More o less about two days ago, a friend asked me a question on a "pure a priori knowledge": what the meaning of sentence -necessary and absolutely independent of all experience is? he asked me. I must admit here my crooked temptation of using the mathematical gimmick of "definition" to respond such relevant question to my friend. But I'm not a such dishonest boy as to block his mind. In mathematics, you know, I told him, a sentence is: or a definition or a theorem. Period. Sometime it is more easy to use a definition than a theorem, of something. A definition doesn't require proof, while a theorem must be always a proved judgment. But both the necessary and absolute predicated on a pure a priori knowledge are a kind of notions contained in the notion of a priori; its connections are cogitated through identity. Then, it is possible to give a simple definition but it's both more exciting and more enlightening to show a best detailed explanation.
The Prussian Philosopher Immanuel Kant, in its "The Critique of Pure Reason" page 25, gives a clear definition about of this kind of special knowledge. He says, "...By the term "knowledge a priori", therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience. Knowledge a priori is either pure or impure. Pure knowledge a priori is that with which no empirical element is mixed up. For example, the proposition, "Every change has a cause," is a proposition a priori, but impure, because change is a conception which can only be derived from experience...".
So, to Kant, all knowledge is temporally preceded by experience. Our cognitive faculty is awakened by mean of experience. The experience kicks off our intellect. But in no way all knowledge arises from experiences -by mean of intermediation of sensuous impressions. In effect, there are knowledges -some predicates- which have no connection with the experience and they are completely -absolutely- independent of it. This kind of knowledge is called "a priori" in contradistinction of "a posteriori" which is raised from experience. A priori knowledge is impure or pure while, respectively, it contain or not empirical elements. A predicated of an a priori judgment is, always, absolutely pure -without empirical elements-, while its subject would contain some empirical elements in which case it is an impure a priori judgment. On another side, the predicated of a posteriori -empirical- judgment is, always, raised from experience, it is always impure.
Immanuel Kant, warned of the importance of the pure judgments, elaborated a simple standard to discriminate a pure from and empirical judgment. In first place, Kant says, "...Now, in the first place, if we have a proposition which contains the idea of necessity in its very conception, it is a if, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely a priori...". En Second place, Kant says, "...Secondly, an empirical judgment never exhibits strict and absolute, but only assumed and comparative universality (by induction); therefore, the most we can say is so far as we have hitherto observed, there is no exception to this or that rule. If, on the other hand, a judgment carries with it strict and absolute universality, that is, admits of no possible exception, it is not derived from experience, but is valid absolutely a priori...".
These two criteria -necessary and absolute- stated by Kant to discriminate between pure or empirical, are both so useful and so simple logically ones. Why are they so important criteria?. First, both criteria yield the same result; a necessary pure judgment is an absolutely universal judgment. Second, some time one standard is more easy to use than the other; it could happen that the necessity -its whole independence of other judgments- is more evident than its absolute universality -its not exceptionality; or it could be that all exception -all attempt of falsification- arises as a self evident contradiction in a way that its not necessity is not. Finally, both criteria are simple and convincing; they characterize a pure judgment as Necessary and Absolutely Independent of all Experience.
The Prussian Philosopher Immanuel Kant, in its "The Critique of Pure Reason" page 25, gives a clear definition about of this kind of special knowledge. He says, "...By the term "knowledge a priori", therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience. Knowledge a priori is either pure or impure. Pure knowledge a priori is that with which no empirical element is mixed up. For example, the proposition, "Every change has a cause," is a proposition a priori, but impure, because change is a conception which can only be derived from experience...".
So, to Kant, all knowledge is temporally preceded by experience. Our cognitive faculty is awakened by mean of experience. The experience kicks off our intellect. But in no way all knowledge arises from experiences -by mean of intermediation of sensuous impressions. In effect, there are knowledges -some predicates- which have no connection with the experience and they are completely -absolutely- independent of it. This kind of knowledge is called "a priori" in contradistinction of "a posteriori" which is raised from experience. A priori knowledge is impure or pure while, respectively, it contain or not empirical elements. A predicated of an a priori judgment is, always, absolutely pure -without empirical elements-, while its subject would contain some empirical elements in which case it is an impure a priori judgment. On another side, the predicated of a posteriori -empirical- judgment is, always, raised from experience, it is always impure.
Immanuel Kant, warned of the importance of the pure judgments, elaborated a simple standard to discriminate a pure from and empirical judgment. In first place, Kant says, "...Now, in the first place, if we have a proposition which contains the idea of necessity in its very conception, it is a if, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely a priori...". En Second place, Kant says, "...Secondly, an empirical judgment never exhibits strict and absolute, but only assumed and comparative universality (by induction); therefore, the most we can say is so far as we have hitherto observed, there is no exception to this or that rule. If, on the other hand, a judgment carries with it strict and absolute universality, that is, admits of no possible exception, it is not derived from experience, but is valid absolutely a priori...".
These two criteria -necessary and absolute- stated by Kant to discriminate between pure or empirical, are both so useful and so simple logically ones. Why are they so important criteria?. First, both criteria yield the same result; a necessary pure judgment is an absolutely universal judgment. Second, some time one standard is more easy to use than the other; it could happen that the necessity -its whole independence of other judgments- is more evident than its absolute universality -its not exceptionality; or it could be that all exception -all attempt of falsification- arises as a self evident contradiction in a way that its not necessity is not. Finally, both criteria are simple and convincing; they characterize a pure judgment as Necessary and Absolutely Independent of all Experience.
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