We return to Kant's introduction of the Categories, or, to give them their proper name, the Pure Concepts of Understanding. "Pure" for Kant, by the way, means "without sensory content." After some pages of Architectonic elaboration, all of which is quite interesting and none of which need detain us in the slightest, Kant gets down to business. He approaches the important task of identifying all of the Categories -- which, you will recall, are the conceptual tools by which we impose some sort of unity on a manyness or manifold of perceptions -- by first considering the Logical Function of the Understanding in Judgments. In other words, he asks, leaving aside content, what can Logic tells us about the concepts we use when we form a judgment to unify some contents of thought? This is already getting gnarlier than I wanted it to, but Kant's notion is this: The cognitive faculties of the mind -- Reason, Understanding, etc. -- have a merely logical employment, which is pretty much the same as what Hume thought these faculties do, namely comparing contents of consciousness, be they perceptions or ideas, organizing them into genera and species, drawing purely logical -- i.e., syllogistic -- inferences about them, and so forth. But these same cognitive faculties also have what Kant calls a Real Use, by which he means a use that leads to knowledge that is not merely a collection of tautologies. Now, Kant says, if we can use our familiarity with Logic to identify and classify in tabular form the ways in which the Understanding, in its merely logical use, introduces unity into judgments, then we will be able to read off from that table the ways in which this same faculty, Understanding, introduces unity into a manifold of sensuous intuition and thereby gains us knowledge of things as they appear to us in space and time.
This is a really complicated, difficult, and powerful idea, and most students of Kant's philosophy spend a great deal of time and energy mastering the details of Kant's story, which we will get to in a moment. But this idea is also, when you think about it, utter hogwash. Why on earth should the mind do one thing -- forming judgments -- in exactly the way that it does something totally different -- namely, unifying a manifold of perceptions? Kant's answer is pathetic, really. He says that since both of these activities are carried out by the same faculty of the mind, the structure of the activities must be the same.
Now, people in Kant's day were very big on faculty psychology [think phrenology without the bumps on the head], and talked easily and at length about Reason, Understanding, Imagination, Judgment, Sensibility, and so on, as though one could ask someone to say "aaahh," look down her throat or up her nose, and just see the different faculties of the mind. But in fact, as is obvious after a moment's reflection, we distinguish one faculty from another functionally, by first identifying different sorts of things the mind does, and then positing a faculty for each one. Two functions, two faculties. So Kant has it totally backwards. You cannot prove that the mind does two things in the same way by tracing them back to the same faculty. You trace two things that the mind does back to the same faculty by first showing that it does them in the same way.
This is the point at which the truly great philosophers are distinguished from the merely important thinkers. [I do hope it is obvious that you are getting here Wolff's interpretation of the Critical Philosophy, and not just the standard story that you can find in any of a thousand books on the subject. For a detailed defense of this radical reading, I refer you once again to Kant's Theory of Mental Activity.] Even though Kant never ever foreswore his Table of Categories [which we have not gotten to quite yet], and even used it as a major organizing tool in his Architectonic, something in him knew that he had not yet really demonstrated the powerful claims he was making with its aid. So in two deep, difficult, brilliant passages, he returns to the problem and nails it. Those two passages -- the Deduction of the Pure Concept of Understanding in the First Edition, specifically the so-called "Subjective Deduction," and the Second Analogy of Experience -- are the very heart and soul of Kant's entire philosophical enterprise. They are, in my judgment, taken together, the most profound philosophy ever written. But it will be August, I suspect, before we get to them.
First things first: The Table of Functions of Unity in Judgment. I cannot get the tabular form to carry over into my blog, for some irritating reason, so I will do this in a somewhat different format. Here are the Functions of Unity in Judgment, reproduced from A70=B95.
I. Quantity of Judgments: Universal, Particular, Singular
II. Quality: Affirmative, Negative, Infinite
III. Relation: Categorical, Hypothetical, Disjunctive
IV. Modality: Problematic, Assertoric, Apodeictic
Good grief, Charlie Brown, where did they come from? Kant claims that they are simply a well-known logical classification, but scholars have poured over 18th century logic textbooks, and not surprisingly have discovered that Kant cobbled this table together from bits and pieces of this and that textbook. All twelve of the "functions" show up somewhere or other, but no text cites them all. This is just more of Kant's manic systematizing. Oh, did I mention that the first and second in each trio are thesis and antithesis, and the third is their synthesis? You think Hegel made that up? Sigh. All of this is just the lead-in to the boffo presentation of the Table of Categories. Here it is. You will recognize some of them, I am sure.
I. Of Quantity: Unity, Plurality, Totality
II. Of Quality: Reality, Negation, Limitation
III. Of Relation: Of Inherence and Subsistence (substantia et accidens), Of Causality and Dependence (cause and effect), Of Community (reciprocity between agent and patient)
IV Of Modality: Possibility-Impossibility, Existence-Non-existence, Necessity-Contingency
If you clear your head and look past this elaborate systematization of notions you never intended to use anyway [Limitation? Totality?], it should be obvious that the real philosophical meat is to be found in the Categories of Relation, and specifically in the second Category of Relation, "cause and effect." That was the focus of Hume's sceptical attack, that was what launched Kant on this whole enterprise and delayed the publication, of the Critique for nine years, and that, if anywhere, is where we are going to find Kant's answer to Hume. Sure enough, that is just the way things turn out. But so much else is happening philosophically along the way, much of it fascinating and important in its own right, that it is easy to lose sight of what is really going on.