Any attempt to understand knowledge inevitably leads to a series of inquiries into the nature of those things that we know and their relationships to those means by which we purport to know of things. Are there objects which are distinct from the thinker? If there are external objects, how can the individual assure herself that her understanding of the world is accurate?
Immanuel Kant proposes a new science by which we would be able to examine and answer these questions. This science, transcendental idealism, finds as its focus the examination of what must necessarily be so to account for the experiences that we have. As part of his project, Kant looked to end the epistemological debate between the empiricists who held all knowledge to be dependant on direct experience and thus excluded any knowledge of abstract ideas, and the rationalists who allowed for innate knowledge of ideas far outside of the realm of experience.
Kant argues for a radical reassessment of the relationship between our knowledge and objects. Rather than the traditional assumption that our ways of thought are determined by our experience with some inherent nature of things-in-themselves, Kant questions whether it may not be that our experiences with things are constructed by our ways of thought. Through this revolution Kant builds a bridge between the opposing sides, allowing for some knowledge a priori (before experience). He distinguishes between the noumenal world, which contains things-in-themselves and other transcendental ideas outside of experience, and the phenomenal world, which is the world as it appears to be and with which we can interact via experience. “We are capable of a priori knowledge solely with respect to how we organize the appearances of the phenomena.”
He identifies two components of our perceptions of appearances, sensibility and understanding. It is by way of our sensibility that we are passively (as we exert no influence over them) given those immediate perceptions (i.e. the sense of a color or texture), which are named by Kant intuitions. Intuitions are then actively organized by concepts through the work of our understanding. “It is through the synthesis of intuitions and concepts that thinking occurs.”
Kant, in an effort to answer both contemporary empiricists and rationalists, finds that he must be able to account for judgments where the predicate is not simply just a part of the subject but in fact adds to the subject, and the whole judgment can be made a priori (synthetic a priori judgments).
Synthetic a priori judgments are the crucial case, since only they could provide new information that is necessarily true. But neither Leibniz nor Hume considered the possibility of any such case.
Unlike his predecessors, Kant maintained that synthetic a priori judgments not only are possible but actually provide the basis for significant portions of human knowledge. In fact, he believed that arithmetic and geometry comprise such judgments and that natural science depends on them for its authority to explain and predict events. What is more, metaphysics—if it turns out to be possible at all—must rest upon synthetic a priori judgments, since anything else would be either uninformative or unjustifiable. But how are synthetic a priori judgments possible at all? This is the central question Kant sought to answer.
Consider our knowledge that two plus three is equal to five and that the interior angles of any triangle add up to a straight line. These common truths of mathematics are synthetic judgments, since they contribute significantly to our knowledge of the world; the sum of two plus three is not contained in the concept of five. Yet, clearly, such truths are known a priori, since they apply with strict and universal necessity to all of the objects of our experience, without having been resulting from that experience itself. In these instances, Kant supposed, no one will ask whether or not we have synthetic a priori knowledge; obviously, we do. How do we come to have such knowledge? If experience does not supply the required connection between the concepts involved, what does?
Kant’s reply is that we do it ourselves. Consistency with the truths of mathematics is a requirement that we impose upon every possible object of our experience. Just as Descartes had noted in the Fifth Meditation, “the essence of bodies is manifested to us in Euclidean solid geometry, which determines a priori the structure of the spatial world we experience.” In order to be perceived by us, any object must be regarded as being uniquely located in space and time, so it is the spatial-temporal framework itself that provides the missing connection between the concept of two plus three and the sum of five. As synthetic a priori judgments, the truths of mathematics are both informative and necessary.
Written in 2005 creeper.