Dear all, Upon inheriting the Looking Glass from our predecessors, we identified a number of key issues. Firstly, there were simply not enough articles being published, due both to a lack of submissions from the school community and limited responsiveness from the previous Academic Team. Secondly, the Looking Glass had not been advertised or explained effectively enough to the wider school community. As a result, we plan to implement a more consistent and engaging stream of articles on the Looking Glass. As part of this initiative, we are looking to recruit a select group of keen writers from across the lower school who would be willing to produce one high-quality piece of writing, discussion, or media each month for publication on the Looking Glass. We believe this will be hugely beneficial both to the school community, which will gain access to a wider range of opinions and viewpoints, and to prospective writers, who will be able to reference their experience contributing to the Look...
Gödel's Incompleteness Theorems and the Limits of Mathematical Logic By Raheel Sultan, L6N Towards the end of the 19 th century, mathematicians began to uncover inconsistencies within the foundations of logic. Set theory was in its infancy at the time, and a complete definition of a set had not been universally agreed upon. One attempt came from Gottlob Frege, who proposed in his book, Die Grundlagen der Arithmetik , a list of rules outlining the behaviour of sets. These rules were constructive, in that the only set explicitly stated to exist was the empty set, and the rest of the rules described how sets were constructed from other ones. His fifth rule asserted that a set exists containing all objects satisfying a given property. For instance, such a property may be that a set contains the number 1; Frege’s fifth rule then implies that there exists a set of all sets which contain the number 1. This seemingly innocuous rule was the source of a paradox, as uncovered by Bertrand Rus...