Thinking Complete

Ethics is complicated. Humans have evolved to feel a hodge-podge of different moral intuitions, each individually useful in facilitating coordination and cooperation in our ancestral environment. This means that the formulation of any ethical framework inherently involves a series of compromises between the relative importance of each of our intuitions, our desire for broad principles which can be consistently applied, and whatever value we place on those principles being widely shared by other people. I highly doubt that any ethical framework exists which doesn't violate at least one cherished moral intuition. Given this, our goal should be to find a compromise which uses consistent principles to align our actions with as many of our most important intuitions as we can. The first half of this essay attempts to reconcile several different ethical traditions, while maintaining that we should approach the most important decisions from a broadly utilitarian perspective; the second co...

I recently sat the All Souls Fellowship exam, called by some the " world's hardest exam ". It requires you to write twelve essays for four papers over two days; the breadth and novelty of the questions make it a fascinating experience. Two of the papers were "general papers" and two were in a humanities subject of your choice (in my case, philosophy); most papers had around 25 questions. I've summarised my answers below, as well as noting some of the other particularly interesting questions. General paper I: 1. How should you prepare for the end of the world? I started off with a somewhat emotional argument about the badness of death on an individual level. I referred to Epicurus' argument that we have nothing to fear from death because when we are dead, we will not have any preferences about it at all - but argued, in response, that having preferences about future states of the world is a foundation of our lives. In terms of the end of the ...

In yesterday's post I briefly mentioned Claude Shannon, founder of information theory. It occurred to me that even most Oxford students wouldn't know who he was, despite his work being crucial for the subsequent development of the "Information Age". How many other intellectual revolutions in obscure fields haven't become common knowledge yet? Perhaps the best way of finding out is just to start listing the greatest and most influential intellectual achievements ever, and seeing if anyone else has more to add - particularly in the humanities and social sciences, where my knowledge is a little shallower. Also, is there anything you expect to deserve a place on this list in the next few years? I'm focusing on achievements which either founded or greatly influenced an entire field (also, although there are many amazing artistic and engineering achievements, to keep things relatively concise I'm not going to include either here). Of course this will be necessa...

I want to investigate the nature of and limits of mathematics. To do that, I'll explore logic, set theory, computability, information theory and philosophy. Be warned that this essay is rather long; it starts relatively easy and gets significantly harder. I hope everyone will get something out of it (including my tutors!) but if you're new to mathematics, that might not be much. If you're philosophically inclined, definitely look at the last section on Truth and Induction. Any discussion or errata are of course very welcome. Let's start with some historical background. Although the Babylonians were able to do some interesting calculations (particularly astronomical), mathematics in the sense of deductive arguments from premises to conclusions began with Thales, Pythagoras and their disciples. Greek maths was focused on geometry, which was formalised by Euclid into 5 axioms - foundational assertions - from which he proved many theorems. Euclidean geometry (as formalis...