Synthetic a priori Judgment by Emmanuel Kant
In The Critique of Pure Reason Kant wanted to prove, that although our knowledge is derived from experience, it is possible to have knowledge of objects in advance of experience. The key question is how are synthetic a priori judgments possible? An a priori knowledge is knowledge which is independent of all experience. A priori proposition is one that can be known to be true, or false, without reference to experience, except so far as experience is necessary for understanding its terms. - An analytic truth can be deduced from the definition of its terms, and a synthetic truth cannot be so deduced. Such propositions as 'All bodies are extended in space' or 'All husbands are male' are analytical, because the ideas of extension and maleness are already contained in those of 'body' and 'male'. Analytical propositions are not dependent on experience for their validations; if true they are necessary true a priori. On the other hand, 'Some bodies are heavy' is synthetic, since the idea of heaviness is not necessarily contained in the subject idea. Synthetic propositions are always contingent; any such proposition is capable of being true or false. Its truth could be known only a posteriori, after it had received validation from experience. An a posteriori knowledge is derived from experience. A posteriori preposition can be known to be true, or false, only by reference to how, as a matter of contingent fact, things have been, are, or will be. 'Every change has a cause', expresses a judgment which is strictly necessary and universal. 'All bodies are heavy' is simply a generalization to which no exception have been observed.
Accoding to Hume, all significant propositions must be either (i) synthetic and a posteriori or (ii) analytic and a priori. But Kant stated that there is a third category, namely synthetic a priori. Kant firmly believed that there is an independent reality outside the world of all possible experience, calling this the world of the noumenal, the world of things as they are in themselves, and of reality as it is in itself. The world of phenomena was the world of things as they appears to us - the directly known world of actual experience.
Kant saw that there are two sources of human knowledge: sensibility and understanding. For him, all that our senses and understanding contribute to knowledge is preconditioned by the 'forms of our sensibility' and by the 'categories of our understanding' that are not learned from experience, but enable us to make sense of our experience. Among them are space, time, quantity, quality, relation, modality, and their subforms. These concepts are essential if any creature is going to be able to make judgments about his experience. We experience objects though the mental, sensory and other apparatus that we have for doing so. What we experience can come to us wholly and solely in terms of the forms and modes and categories mediated by that apparatus. What appear to us as the objects of our experience are being produced for us by our experiencing apparatus, we cannot apprehend objects without the intermediacy of our sensory and mental apparatus. But we don't synthesize reality, make it up, it exists independently of us, and because reality exists independently of all possible experience it remains permanently hidden.
Thus Kant's conclusion was, that cognition is restricted to the realm of phenomena. We can know nothing which cannot be given through our senses. Within these limitations we may have valid empirical knowledge, and a cognition a priori of the universal conditions which make nature itself and a science of nature possible.
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