How far can we rely on our reason to give us reliable knowledge in two areas of knowledge?

     Reason is the main way of knowing, as, although other ways of knowing, such as sense perception, emotion and language are also important, we rely on reason, which is thinking in a logical way, the most.

    In all areas of knowing, from maths to history, even despite ourselves, we use reasoning. In maths, one can deduce the size of the third side of a right angled triangle. For instance, we know that triangle ABC, is a right angled triangle with sides AB= 3cm and AC= 4cm. We know that according to Pythagorus' theorem that in a right angled triangle, a²= b² + c², where a is the hypotenuse. Therefore, 3² +4² = BC², so BC is 5 cm. This is deductive reasoning as through arguments and premises, we have reached a conclusion. One could argue that the large use of reasoning is only in mathematics or natural sciences as these are the naturally more logical areas of knowledge, in many others the other ways of knowing are more prominent. However, this is untrue, take History as an example: we use lots of deductive reasoning. For example, we know that these sources are all on the Russo-Japanese War. We know that they are written by different people from that era. We therefore know that the truest perspectives are the most repeated ones. For instance, "it was an extremely humiliating defeat".  

    However, reasoning is more prominent in some areas of knowledge, such as maths. This is because logic is key to maths, for instance, if a boat sails 60km at a bearing of 70 degrees, stops at point A and sails for 120km to point B and we know that B is 55km from the starting point. We can find out at what bearing the boat sails from point A to B by using the cosine rule. We use our reason to deduce that the cosine rule has to be used. On the other hand, there are other ways of knowing that are involved in maths, like emotion and language. This can be shown in the way Andrew Wiles discovered the proof to Fermat's last theorem. Emotion drove him to solve it and language helped him communicate with other mathematicians to give him ideas and check that he was correct. Nevertheless, reason is the way of knowing that is used the most in maths, as Andrew Wiles could have solved the theorem without emotion and language but not without reason.

    In other subjects, such as history, however, reason is less used but still needed more than other areas of knowledge. For example, in history, one needs reasoning to assess how truthful sources are. You would take into account the origin, the purpose, and many other things and then use reason to see which one is more reliable. But, the sources would not be communicated without language. Nevertheless, there is not much point reading a source if it is unreliable. For instance, an account by Tsar Nicholas II about the living conditions of the peasants throughout his reign would be unreliable, however, if a historian didn't know that it was by Tsar Nicholas II and that it was therefore unreliable, they may believe it was true and assess the peasants' situation throughout the early 20th century in Russia based on false knowledge.