General

One of my motivations for starting a blog was Eugenia Cheng’s book The Joy of Abstraction 1. It’s a surprisingly accessible, gentle introduction to category theory, a topic that is usually only taught to graduate students in math. She compiled part of the book using notes from a class that she teaches at the Art Institute of Chicago, a testament to the aesthetic appreciation that one can expect to gain of category theory irrespective of their academic background! In this post, I will introduce the main ideas in category theory (as I best understand it) and show that it offers an elegant way of thinking about mathematics. ...

In my earlier post I suggested that there is no objective notion of logical truth, that whether a statement is ’true’ can depend on the system of truth that one is operating in. Here we will develop that argument further using the concept of axiomatic systems. This is a long one, but I’m excited to talk about it! Axiomatic Systems An axiomatization is an assignment of rules (axioms) such as “one plus one equals two,” making up an axiomatic system or a formal system. If you happen to be within that formal system, then you must follow all of the assigned rules. The choice of axioms dictates the degree of expressiveness that one has within the formal system. For instance, North Korea has a small number of state-approved haircuts that everyone must choose from, which does not sound like a very expressive system. ...

This is my first post! It discusses the question of whether spoken and written languages like English could be ’logical’ by design. I will break this post up into two parts. The first one does not require a mathematical background whatsoever, whereas the second touches on the concepts of axioms, theorems and proofs. Fallacies The word logic as it is used in everyday parlance refers to informal logic (as opposed to formal logic , which is instead a rigorous mathematical construct). You’ve probably come across logical fallacies such as the false dilemma , which goes something like this: ...