# TOK – Knowledge Question #2- Mathematics

To what extent is “complete certainty” achievable?

 Claim TOK Terminology Complete certainty is never achievable. Getting a result more than once never assures complete complete certainty. Even if you prove something right, 8 million times, in the 8,000,001st time an alternate response could give another result. There is no physical way of ensuring that something is going to come out with the same outcome every time as nobody will go through an infinite amount of trials in order to confirm something. We can get very close to complete certainty but can never fully achieve it. Real Life Example AOK Terminology When confirming that triangles’ angles always add up to 180 degrees, mathematicians have not tried their theory on every single triangle that ever exists in the world. They may have tried it out on billions of triangles and have come to the conclusion. This makes their theory highly reliable and most probably certain but there is always a small slight percentage of the theory being falsified. With an increased number of trials, this percentage dramatically decreases and begins to approach 0 but it will never reach 0. TOK Analysis TOK Terminology (+AOK Terminology) In any areas of knowledge, we can never be 100% completely certain that a theory or part of knowledge is correct but mathematics is the one area of knowledge in which theories and knowledge is the closest to being completely certain. As mathematics requires rigorous proofing before they can confirm a theory, this makes it the only area of knowledge to approach 0 on the scale of complete certainty. Counterclaim TOK Terminology People may argue that everything in mathematics is completely certain as math comes in the forms of questions with only one possible answer but multiple ways to get to that answer do exist. Complete certainty can be said, to be reached only in mathematics. There is only one answer to every equation and question, therefore complete certainty is reached. Real Life Example AOK Terminology 2+2 can only ever equal 4. The world is absolutely certain that 2+2 can only ever equal 4. Even in an alternative universe, 2+2 will always only equal 4. This is complete certainty. TOK Analysis TOK Terminology (+AOK Terminology) Complete certainty is about there only being one ever answer that we are 100% sure of. Mathematicians do enough tests to ensure that something is completely certain and before knowledge in mathematics can become public knowledge it has to be completely true. Without this, that part of mathematics cannot be taught to children in school and therefore everything in mathematics is completely certain. ShortEvaluation To conclude, complete certainty is never achieved. Despite this, mathematics is the only area of knowledge that comes close to confirming complete certainty.