a priori, universality and necessity, all possible worlds, existence. “....I apply the term transcendental to all knowledge which is not so much occupied with objects as with the mode of our cognition of these objects, so far as this mode of cognition is possible a priori....”
“....(Is there) a knowledge altogether independent of experience, and even of all sensuous impressions? Knowledge of this kind is called a priori....”
“...But the expression, "a priori," is not as yet definite enough...”
“...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....”
“...The Human Intellect, even in an Unphilosophical State, is in Possession of Certain Cognitions "a priori"....”
A.) “...if we have a (judgement) which contains the idea of necessity in its very conception, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely priori....”
B.) “...an empirical judgement 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....”
C.) “...If, on the other hand, a cognition 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....”
“....When strict universality characterizes a judgement, it necessarily indicates another peculiar source of knowledge, namely, a faculty of cognition a priori. Necessity and strict universality, therefore, are infallible tests for distinguishing pure (that is, a priori) from empirical knowledge, and are inseparably connected with each other....”
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It doesn’t matter the objects in general we know about when considering knowledge itself, because such things are already given, or at least possibly given, by perception as appearances, but rather the theoretical, or indeed speculative, methodology under which human knowledge is possible. The old...knowledge *of* vs knowledge *that* dichotomy, so to speak, insofar as the judgements “gold is a yellow metal” and “water is a clear fluid” are understood empirically as immediate yet incomplete knowledge *of* gold and *of* water respectively. Reason wants it known under what conditions are we authorized to signify or designate gold and water.....and every other damn thing in the world....the way we do, such that knowledge *that* gold is a yellow metal and knowledge *that* water is a clear fluid, are derived from valid, that is, non-contradictory, cognitions.
Reason doesn’t want to know if any other immediate empirical intuition can be given to gold, but only that the intuition of, e.g., “yellow”, “metal”, actually does belong to it, not because perception, from which the empirical appearance comes, says so, but because understanding, from which such necessary justification alone comes, says so. But understanding does not intuit, it has no say in assigning “yellow” to “gold”, that having already been accomplished under the auspices of the faculty of intuition, which gives appearance to phenomena by means of imagination, and which then becomes rationally authorized as representation.
But we already know from experience what the intuitions of yellow and metal may represent, other than gold. We also know from experience the intuitions of clear and fluid may represent other than water. Therefore, we can say that the assignment of certain predicates to gold is an empirical cognition when gold is directly perceived, and, more importantly, we can thereafter cognize a priori, that gold is a yellow metal when no appearance of gold is given at all, because such appearance has already been represented and hence judged as non-contradictory. This is, of course, impure a priori knowledge, having it base in experience, no matter how remote. It is perhaps more easily considered as indirect, as opposed to direct, knowledge, although this qualification is not suggested as intrinsic to the transcendental philosophy of continental Enlightenment era epistemological theory.
Now of pure a priori knowledge, it must be admitted that whatever conditions, and therefore the principles which legislate those conditions, already explicit in impure and empirical knowledge cannot apply, for such is entirely circular and of no use whatsoever. That condition and principle being the logical law of non-contradiction, it follows that whatever legislation reason requires for pure a priori knowledge as its ends must have for its means some other fundamental ground. While it may be easy to dismiss the conditions given from experience, which the very idea of pure a priori requires, it is very far from easy to dismiss the cognitive operational procedure of human rationality. Therefore, a line must be drawn as to where and how we think objects, without there being objects to think about. If the line be drawn at the point where empirical influence stops, but the remainder of the cognitive system continues, such should be sufficient ground to establish the possibility of pure a priori knowledge. From the quotes above, they being taken in their respective order of print, it is clear knowledge works backwards, from itself, through cognition, through judgement, through understanding, through representation, through intuition. But all intuition is given from perception, which is always empirical, thus the line must be drawn before intuition when proceeding backwards, or that of which is a consequence of it. But if intuition is dismissed as a faculty for representation given to understanding, there must be some other source from which understanding may draw, in order to make its judgement, from which a cognition may follow and from that knowledge may follow.
This source resides in the understanding itself, they are the pure conceptions of the understanding, called noumena, and are, in effect, nothing more than the names of the properties or attributes a merely possible object, or, which is the same thing, an object as it will be represented upon the experience of it, must be given before any judgement whatsoever is possible of it. Because there are only these two sources of possible relations for the understanding to employ in its judgements, that is, intuitions and conceptions, and because intuitions, which have non-contradiction as their principle, have been dismissed in the determinations of pure a priori knowledge, the principle of necessity for the existence and the employment of the conceptions of the understanding, and furthermore the absolute universality of their application, serves as sufficient ground of pure a priori knowledge.
(Universality herein means only insofar as reason is investigating the realm of possibility; the pure conceptions of the understanding have no standing in what is called “transcendent”)
Does it matter if the pure conceptions of the understanding really exist? Does it matter they were incorporated post hoc ergo propter hoc as a means to inhibit infinite regress? No, not really, because we do not doubt we are in fact in possession of pure a priori knowledge, which makes explicit we must have pure a priori cognitions, which in its turn makes explicit we must have made pure a priori judgements, which in IT’S turn makes explicit we must have something purely a priori in our faculty of understanding. This is why it is said we do not and cannot know noumena as real objects of conception, even though we are permitted to name them because we think them as necessary, and if that is so, they are so much confused with the “thing-in-itself”, which we also know absolutely nothing about. Noumena, along with imagination and schemata, should be considered as a facilitators in the rational procedure of faculties, but not in themselves cognitive faculties.
All that remains, in the consideration of empirical, a priori and pure a priori understanding, judgement, cognition and knowledge, is whether or not the claim for the reality of pure a priori knowledge has something applicable to it. What can we know a priori? Simply put, anything we know that has no empirical content whatsoever is known a priori. Upon reduction of anything empirical or possibly empirical out from thought in general, all that remains is nothing but thought itself, the thought of something, and is purely a priori; that which exists as nothing more than a thought of something, is a proposition where the subject and predicate are connected by the pure conceptions of the understanding, whereby the predicate follows universally and necessarily from the subject. “Plurality is succession in time”, “No sum is less than its constituents”, “No cognition of three lines will ever allow cognition of a triangle” serve as examples of pure a priori knowledge. It should be noted, that because pure a priori knowledge has no empirical content, no truth value can be assigned to any pure a priori proposition, such truth coming from experience alone. These propositions serve only as the form this kind of knowledge must have.
These are the conditions for deriving the grounds of analytic and synthetic propositions, and the knowledge which follows from each of those kinds, and these from a particular epistemological theory. There is no reason to suppose this theory is better or worse than any other, even if it is logically consistent.