I agree with the conclusion of the essay by Wolf. Mathematical knowledge and philosophical knowledge go hand in hand. One effect can in no way unmistakably proceed from a particular cause than in the case where a quantity of an effect is equivalent to the power created by the cause. Therefore, based on the above fact, knowledge of philosophy gains total certitude from the knowledge of mathematics.
Perhaps what is even more important is the fact that all three types of human knowledge named philosophy, history, and mathematics rely on each other. Historical knowledge refers to the knowledge of the issues or things which exist in the physical universe or the immaterial things or substances. This knowledge is held by a person who understands through experience that the sun is seen in the morning and sets in the afternoon. The things which happen or occur have a reason which can be well understood, why they end as such. On the other hand, the understanding and knowledge of why things happen or occur are known as philosophy.
The difference between philosophy and history is obvious. History relies on the basic understanding of the facts surrounding occurrences. Philosophy, on the other hand, goes ahead to give a reason for the facts so that it can be better understood why things happen as they do. Hence, it can be deduced that historical knowledge is the foundation from which philosophical knowledge is developed. It means that historical and philosophical knowledge can in no way be separated as well.
The knowledge of the amount or quantity of things or matter is called mathematical knowledge. The knowledge of the amounts in different proportions of things has mathematical knowledge. The person who understands the quantity of a thing that has been assigned by another person has historical knowledge. However, the individual with the ability to demonstrate how the quantity has been arrived at by the other person has mathematical knowledge.
Hence it is important to understand the reason how main quantities are attained and why they are attained as such to possess historical, philosophical, and mathematical knowledge. It is, therefore, true that there are instances where historical and mathematical knowledge offers a basis for mathematical knowledge. It means that historical knowledge precedes philosophical knowledge. Philosophical knowledge then precedes mathematical knowledge.
Those who do not support this view might argue that philosophical knowledge and mathematical knowledge do not agree. The certitude that can be obtained from a knowledge of philosophy relies mostly on mathematics. As part of the proof, mathematical elements used in physics make use of mathematics while conducting experiments. The same mathematical elements are, also used with universal elements due to their significant importance.
Because of the above facts, mathematical knowledge should be joined with philosophy if one desires to attain the highest level of certitude. It is because of this that we additionally offer mathematical knowledge a chance in philosophy in as much as mathematics and philosophy are distinctly defined. Therefore there is nothing that can be as important or even more important than certitude. What is definite for all to understand is that the facts of nature are at times, so incomprehensible that they fail to spontaneously remain open even for an attentive person.