Daan Hendriks
The Edge of Logic: Reflections on Gödel’s Incompleteness Theorems
In the early 20th century, a young Austrian logician named Kurt Gödel did something remarkable. He proved a pair of theorems that would shake the foundations of logic and forever alter how we think about truth. These findings, now known as Gödel’s Incompleteness Theorems, revealed something deeply unsettling: in any reasonable formal system powerful enough to describe basic arithmetic, there will always be true statements that cannot be proven within the system itself.
An axiomatic way to life
Circa 300 before Christ the mathematician Euclid created the 13-book series The Elements. The most influential textbook of all time. Shaping logic as the way we know it today. Making use of definitions, common notions and axioms, which are unproven statements generally accepted to be true. Creating a framework which can be used to prove its propositions. This axiomatic approach has been extremely influential and can now be found in any field relying on logic. In this article I want to reflect on the influence of The Elements and talk about the axiomatic approach to reason that it formally introduced to the world.
Does True Randomness Exist?
Have you ever wondered what randomness is? According to Oxford Advanced Learner’s Dictionary, randomness is the fact of being done, chosen, etc. without somebody deciding in advance what is going to happen, or without any regular pattern. Hence, it is a nondeterministic event (an event that can not be directly determined by another event). In [...]
The 100 Prisoner Problem
Imagine if tomorrow you were abducted, and before you knew it, you were trapped in a room with 99 other people who seemed to know nothing more about what was happening than you. You notice that everyone is wearing an orange jumpsuit, which is uniquely numbered. You also notice a door, and you can not […]