The brief missive to Herz sheds considerable light on Kant's Critical project. Herewith, some notes for my edification if not yours.
1) How is metaphysica specialis possible as science, als Wissenschaft? Having been awakened by David Hume from his "dogmatic slumber," Kant was puzzling over this. It occurred to him that the key to the riddle lay in raising and answering the question:
On what ground rests the relation of that in us which we call representation to the object?
Representations 'in us,' i.e., 'in' our minds, are of or about objects 'outside of' our minds. What makes the representation of an object about the very object of which it is the representation? For example, what makes my visual awareness of a particular tree an awareness of that very tree?
There are three cases to consider.
2) If the representation in the subject is caused by the object, Kant thinks that an easy answer is forthcoming: the representation is of or about the object in virtue of its being caused by the object. The tree, or the light reflected by the tree, affects my eyes, thereby causing in me a representation of that very tree. We set aside for the time being the question whether this easy answer is a good answer.
3) We also have an easy answer to the above question if representations are active with respect to their objects, as opposed to passive as in the case of my seeing a tree. Suppose the object itself were created by the representation, as in the case of divine representations. In cases like this, Kant tells us, "the conformity of these representations to the object could be understood." (82)
4) Now for the third case, the hard case. What are we to say about the pure concepts of the understanding, the categories? These conceptual representations, being pure, are not caused by sensation. But neither are they creative with respect to their objects. What then gives them objective reference?
As pure concepts, the categories have their seat in our understanding. They are thus subjective conditions of thinking, not categorial determinations of things. What gives these subjective conditions of thinking and judging — to think is to judge — objective validity? That is the problem which Kant sets forth in his letter to Herz. But he does not in that letter propose a solution.
5) He gives his solution in 1781 in the Critique of Pure Reason. Can I sketch it in a few sentences?
I touch a stone. I receive a sensation of hardness and warmth. No judgment is involved. Judgment enters if I say, "Whenever the sun shines on the stone, it becomes warm." But this is a mere Wahrnehmungsurteil, a subjective judgment of perception. It lacks objective validity. It records one perception following another in a subjective unity of consciousness, as opposed to a consciousness in general. The judgment does not record causation, assuming that causation involves necessitation, as Kant does assume. All we have at the level of perception are Hume's spatiotemporal contiguity of perceived events and their regular succession: the sun's shining on the stone followed by the stone's becoming warm. Kant is of course convinced that there has to be more to causation than regular succession.
But if I say, "The sun warms the stone," then I make an Erfahrungsurteil, a judgment of experience which is objectively valid. I am not merely recording a succession of perceptions, but an instance of causation in which the cause necessitates the effect. The necessary connection is not out there among the things; it enters via the understanding's imposition of the category of cause on the sequence of perceptions. The objective or transcendental unity of apperception, as the vehicle of the categories does the job. Just don't ask me how exactly. Here is where things get murky. This is what I wrote my dissertation on.
6) I am now in a position to answer in a rough way the question of how the pure concepts of the understanding have objective validity. They have objective validity because the objects of experience are products of the categorial formation of the sensory manifold within a "consciousness in general," a transcendental, not psychological, unity of apperception. It follows that the world of experience is an intersubjectively valid but merely phenomenal world and not a world of things in themselves. The "highest principle of all synthetic judgments" is that "the conditions of the possibility of experience in general are at the same time the conditions of the possibility of the objects of experience themselves, and thus possess objective validity in a synthetical judgment a priori."
Since "the understanding is the lawgiver of nature," Human skepticism bites the dust, but so also does Leibnizian-Wolffian rationalism. This is because the Copernican revolution, at the same time that it validates synthetic a priori judgments in mathematics and physics for phenomena, restricts them to phenomena and disallows them for noumena such as God, the soul, and the world as a whole, the objects of the three disciplines of metaphysica specialis.
Unfortunately, Kant's system raises as many questions as it answers. But that is the fate of every philosophy in my humble opinion. The dialectical nature of reason, which gives rise to dialectical illusion with respect to noumena, unfortunately infects everything we do in philosophy even when we draw in our horns and stick to phenomena.
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