The Notion of Manifold in Kant's Transcendental Deduction of the Categories
Here I am focusing on the A version of the Deduction, Part II, section 4, paragraph 6, sentence 5.
But now the representation of a universal condition by which a certain manifold (regardless of what it might be) can be posited is called a rule, and if it must be so posited [or granted], a law.
I look out and see a tree. I see it as a singularity, i.e., all together and separate from all else in the same way that the face in the cloud or on a person's head. I see it immediately as a singularity and then also as a manifold, of an expansion and intensity (of color), a shape and a material.
Now this is actually an Anschauung or view of things or intuition, i.e., what we get out of something, e.g., the face in a cloud. It is very common but it is nonetheless only our own view of things, and there are other views which can also be legitimate. I am inspired by my dog Jackie and will try to see if I can come up with a different take on things. I was just thinking of the leaves. As I see them some are individual and some are clumped together. Well, why couldn't these then be like the clouds that appear (either in mid air or from a distance) and then depart like the birds which flitter here and there. Why couldn't these leaves be such things as the clouds and the birds and, evidently, have chosen to remain close to the branches, so much so that a tug of war of sorts is necessary to get them to let go of the tree. And so then the leaves and the clumps and the various branches and the trunk (and there's where we let go of the tree, at least for common talk, and stop at the ground). But I don't know if the ground is any more or less of the tree, if I look with the eyes of Jacky. Obviously a take on things or a view of things.
So in a word the tree does not exist for Jackie, for a tree (as an object) is a necessary unification of the leaves, branches and trunk and to the exclusion of the ground (and of the sky, for that matter). For Jackie there are these things which hover together, much as the nose and the eyes and the mouth tend to hover around together, but not at all necessary (as is required for an object). In a shorter word: there is no more necessity in his view of the various elements of the tree (leaves, etc.) than there is in his view of the face in the cloud, or on the head of an animal.
Now we are sure that our take or view of intuition of the elements of the tree is connect and that of Jackie's is wrong. And the difference is that our take is an objective take (as we will see) and that of Jackie is merely a subjective take. And so we will want to see how it is that we transmute from a subjective take (for that is the take of the tree in terms of its appearance or, as I call it, its specter [especially on the retina]) which is contingent (as we know of the face in the cloud), and come to an objective take?
How in a word do we come to this necessity? What is it? Well, obviously it is something that we bring to the table ourselves as perceiving beings; it is the make up of the consciousness of self, namely understanding. We have an understanding of things which is based on laws which we provide to the specters in order to bind what is in view, and not merely to remember the configuration of the specter, e.g., leaves here, branches there, etc.
We need to see how it is that the understanding can supply a necessity to the specter in terms of any possible object that can appear (while maintaining a unity of self consciousness, namely that all possible objects can only appear in accordance with the make up of our understanding). And we need also to see how we came to presume that there were objects in the spectral vista in the first place (such that it would occur to us to be intrigued with possible connections*).
[* The categories of understanding are the form of rules for combining multiplicities into one, like combining 7 and 5 into a 12 or the several specters of leaves, etc., into a tree. These rules, as forms, are of quantity, quality, relation (including especially causation) and evaluation of recognitions (my own term). It is in the application of these rules that we aree able to combine the manifold tentatively and contingently sighted (the specters) into parts of an object and come to recognize the objective take on things. Jackie, I don't think, ever does this.]
Now the way becomes more difficult. So much is dependent upon our imagination. We see the tree as a shape of a certain intensity and diversity, and we are intrigued by the single thing in view before us, all together. Imaginatively we apprehend this apparent singularity (in the view or envisagement or intuition [Anschauung]) and reproduce it by keeping all the elements together as a singularity in a common consciousness of self. And then we not only apprehend and reproduce it (keeping it in mind) but we wonder about it. The hovering is on-going, much closer than the various clouds or birds. We then, prompted by the categories of the understanding (ever anxious and eager to apply a rule to unify a manifold), imagine to ourself a thing which consisted of leaves and branches and trunks and which sits in the ground, and so where it was easy to see why the leaves stuck so closely to the branches, i.e., they are the leaves of the tree.
What we have done is to combine a spectral manifold into a single and real thing, a tree. We did it by supplying a rule (in the concept of a tree as made up of trunk, etc.) which held the parts together, and indeed first made parts of them, i.e., as being all together a single thing.
In this way we have maintained a unified consciousness instead of being stuck, like Jackie, with just getting used to the hovering of the specters.*
[* I see a dog at the distant corner. As I get closer there is a confusion and then a mailbox appears. This is a manifold of the specter, namely where I can supply a rule of description, i.e., the dog vanishes in a confusion and the mail box appears as I draw closer to it. This is a subjective perception.]
For me personally at this stage I need to clarify what Kant means with a manifold. This (Mannigfaltigkeit) is usually translated as manifold, and perhaps that is even better. What are we to understand with a manifold?
A manifold or manifold is a diversity which is held in a common consciousness. For example I could look at the tree and the window frame and could just be conscious of the two together. This will not count as a manifold because there is no rule which can hold them together (except merely like the ABC's, i.e., by rote, i.e., tree and frame. Now if I notice the fact that the tree is always within the window, i.e., look at the tree or the frame several times, then I have something to which a rule might be applied, namely: every time I look at the tree or at the frame I see the other also. This then would constitute a manifold because it is a subjective perception, i.e., of a fact (but without necessity and thus only thus far.) If I can now go further and conceive of an object which must appear like this, i.e., made up like this, then that would bind the manifold and make it necessary. Such an object would be the vista in a certain direction from my seat. It would be an envisagement/intuition/Anschauung which is necessary, i.e., I could require it of all who sit in my chair.
And so we come to the spectral fray before (and within) us with the presupposition that before us are objects (Kant speaks of the Transcendental Object = X), i.e., the specters are driven via laws of a single nature [and which corresponds to the categories]), and we are thereby on the look out for evidence of these objects, and that means on the look out for a manifold, i.e., that which can be subjected by a rule. This means then of course that all specters must be subject to the categories as the form of an apperception which is identical and totally unified. The specters are therefore subject to our apprehension, our reproduction, out association (configuring) and unification through the provision of an object according to the categories of our understanding.
Here is a subjective perception (from Wolff): I notice that shortly after the Noon whistle a train departs the station. This is the reproduction of a manifold (whistle and train) according to a rule. But until a law has been applied there is no necessity and it remains merely an empirical rule, namely as far as we noticed this has always been the case. The law comes in the understanding that the engineer is required to leave the station at 12:01 PM and the whistle notifies everyone that it is Noon and him that it is almost time to leave. This is binding for the engineer is under a law (of acting in a certain way for his sustenance).
Kant asserts that all specters together make up a single nature, namely that all specters are necessitated by laws. It is entirely based upon the presupposition that we would ever in the first place presume to apprehend and reproduce and associate any specter in the first place, i.e., in pursuit of a connection which is known to be present, in that all specters are law driven by a single nature (and so where any particular manifold may have only a remote connection and reveal no evidence, e.g., a sneeze and a flash of lighting). And even here it is only by virtue of the affinity of all specters in accordance with laws that we even take note of the sequence of sneeze and lightening, for they are distinct consciousness.* So it is in pursuit of this transcendental affinity (connection) of all specters that prompt us in the first place to take note of the sequence of sneeze and lightening, instead of immediately focusing on the flash of lighting and ignore the sneeze entirely.
[* If lighting should strike every time Jackie sneeze, the feeling of a coming sneeze would be associated with a feeling to take cover, and his behavior would be affected.]
Thus all specters are necessarily in an affinity, and it is as a consequence that we seek out the actual connections between diverse specters. Without this (which is based on the identical and how it comes to be a unified consciousness) we would never consider the first manifold, i.e., apprehend and reproduce and associate it, for that is always in anticipation of a unifying concept (required for the unified self consciousness).
It's like comparing the actual recitation of the ABC's with the consciousness of reciting the ABC's. Jackie could conceivably learn the ABC's, but he would never consider them as the ABC's but rather would just start of A and then B and then finally Z and would look about for what to do next. We cannot only recite them but realize what we are doing, namely presenting the manifold of an object, namely the ABC's
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