“.....In whatsoever mode, or by whatsoever means, our knowledge may relate to objects, it is at least quite clear that the only manner in which it immediately relates to them is by means of an intuition. To this as the indispensable groundwork, all thought points. But an intuition can take place only in so far as the object is given to us. This, again, is only possible, to man at least, on condition that the object affect the mind in a certain manner. The capacity for receiving representations (receptivity) through the mode in which we are affected by objects, is called sensibility. By means of sensibility, therefore, objects are given to us, and it alone furnishes us with intuitions; by the understanding they are thought, and from it arise conceptions. But a thought must directly, or indirectly, by means of certain signs, relate ultimately to intuitions; consequently, with us, to sensibility, because in no other way can an object be given to us.The effect of an object upon the faculty of representation, so far as we are affected by the said object, is sensation. That sort of intuition which relates to an object by means of sensation is called an empirical intuition. The undetermined object of an empirical intuition is called phenomenon....”
Follow the bouncing ball, so to speak. What is herein called “object” is matter external to us. If it is external it is empirical, hence these objects without qualifiers are empirical objects. The definition of “phenomenon” is given, and it is itself an object but carries the qualifier “undetermined object of empirical intuition”, to distinguish it from an empirical object of the senses. An empirical object and a phenomenon are related, because the phenomena we call intuitions will eventually represent the empirical object of sense as soon as the “undetermined” part goes away, or, as soon as understanding cognizes what it is, but they are not synonymous, insofar as they are not interchangeable.
A lot of times Kant will put something in print, then paranthesize something right after, as if one is meant to equate to the other. This is not the case, for he means the one relates to the other directly, as in “....(the raindrops of course are not such, for they are, as phenomena, empirical objects)...”. Here he means rain drops are empirical objects in the world.....obviously....but they are phenomena to the faculty of representation.
And here: “...Although all these principles, and the representation of the object with which this science occupies itself, are generated in the mind entirely a priori, they would nevertheless have no significance if we were not always able to exhibit their significance in and by means of phenomena (empirical objects)....” This is working backwards, that is, instead of external sense of objects then inwards to understanding, working from a priori understanding through intuition to outward objects of sense. The science is mathematics, and he’s talking about figures, lines and points and such, the principles for which lie a priori in the mind but are worthless and unprovable until we draw the figures, or do the math, etc., at which time the phenomena become empirical objects of sense.
On space and time:
They are not transcendental properties, and it is shown they are not properties of any kind. Instead they are pure intuitions a priori, thus not derived from experience. The means for arriving at the conceptions of space and time is the transcendental exposition, which is the ground for the truth of synthetic a priori propositions with respect to natural phenomena, and therefore our knowledge of them. For these to be the ground of something like that, they must be unconditioned, and are shown to be those unconditioned intuitions upon which the possibility of experience itself rests.
But wait!!! There’s more, so much more.......always more.