The Certainty Of Maths
Above All Other Areas of Knowledge the Certainty of Maths Reigns Supreme?
The process of good mathematical reasoning is the process of checking for contradictions in a mathematical proof. If there are none then there can be complete certainty about the final statement. Therefore mathematical proofs are said to be a complete and unshakable guarantee that the statement being questioned is true. A number of problems arise straight away since proofs always need premises to work and provide complete certainty. Proofs rely on a large body of logic and information to be the foundation or framework for the proof. At the very least proofs have to rely on a number of core axioms.
Axioms, which are statements that are assumed to be true and are used as the core of a reasoning system like mathematics, are what prevent any proof from being able to provide complete certainty. Even if the proof depends of very clear self-evident axioms, there is always the possibility that the axioms are invalid which takes away any certainty of the proof. René Descartes created a philosophical statement based on one premise “I think, therefore I am.” Even this depends of the assumptions “that which thinks, must exist” and “I think” therefore “I am and I exist.” Like the other areas of knowledge mathematics too cannot actually achieve complete certainty but even so it gets a lot closer to the truth then any other way of knowing can ever hope to achieve.
It is impossible to get certainty in history because it is basically a large collection of differing viewpoints obtained from several sources. One does not directly experience history and must rely on the compilation of viewpoints; therefore one cannot be sure about what really happened in the past. The cause(s) of the Second World War has always been a subject that historians have been arguing about for years. It could have started due to any or all of the following reasons: the great depression,...
Please login to view the full essay...