Priori and Posteori knowledge
Knowledge is priori if it is the type of knowledge that is independent of experience. It is strictly based on reason and applies only on stern uniformity and not on experiences which have been felt. On the other hand, posteori knowledge is the knowledge that comes about as a result of experience, and as such is severely uncertain and confined when it comes to applications in particular cases.
Analytical and Synthetic judgments
Analytical judgments are those judgments whose implied concepts of the motion are included in the concepts of the main subject. Such judgments can be drawn from the rule of non-contradiction since they are explicatory and do not, in any way, add anything to the subject concept. On the contrary, a synthetic judgment is that judgment whose implied concepts are wholly separate from their main subjects. They are educational but require an explanation from some principle on the outside of the subject, by reference.
A synthetic a priori judgment is a judgment that gives knowledge which is legitimate and factual. An example of such is Mathematics. It is common knowledge that one plus eight equals nine and that the addition of all interior angles of a triangle is sum to a straight line. According to Kant, these together with other mathematical facts, are synthetic judgments by nature because they have a significant contribution to our world-based knowledge. However, it is also true to say that they are priori due to the fact that they are based on reason and are only applied on strict uniformity, universally to each and every object we have come across without necessarily deriving knowledge from the said experience. In such cases, nobody will inquire if we possess the synthetic a priori knowledge but rather he or she will want to know how we possessed such knowledge; which brings us to the question of what connects concepts involved if not experience?
The answer according to Kant is that we provide the connections all by ourselves. After all, it is we who enforce the truths of Mathematics on objects we experience. Just as previous philosophers noted, the nature of bodies is brought to light by the geometry of Euclidean bodies which dictates a priori the form of the world we exist in. For objects to exist according to any human being, it must be exclusively allocated in time and space and therefore it is the humans themselves who provide these missing links.
Understanding Mathematics in this way gives us a competitive edge against rationalists and empiricists who have never come to an agreement on the nature of time and space. Whereas rationalists argue that time and spaces are not elements of the world but rather result from the human thoughts, the latter argue that space and time are definite, and are not just creations of the human mind. Kant, however, argues that both schools of thought are correct; space and time are indeed definite and are also extracted from our mind, a perfect case of a synthetic a priori judgment as it is not only necessary but also informative.
Kant’s argument method based on the fact that we have some sort of knowledge allowing us to conclude that nearly every logical presupposition bestowed on such knowledge require satisfaction. However, we need to understand that certain prices may be paid in regards to the certainty that we earn in such manners. Given that mathematics, for instance, emanates from our sensible individual situations, there is an absolute surety that such practices apply to almost every action that we are involved in, but at the same time hold no reason for being assured as things might turn out differently from how we perceive them.
