Immanuel Kant, a Prussian philosopher during the 1700s, examined the basis of human knowledge and its existence. Through rationalism and empiricism, Kant developed an individual model that supported the concept of pure mathematics. Kant’s logic allowed him to prove concepts that appeared unable to be proven. Pure mathematics, as an a priori cognition, can be considered to be an example of a concept that may have seemed unable to be supported through facts (Rohlf).
Mathematical principals, all consist of concepts that develop from intuitions. However, these intuitions are not able to develop as a result of prior experience. Fortunately, it is possible to intuit something a priori. An intuition of an object can occur before the actual experience of the given object occurs. One’s intuition contains the mere form of a sensory experience (Kant pp. 18-31).
Human beings, through the slightest form of sensuous intuition, are able to intuit things a priori. However, because individuals are only able to know an object as it appears to them personally, they may not be able to perceive the object as it actually exists. Mathematical concepts are constructed from a combination of intuitions, and not an analysis of concepts. Space and time are both examples of pure a priori intuitions (Rohlf). Geometry is derived from the pure intuition of space. The concept of a mathematical number developed from the addition of successive units of time. Therefore, space and time are pure a priori intuitions. Space and time exist in human beings prior to all other intuitions of objects. Therefore, both the concepts of space and time are considered to be prior knowledge of an object as it appears to an observer through the senses (Kant pp. 35-48).
Pure a priori intuition of space and time is the foundation of empirical a posteriori intuition. Synthetic a priori, in regards to mathematics, makes...