From a logical point of view, the propositions that express human knowledge can be divided according to two distinctions. First is the distinction between propositions that are a priori, in the sense that they are knowable prior to experience, and those that are a posteriori, in the sense that they are knowable only after experience. Second is the distinction between propositions that are analytic, that is, those in which the predicate is included in the subject, and those that are synthetic, that is, those in which the predicate is not included in the subject. Putting the terms of these two distinctions together gives us a 'fourfold classification' of propositions. Analytic a-priori propositions include such statements as: 'All bachelors are unmarried' and 'All squares have four sides.' Analytic a-posteriori propositions do not exist, according to Kant, because, if the predicate is conceptually included in the subject, the need for experience is irrelevant and unnecessary. Also, "the negation of an analytic proposition is a contradiction; but, because any experience is contingent, its opposite is logically possible and hence not contradictory." Synthetic a-priori propositions include such statements as: 'Every event has a cause' and '7 + 5 = 12.' Although it is not part of the concept of an event that it be a cause, it is universally true and necessary that every event has a cause. And, because 12 is a different concept from seven, five, and plus, it does not include any of them singly or jointly as a part of it. Finally, synthetic a-posteriori propositions include such statements as: 'The cat is on the mat' and 'It is raining.' They are straightforwardly and uncontroversially emp...
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...ven though the categories seem to vary, such differences are due only to differences in the "surface grammar" of language, the ways in which things are understood as meaningful. When asked why languages are structured in certain ways, some theorists claim that the brain and our neural networks form the "deep grammar" of what things mean.
Though many disagree with these ideas, I believe that synthetic a-priori propositions are indeed possible. Not only that, but I think they are firmly fixed in our minds and thought patterns for example, almost the entire field of mathematics is based on things we can't actually see and feel in front of us. Yet we base our lives around these systems, and so therefore I would think that by denying the existence of this type of knowledge would also be denying a 'part' of our minds, which really have the potential for greatness.
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