Wow, I thought I’d get more put up but Kant’s logic runs deeper than I thought. Next time we can get into all those fun judgments and categories that everyone loves so much, but for now I’m just going to deal with the introduction. If any of you Kant scholars (or logicians) out there see any glaring mistakes please do let me know. Enjoy!
The Transcendental Logic Introduction
In the introduction to the Transcendental Logic Kant gives some definitions and expounds a bit on the different forms logic can take. To begin with §1 “On Logic in General,” we come to the major divide between sensation and thought that Kant split between the Aesthetic and the Logic. Accordingly, in the Aesthetic we saw that the mind has the receptive ability to have representations given to it, and in the Logic we are going to see how the mind actively cognizing these representations into thoughts. This active process of thought is what produces the concepts we have of representations. Kant also tells us of the important relationship shared by intuitions and concepts. Remember that intuitions are the relations between cognitions and objects immediately given to the knower either through sensory experience or in the imagination. The representations associated with these intuitions are then mulled over by the understanding (i.e. they are thought about), and out of that arises a concept. Intuitions and concepts “constitute the elements of all our cognition;” (A50/B74) both are necessary for cognitions; there cannot be one without the other. Just as with intuitions, concepts can be empirical or pure depending on if they contain any sensory data. Pure concepts are those that contain no empirical data whatsoever, and contain “only the form of thinking of an object in general.” (A51/B75)
Just as Kant termed the receptivity of the mind to receive representations sensibility, the active (or spontaneous) part of the mind that brings forth representations in the form of concepts is the understanding. Both these capacities are needed in order to comprehend the world in the way we do: “without sensibility no objects would be given to us, and without understanding none would be thought. Thoughts without content are empty, intuitions without concepts are blind (my emphasis).” (A51/B75)
In the Aesthetic Kant used a “science of the rules of sensibility in general” (A52/B76) to derive the pure intuitions of space and time. When it comes to finding the generalized rules of the understanding Kant’s tool of choice is going to be logic. There are two major divisions in how logic can be applied: general and particular. General logic is analogous to what we might observe in a university logic class. It contains abstract rules which set the framework (or the form) of argumentation, but they themselves provide no content. Kant frames it as the “absolutely necessary rules of thinking, without which no use of the understanding takes place, (and has) no regard to the difference of the objects to which it may be directed.” (A52/B76) Particular logic, on the other hand, is the sort of reasoning you would find within the various physical sciences, and just as the rules for biology might differ from those in chemistry, so too do the rules of different particular logics.
Kant further divides general logic into pure and applied logic. Pure logic has to do only with propositions that are completely devoid of empirical content. This limits pure logic to analytic and synthetic a priori propositions. Applied logic, by contrast deals with a posteriori propositions. Therefore, a general pure logic deals only with a priori principles, whereas general applied logic deals only with empirical principles.
In §2 Kant introduces what he terms transcendental logic. The need for this new form of logic stems from what Kant showed in the Aesthetic; namely that there are both pure and empirical intuitions. In general logic the goal is to abstract all content from cognitions, but what Kant is looking for is a logic that “distinguishes between pure and empirical thinking of objects.” (A55/B80) The difference here between the general forms of logic and transcendental logic is that while general logic is concerned with the form cognitions take, transcendental logic is concerned with how our understanding is able to acquire knowledge of objects. In other words, it concerned with the way in which we know the object. Thus, Kant tells us “In the expectation, therefore, that there can perhaps be concepts that may be related to objects a priori, not as pure or sensible intuitions but rather merely as acts of pure thinking, that are thus concepts but of neither empirical or aesthetic origin, we provisionally formulate the idea of a science of pure understanding and of the pure cognition of reason, by means of which we think objects completely a priori.” (A57/B81)
In §3 Kant talks about the division of general logic into analytic and dialectic propositions, and talks a bit about what is meant by truth. Presupposing the nominal definition of truth (i.e. that cognition is in agreement with its object) Kant moves on to tell us that no real information can be garnered from a general criterion of truth, for all content would have to be stripped out of cognition leaving them bare; and since it is exactly this content that truth is concerned with, this criterion simply will not do. In other words, if we are operating from this general criterion of truth (i.e. something that is true of all cognitions regardless of what their objects might be), then we will never actually be able to find out what is true of anything, since the content of the cognitions has been stripped out of them (just as general logic strips all the content from cognition). This would also lead to self-contradictory statements since the general form would include both affirmations and negations of the same object (for instance, “The book is open” and “the book is not open” would both be included). Kant has a nice way of putting the point in (A59/B83): “Since above we have called the content of a cognition its matter, one must therefore say that no general sign of the truth of the matter of cognition can be demanded, because it is self-contradictory.”
There is one important point that a general criterion of truth does elucidate and that is the form of cognition, for anything that does not agree with this form would contradict the general rules for thinking and thus be false. So with a general criterion of truth nothing concerning the actual truth of the matter can be said about objects, but the truth of the matter can be determined with regard to the form. This is as far as logic can take us with regard to truth.
Kant tells us that “general logic analyzes the entire formal business of the understanding and reason into its elements, and presents these as principles of all logical assessment of our cognition.” (A60/B84) This is the analytic side of general logic and it cannot go any further with respect to making truth claims about the content abstracted out of cognition. On the flip side of the coin we find dialectic reason which tries to use logic erroneously to find truths in the content of cognition. This form of reasoning Kant calls the “logic of illusion” (A61/B86) and will be the subject of his negative thesis that this form of reasoning is always fallacious and illusion. But before delving into the misuses of logic, Kant first wants to examine “the elements of the pure cognition of the understanding and the principles without which no object can be thought at all.” (A62/B87)