To answer this question we must first find the amount of doubt being questioned. “To what extent” of the amount of “doubt” is very ambiguous as doubt cannot be measured in a scale. Do we doubt all things? Or are we merely curious? And is doubt really the way to achieve knowledge? The word “Key” is a powerful metaphor which can lead us to believe that either doubt is one of the methods of achieving knowledge, or that doubt is the way to achieve all knowledge. Does doubt only help us achieve knowledge or can it also hinder us on our path to knowledge?
To make up for these uncertainties and to answer this question, we can state the question “To what extent can knowledge help us on our path to knowledge and in what ways can it hurt us? ” In this method we can truly analyze how doubt can help us achieve knowledge as stated in the question, but also allows us to view the negative side effects of doubt. Another way to analyze this question would be “To what extent is doubt actually key to knowledge? ” Doubt can be of great help on our search to knowledge. Take for example a high school senior who believes she knows all she needs to about mathematics.
She finds mathematics safe, precise, and exact. Only to find out from her ToK teacher that mathematics is based on premises, premises from inductive reasoning which are not certain, meaning they are not safe anymore. Needless to say, I was that girl. Mathematics is widely thought of as a safe subject where doubt cannot be found, given that mathematics is mostly based on deductive reasoning and reason, which is as close to certain as we can hope to get. Reason is also widely thought of as a way of knowing that has no faults, it is only based facts and truths.
The problem arises in mathematics with theorems such as the prime number theorem, created by Gauss to view the distance between prime numbers. Theorems are inductive reasoning, which create premises for deductive reasoning; therefore the question arises as to how close we really can get to certainty in mathematics. This theorem has been tested; however it could only be tested for a number of trials. Though we have gotten very far with this theory, into the billions and it has worked, there are always ways it can be proven wrong.
Based on the fact that this theorem is mostly inductive reasoning, it is not certain. Therefore, doubt can be expected. Doubt should be expected in even a subject of certainty such as mathematics, the questions lead us to answers. With Gauss’ problem one might use doubt to analyze the equation, using reason and analytical thinking, to find prime numbers in order to view the methods in which finding prime numbers is used. In this way, they achieve a closer relation to knowledge. However, doubt cannot lead us to an extreme where we doubt everything in life.
If a boy spent the rest of his life trying to find if Gauss was correct, he would not only waste his life but he would never find the answer. This being said we can also not expect someone to be completely doubt free, the thought that one knows all knowledge is impossible. If this person believed there was no reason to doubt anything, and the facts given were perfect, he would not understand that if something he believed in was thought to be wrong he would not comprehend how to manage. Our world is constantly evolving and making changes to things we already know or thought we knew.
Therefore as the question asks, doubt can be the key to knowledge but there must be a balance between doubt and belief in order to be able to think and ask questions about knowledge but to also be able to get forward in life and discover new things. As shown in the question, doubt is required for knowledge as the Proverb states, however complete doubt will not give you knowledge, and it will hinder you on your path to knowledge. Mathematics is a subject where the least doubt can be found, however even mathematics is not perfect and it can be incorrect.