There are many ways of aiming our thoughts and discourses about a topic at what is relevant to us and the distinction between the pure and empirical concerns such a directing of consideration. To understand how these modes of considering objects differ it will be important to work out how a process of abstraction can illustrate objects in their pure and empirical modes.
The Distinction
The common ancestor of the pure and empirical is the consideration of something with regard to the complete experience of it. The distinction then is made as follows: considering something empirically means with regard to what is given of the object by intuition, while considering something as pure considers it so far as it is not given by intuition.
Considering an object empirically we note the particular coloration, size, behavior, &c. That it is an object that falls under a particular concept is not given by the intuition, but the concept is determined on the basis of the intuition, so it is still known empirically. We can abstract away all of these contents (as well as others) to the notion of an object in general. The object has some extensive magnitude, some intensive magnitude, preserves itself over time, and it is actual (or for those just imagining an object it is possible). If we were to attempt to imagine an object with no extension, we would find no object that could be given to us through intuition that would fit, and the same thing can be observed with relation to representing an object with no qualities (no internal magnitude), &c.
Phenomenological Demonstration
By trying to make the distinction sensible I will more directly be exploring the process of abstraction. I will also try to employ Kant's own method, which one can glimpse throughout his work (the lectures on logic are particularly helpful here).
Any concept of an object is already the result of abstraction from experience or from the combination of abstracted content. Whatever representations that fit under the concept add empirical content back to the concept synthetically. (If you need to brush up on synthesis you can take a look at the post on the distinction between analytic and synthetic judgments.)
The concept of an object abstracted from experience is still not considered pure since it involves contents from experience. Abstracting all empirical content away will always lead to the concept of an object in general.
I will assume that we are experiencing a plate. Considering this experience with regard to its pure content it does not matter that it is an object that falls under the concept of plate, because if it had not been recognized under this concept it still would have appeared to us, so we disregard that. The particular colors could also have been different, and it still could appear for us, so we can disregarded those. If it was a different shape it would still appear, so the particular shape can be disregarded. At this point I will discuss what is meant by 'disregarding.'
Above when I spoke of disregarding the color of the plate (and other qualities), I meant that one could imagine the plate with whatever color one wishes and it would still be the correct object we were discussing. These properties that we can vary are exactly those that we will not discuss in pure considerations of it.
If this object were of no magnitude at all, then it could not have any shape at all and could not appear to us, so while we can disregard the particular shape we cannot disregard extensive magnitude generally. If there was no intensive magnitude at all (no degree of quality) it would not be able to have a color at all, and so could not appear to us, so we cannot disregard intensive magnitude. These are the kinds of abstractions that one makes when one begins to consider an object purely, and this abstraction eventually leads to the concept of an object in general which is still described by so-called pure concepts (categories).
Importance in Kant's Work
A grasp of the distinction between pure and empirical is important for following Kant's procedure throughout his work since all of Kant's critical (transcendental) philosophy considers things purely, rather than empirically.
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