the ideas change form, sometimes quite dramatically. We also see a simple idea getting developed so much that it becomes very complicated, or at least the source of very complicated ideas – and then disappears, to re-emerge, perhaps, as a new idea. Another aspect is the way the role of logic has changed. Logic was at one time the queen of the (mathematical) sciences. Now she is definitely not, but she has certainly become the handmaid of computer science, playing many roles. To assist our enquiry we address four questions. 1. What logics do we need? 2. What are logical systems and what should they be? 3. What is a proof? and briefly, 4. What foundations do we need? We take an historical approach rather than a highly technical one.