Circles in the Air

Near the end of his highly influential Enquiry Concerning Human Understanding David Hume makes a rather candid admission regarding a major deficiency of the empiricist system of knowledge which he had just expounded in that very essay, namely an inability to account for the constancy of the objects of human experience and for their independence of the viewer, one of the most primitive and fundamental facts of human experience, and one which he describes as follows:

"The table, which we see, seems to diminish, as we remove farther from it; but the real table, which exists independent of us, suffers no alteration: it was, therefore, nothing but its image, which was present to the mind."*

The problem, Hume continues, is that nothing in addition to the images of the table is given to him which might be set in opposition to those images as the table itself, on its own, such that he were then able to recognize that what he see is merely an image.** Now the simplest and, by far, the most intuitive course for Hume would be to take the image for the object, i.e., as a thing on its own, a thing which changes shape and size. But Hume does not do this (any more than we do), but instead comes up with an idea of a uniformly existing object which is independent of the perceiver; but does so in a way which is inexplicable to him. In a word: Hume cannot account for the very object which is the source of knowledge per his own system, i.e., experience with objects.

[* XII.118, 3rd paragraph; emphasis added. (see quotation of 118--use back button to return here.)]

[** One might think that a drawing of the table would serve as an example for Hume; but the drawing (or color photograph for us today), subjectively speaking, is no different from a host of actual sightings of the table, each of which is slightly different. Indeed, according to the parallax theory of stereographic sight, once an object is some 50 meters away, depth perception vanishes and the mental image is as flat as any drawing, and thus is no more similar to the same table close up than is the drawing.

It might be quite fruitful to characterize Immanuel Kant's Transcendental Deduction of the Categories as an attempt to solve Hume's problem, and to do so by providing a bridge between the image which is given to us (and indeed which is all that is ever given to us) and the uniformly and independently existing object which is not given to us (and which in fact may be entirely imagined), but the knowledge of which we most certainly have as the necessary basis for making the very distinction between image and object that Hume is referring to; and without recourse to any notion or recognition of an independently existing object, such as a table, which (notion) were with us at birth, i.e., without recourse to traditional rationalism, which both Hume and Kant had already independently rejected as inadequate for other reasons.

In his earlier days Kant would most certainly have utilized the rationalist assertion (per Wolff and Leibniz) of an innate knowledge of specific objects, e.g., table, in order to recognize that Hume's table were enduring and unchanging and that what was perceived were merely a confusion of the senses. But subsequently, after realizing the incapacity of the rationalist to differentiate the left and right hands,* he conceived of a rather ingenious, middle path between empiricism and rationalism in which the objects of the world appeared in space and time (independently of the intellect) and then were joined by the intellect into systems of objects through the application of certain, general laws (which could be abstracted and enunciated by attending to the actual workings of the mind in experience). This called for a subjugation of the objects of sense to the intellect by means of these laws. Eventually Kant's gave formal expression to this theory in his so-called Inaugural Dissertation. But shortly after publication of this system, Kant recalled the devastating attack on the assumptions of such subjugation in Hume's Enquiry, and rethought and reformulated his entire system over the next several years to a degree where the senses no longer presented objects, but only empirical elements (Hume's "images") which, when subjected to a certain connective treatment (called synthesis), were mentally provided with an object (subjectively a product of the human imagination) and thereby transformed representationally into views of that object. The details of this system are outlined in that section of his Critique of Pure Reason called the Transcendental Deduction of the Categories (a category being one of the mental modes for combining these elements into objects and into systems of these objects and also of thinking about these combinations, e.g., total, substance, causation, possibility). It is to the exposition of the first (A) version of this Transcendental Deduction (TDA), and more particularly to the second of the three parts of that work (TDA II) that this article is dedicated.

[* The description of each of a person's two hands fits the other equally well, which means (especially given an idealized point-for-point mapping) that the two are indistinguishable, intellectually speaking, and yet the two are obviously different, but which difference can only be noted by a viewing in space; but space is a non-thing, according to the rationalist (Leibniz), and entirely a relationship among of actual things (like hands), and therefore not available within that system for making this left-right distinction.]

A certain, preliminary grasp of the pre-object world conceived of by Kant is utterly necessary in order to understand his argument in the TDA. One of the most suggestive terms for what we are initially faced with (speaking subjectively, from the standpoint of a perceiving subject) is specter* (Erscheinung), and precisely because what we see, as Hume noted above, does not at all exist on its own in the way we see it, but is more like a ghost which exists only in our minds. The table that Hume never sees (and thus can only think) presents only specters to his eye which vary according to the distance and angle and illumination of his sighting. That these specters change shape and size with his every move is one of the clearest and most intuitively appealing impressions of our senses. It is only through judgment and thinking that we let these specters depict objects to us. Thus the quickest way, perhaps, to grasp the notion of specter is to eliminate from the impressions of the senses all references of judgment, especially the terms "appear" or "look like" or "seem." According to this procedure telephone poles will not simply seem to expand and move toward us as we move toward them, they will actually do so on their own. And my tongue will not merely seem like a serpent darting in and about rows of whitish stones (my teeth) when the cave (my mouth) opens beneath the frog (nose) clinging to the front of my head below the two cave-encased snails (eyes), but be one, etc.** One helpful rule in this regard is to consider whatever appears as different to be different, i.e., a totally different being. In this way I before a bath and after a bath, and myself in a blue suit and then in a brown suit will be different beings.*** Conversely we will take whatever appears the same to be the same, i.e., the very same. Thus instead of appealing to any mistaken identity, where someone looks like me from a particular angle (which is also like noticing that an infant has the nose of the father and the chin of the mother), we shall now treat chins and noses and eyes and profiles as things on their own which flitter about and alight here and there.# The result of all this, briefly stated, is the abolition of all objects of human experience in favor of sheer specters (which [like the images of Hume's table] do not even themselves exist on their own, but only within us).##

[* And not "image," which is not quite accurate. The "table" on my retina is called an image for it corresponds to an actual table which stands before me, but the rainbow (to use Kant's own example) in the eye (or in the camera) has no corresponding object in the rain (and vanishes as I approach), and therefore is not an image but merely a specter. And so while all images are specters, not all specters are images. The term is well chosen, for as the rainbow does not exist except in the perceiver and is dependent upon a particular perspective of the rain, so Kant generalizes and speaks of the specter, which (transcendentally speaking) includes the rain itself, as that the existence of which is dependent upon perception. Thus the various images of Hume's table (or of the rain) have no existence apart from a perceiving mind (which, at first glance, seems to bring us back to Berkeley [although, as will become clear, actually does not]).]

[** The marvelous paintings of Giuseppe Arcimboldo (1527-1593) strongly suggest this way of looking at things. In his "Water" a human face, upon closer inspection, reduces entirely to a swarm of diverse sea creatures. Likewise a very emphatic example of spectral data is obtained by watching high speed traffic from an overpass; when about 50 meters from one's vantage point there is a dramatic, sudden and even humorous alteration in the size and shape of the vehicles (as perceived).]

[*** A very interesting consideration! For accordingly it might be easier mentally to associate me when in a blue suit with my father or brother or even a stranger in a blue suit than with my own self (naked) at bath, and therefore it might easily be possible that some beings, e.g., dogs, never realize that many of the specters of myself are one and the same person at all, but rather see a world of countless similar and yet still distinct persons (or even twins or clones [but who, it so happens, never appear together at the same time!]): some tall (close up), some small (far away), some smelling this way (before a bath), some smelling that way (after a bath), etc., ad infinitum, but with enough similarity to induce a fairly constant sense of ease among all of this diversity. Hume's concept of family resemblance is highly provocative in this regard.]

[# I may suddenly see a 5 meter long lizard by a river bank and then notice upon closer inspection that the lizard has vanished and has been replaced by a log remotely shaped like a lizard. And only time will tell what the log/lizard will turn into next (according to this way of thinking about things); for nothing in the lizard/log picture suggests any ultimate reality before my eyes any more than my skin appears as some sort of ultimate garment in comparison to the layers of clothing I might be wearing. The recently developed computer technique of morphing, i.e., replacing one face with another without perceivable interruption, models this psychological phenomenon especially well.]

[## And which the reader must thoroughly grasp (conceptually) in order to expect progress in understanding the TDA.]

Another concept which is critical for an understanding of TDA (and which will also shed light on the meaning of specter) is that of envisagement or outlook (Anschauung, the at- or on-look). For a rapid grasp of this term we draw a square ABCD, and picture to ourselves (but not draw) the diagonals. We extend AC from C to E, letting CE = BC . We draw BF and DG, each parallel to CE and equal to CE and to the same side of diagonal BD as E. Finally we join F and E and E and G. Now I say that whether someone sees the resultant figure as flat or in space depends upon that person's envisagement; and if the latter, then it is also an envisagement as to whether the drawing is seen as the outside or the inside of a box-like structure.

This exercise exemplifies some of the essential aspects of the envisagement, e.g., that there are various ways of looking at something. And, as we might expect, it also indicates that there is no guarantee that any two persons will ever be able to see things in the same way.* I may spy a face in a cloud and describe it to you with great precision and yet you may never be able to see that face.** Envisagement also suggests the suddenness of a particular depiction. If you are able to spy the cloud face, the envisioned object arises suddenly in the same way that the "box" that was drawn above comes suddenly into view. Furthermore an envisagement always comprises a multiplicity which is seen as a singularity as, for example, the lines of the sketched box in the example above or the various parts of the cloud face are all components of a single object, respectively. Finally there is a certain forcefulness and naturalness to the envisagement. When the face in the cloud comes into view, it is seen quite clearly and as though it were actually there objectively in the cloud on its own and that I simply had not been looking rightly earlier. And so it is with the "box;" although I know that my imagination is at work in whether it protrudes out toward me or away from me, I do not imagine that I see it in the way I do; the appearance is quite clear and, once spied, (almost) unavoidable.***

[.* This constitutes a major task for the Critique, namely to explain how it is that an objective envisagement is attained which, therefore, were object-based, but where there are no objects in view, but only specters; for the specter is an object only as a depiction, in the same way that a dream can be an object (of conversation or inquiry), but not otherwise (per A 104, §3, paragraph 3, 2nd sentence [and where "A" refers to the first version of Kant's Critique of Pure Reason).]

[** The term "envisagement" is particularly appropriate, I think, due to its suggestion of "putting a face on something," e.g., on a cloud; and far more so than the more traditionally rendered "intuition" which, regarding a face in a cloud, could even be misleading.]

[*** I sometimes tell my friends that when I discipline my dog with a rolled up newspaper she looks at the newspaper as acting on its own, while my hand (which normally pats and rubs her so nicely) is trying to restrain it and protect her. My friends laugh at this and think I am silly. But once they come to understand the meaning of the envisagement, they realize that it might not be so silly after all, and that if different beings can see different things in the clouds, they might very well look at all things quite differently. Thus originally for us (and perhaps always for the animals) a person will not be seen to go through a room, but rather a head and a shirt and a hand, etc., will glide by individually such that they are actually independent of each other and, at most, subject to (a subjectively seated and perceived) association but not to any necessary connection. Spectrally speaking these (garments and parts of my body) are all quite independent of each other and, as far as I might know, able to go their separate ways on their own, like individual birds in a flock. In fact we might think of them as such with this one difference: here (with the parts of my body and by clothing) it is birds of an unlike feather that flock together.]

Surely the most profound envisagement, and one that is common to all humans (and which may even be unique to them), is seeing things in space and time. It is certainly an envisagement as to whether I see two objects as merely different (colored differently, perhaps), or whether I also see one of them to the left of the other; or whether I see a table or an empty table. And it is equally an envisagement as to whether I notice the cup of coffee in my hand and nothing else, or whether I notice that it is the third cup this morning, or the first one after having heard the sound of my children scurrying about, etc. Once I begin to see things in space and time (and that will have occurred suddenly) the envisagement of that is so forceful that it will be almost impossible to see them in any other way or even to imagine a world in which things did not so appear; which prompts the very natural conclusion that things are in space and time on their own even as it seems that the face spied in the cloud is actually in the cloud (although we know [as experienced adults] that it is not).* Now if space and time were really the "containers" that Newton and the empiricists (and perhaps even a somewhat younger Kant) would have them be, i.e., which really "existed" on their own apart from us, then unless there were an intuition of these two, all-reality-containing, non-existing things (a rather bizarre use of the term "intuition"), it would be impossible ever to be able to take notice of them. And therefore, even granting (for the sake of argument) the actuality of a space and time which were independently real on their own, our own knowledge of them could only arise if they also were envisagements embedded in our sensitivity.

[* As Kant himself observed (Dissertation, II 404), if we wished to fabricate mentally a world which were not in space (as we have just been doing in this article in an attempt to grasp an appreciation of the concepts of specter and envisagement), we would still have to utilize the concept of space as a means to do that. When I, for example, imagine that things actually grow smaller as they get further away, the "further away" is itself, of course, a spatial expression. (A humerous consideration of a different way of looking at things can be found in the short description of Captain Hook and the Rainbow).]

In a close parallel to this consideration and understanding, we (like Hume) are all very certain of the existence of Hume's table as a thing which is independent of our viewing, and yet such information could not possibly have arisen in experience since all we ever have from that quarter are the ever changing appearances of the specters. Our certitude, therefore (as Kant will endeavor to establish), will be based on some undertaking by the mind; but this is not to say that the independence of the table is an illusion or only imagined: the table truly exists as a uniform object and independently of the perceiver, but (and this is the point) we know this not because of some intuition, as it were, but rather because we imagine it to exist in that way and thereby are able to explain and see (envision) the specters as views of that (imagined) something. Thus we paradoxically imagine something which is (imagined to be) independent of our imagination and perception, a so-called transcendental or critical idealism.* And the explanation of this work of our productive imagination, and how it is that it is nonetheless objective and can produce an objective envisagement of an object, even though imagination, is one of the primary tasks of the Transcendental Deduction.

[* Which, since the objects are thought to be independent of perception, and therefore also independent even of the perception of God, is quite different from the dogmatic idealism of Berkeley for whom there was no (external) object at all, but merely diverse perceptions which might be referred indiscriminately to the same term, e.g., table. According to the transcendental idealism of Kant, on the other hand, we dream up an object which is conceived to be a non-depiction (not dreamed up), but rather a real, independently existing object which then in turn becomes the basis for an envisagement in which we actually spy that object, but always only as it appears in space and time, as Hume did with his table. So the table really does exist (empirically speaking), but which existence (transcendentally speaking) is merely a depiction, but, again, of a non-depiction (all of which is obviously very difficult to express).]

All thinking, Kant informs us, is aimed at producing an envisagement, for the envisagement is the (very forceful and natural) evidence of the object itself, the immediate contact with it and what we actually see when we look (A 19). The correspondence of a concept (of some object) with an envisagement is called a recognition or knowledge (Erkenntnis) of that object (A 92). When I look at an outstretched index finger, I can see any number of things: a finger, a scratch, a color, a finger nail, an index finger, a representation of the number one (or perhaps the number 11 when counting from 7),* a pointing finger (where the finger serves as the first of two segments of a straight line, i.e., a ray, the second of which is not only entirely imaginary, but the far end point of which "touches" some distant object), and so on ad infinitum.** When what I am looking at (an envisagement) corresponds to what I am looking for (a concept), then I recognize an object (thus which is thought via the concept and seen in the envisagement).

[* Letting the little finger represent 8.]

[** This consideration belies the empiricist's assertion that knowledge of the object arises merely from an exposure to the object, for what is seen as object is always a function of the envisagement, which is within us individually.]

A recognition is either pure (and hence also a priori), or it is a priori and not pure (thus having an empirical component), or it is entirely a posteriori. For example, I think of the imaginary or ideal plane outlined by the frame of an open door and constituting the boundary between an inside and an outside of a room as a pure recognition, i.e., devoid of all empirical content;* the actual entry (movement) of an object into the room (through that imaginary boundary/plane) as an a priori recognition (but not pure, due to the need for the moving object); and the physical capacity of that object to make such movement (which constitutes an experience with that object) as an a posteriori recognition.**

[* This imaginary plane can actually be "seen" by looking at its position in space within the door frame, i.e., where the door would be if closed; this usually calls for a sighting in a slightly cross eyed fashion.]

[** These examples also provide us with an easy distinction between space as the way we look at and see things, e.g., in relations of space where the entering object goes from one side of the door, and then through the door to the other side (which relations are entirely ideal); and space as an envisagement in its own right, as an object (also entirely ideal), which is exemplified here by the invisible plane delineated by the door frame and by means of which alone any reference to the two "sides" of the room (the inside and the outside) is meaningful, and upon which also figures might be "drawn", as we shall shortly endeavor to do.]

I now turn to the TDA proper and will give an example of the recognition of an object via a pure envisagement in order to exemplify the subjective components of a recognition generally as delineated in TDA II.1 through II.3.6.* The object will be a circle (loosely speaking) drawn in mid-air with the tip of a finger. I call such an object a "pantomimic" and in this case will use the analogy of a traditional (analog) clock to illustrate the mechanics of the construction.

[* In this article references to the Transcendental Deduction are ordered according to this scheme: TDA II.3.2.1 = the first (A) version of the Deduction, 2nd section, 3rd part, 2nd paragraph, 1st sentence.]

Apprehensions of the Elements (TDA II.1) The first, subjective step in seeing a pantomimic circle is to apprehend the elements, and this calls for a certain differentiation of time. I must ignore the movement of the finger tip as it moves to the 12 o'clock position, and then attend to it as it moves from the 12 to the 1 o'clock position and on back around to 12; after which I must again ignore it. This is obviously an action of the self where the capacity for understanding determines the inner sense in distinguishing between the relevant and the irrelevant in relations of time. Without this capacity and the mental action issuing from it there would be no beginning, expanse and end to the object, subjectively considered.*

[* In some versions of the game of Charades, no speaking at all is allowed, not even to indicate the beginning or ending of a clue. This constitutes a severe difficulty, not unlike our first encounter with what will become our native language, for the sound (or sign) for, or a pointing (or clue) to, an object is itself an object; thus indicating the need for an objective envisagement as the basis of language.]

Reproduction of the Elements (TDA II.2) Secondly I must keep the apprehended elements in mind, remembering and recalling the 12 position when at 1, and the 12 and the 1 when at 2, and so on. And this is more than a recall of a cluster of positions, a 6 (position) and a 1 and a 10, etc.; it is an ordered grouping of the elements, i.e., it is the path of the finger.* This retention not only enables me actually to apprehend all the elements as a group (thus facilitating the apprehension itself), but independently of this (and very importantly) provides a fodder, as it were, for the machinations of the productive imagination in the next step toward recognition.**

[* Paradoxically I must actually ignore the finger (the only empirical object present); for as long as I concentrate on the finger I miss the circle. I have to look at the "plane" on which the circle is being "drawn" or pointed to (and which is entirely imaginary).]

[** Incidentally we have here a pure multiplicity [reine Mannigfaltigkeit], a grouping or plurality which is sensitively, but not empirically, provided, namely the path.]

Conceiving the Object (TDA II.3.1-6) Thirdly (and finally) I must not only keep all these elements in mind, I must remain aware of what I am doing, i.e., I must grasp all these elements together as a singularity, which requires a certain presence of mind*; in other words I must conceive of (dream up via the productive imagination) an object such that the elements apprehended and reproduced are necessitated, i.e., the elements of this thus far only subjectively valid and tenuous multiplicity (held together at first by rote, as it were) are transformed into components of an object. Hence the object must be provided.** This comes in the form of a concept called the circle (which denotes a unified consciousness of the otherwise disparate elements, a critically important aspect which will be discussed shortly in some detail). This concept is merely a rule for producing such an envisagement and it encompasses all the multiplicity attributable to it. We might call the figure a line which loops back and connects with itself, e.g., "starting here we begin drawing and continue on around until we come back where we started," to which sounds or words nothing corresponds except a pure envisagement.

[* Such that when I have finished, my mind is not simply focused on the last element as the last of several, but rather I understand that a total has been achieved. In counting to 12, for example, the 12 is not simply to be the last of a series of numbers, but rather, if we are talking about addition, is to encompass all of the others as a unity or singularity, i.e., not the 12th of 12 items, but the total of 12, i.e., all of them together.]

[** The rather remarkable principle underlying all of this, namely that there is more here than meets the eye, and therefore more than a mere finger or even a moving finger, will be discussed later when we come to the notion of empirical objects.]

Briefly then: we apprehend and retain a multiplicity (which as such is only arbitrary, a merely subjectively valid envisagement); we "treat" this multiplicity via the productive imagination and arrive at a synthesizing object (the concept/rule) such that we can both necessitate the multiplicity (transforming the otherwise independent elements into aspects of the object) and identify an object in the envisagement (making an example or view out of the multiplicity); whereupon finally we see and recognize the object (the circle) and a "light goes on" much as when we finally and suddenly see a face in the cloud that others have tried to point out to us. The subjective envisagement has become objective by the addition of the object (which really is the comprising concept) to encompass or embody, i.e., necessitate, the multiplicity and to enable us to point it out in space as a singularity. For we actually do see the circle and are able to show others (which is the mark of objectivity), and if someone else cannot see it, we say they are not "looking right;" and all the while admitting that there is nothing there. Indeed it is a pure envisagement which differs from a face in the cloud (or even a face on the front of a person's head) only in the latter, as an empirical object, being constituted by certain textures, shadows and contours which are entirely absent with the pantomimic.*

[* And for which reason we say that while both are sensitive, the pantomimic circle is pure (being rendered through merely one of the forms of the senses, space) while a human or cloud face, with its textures and shadings, is empirical.]

Turning from a pantomimic with its pure multiplicity to an empirical object we can now also imagine how Hume might have formulated and thereby first recognized a table. In an exact (though empirical) parallel to the provision and subsequent recognition of a pantomimic circle, he will (while a child) have noticed the use of the term "table" when certain specters were in sight, and will have slowly associated and isolated a particular multiplicity (through trial and error), and eventually will have conceived of a rule for the assembly of a flatish surface and some columns into an object called a table, whereof these elements became the top and legs, respectively.* The result of this concept/rule would be (1) the necessitation of the envisioned elements by mentally transforming them into parts of the table, where before they were joined merely arbitrarily and contingently** and, of equal importance, (2) the capacity to make an identification of a table among the specters and thereby to recognize it, and indeed as independent of the perceiver.

[* He will likely have confused chair and table at first, and (as a result of confirmatory trials and experiments) will have heard such comments as, "No, that's a chair; see the back; tables don't have backs," whereby he would have realized that what he thought was a table was actually a piece of furniture, and examples of which were tables and chairs. (Also we see here the provision of an empirical multiplicity before the object, and thus presumably the solution to a problem involving an unsynthesized multiplicity which was raised by Robert Paul Wolff in Kant's Theory of Mental Activity, pp. 157-9.)]

[** Much as we might spy particular configurations of textures and shadows in clouds, but to which no object corresponding to them comes to mind (in contrast to the face in the cloud which is a determined relationship of nose, eyes, etc., due to the empirical concept of face) and which therefore never make a strong and lasting impression, but rather tend to be immediately dismissed as sheer imagination and forgotten.]

Now once given an object, e.g., a table, it becomes possible to develop experiences with that object. In the same way that the young Hume will have accumulated, retained and unified the elements of table, transforming them thereby into parts of the table (by mentally providing the table itself), he will have noticed certain relationships of the table through experimentation and trial and error, and will have discovered, e.g., not only that the top is always up (a perception), but also must be up (which is an experience with, and not contained in, the just developed concept of, table).* This further necessitation beyond that embedded in the concept of the table itself, which is added synthetically to that concept, would have arisen when he learned (realized) that a table serves to support items at a height suitable for humans, and therefore must of necessity be upright.

[* A critically important distinction, touching the heart of this article, and which will be discussed below.]

The result of the necessitation (be it of the object or of the experience with the object) is a given and fixed multiplicity from which, oddly enough, deviations can then occur.* The object of the empiricist, in contrast, is a constantly developing and shifting mean or average of all observations ascribed to the object (based on felt similarity). Thus there can be no deviation but only a variation about this mean. For example no table can be broken and in need of repair, according to strict empiricist thinking, for the wobbly state of a(n actually broken) table would be merely one of the several observations going (continuously) into the mental makeup of the object in the first place, e.g., while sometimes the table is stable, at other times it is wobbly.** It is only through (the concept of) a set, definite object that a deviation can occur, e.g., that a table can be broken and in need of repair. And so, paradoxically speaking, it is only the necessitated objects of human recognition (sheer depictions) that can be "out of whack or kilter" and in need of explanation, e.g., "Its no wonder the table is on its side, one of its legs is broken."

[* See Robert Paul Wolff, pp. 121-125, for an excellent discussion of rule-directed sequences which provide a norm such that deviations can be recognized.]

[** One of the more common problems of modern life is having to decide whether a given stop light is broken or merely slow or long on red, but which is not a problem for a strict empiricist who has no reason to assume that some signaling cycles might not take several years to complete, where the Kantian (or transcendental) idealist, in contrast, is able to see (or at least suspect) a broken signal.]

We can see a parallel now between the conception of the object and the extension of knowledge concerning the object (which constitutes experience with the object). We apprehend and treat the spectral elements of an empirical envisagement by means of a synthesizing concept/rule such that the elements are transformed into parts and thus can be derived from the concept* and also that an example (an envisagement) can be identified. Then we likewise apprehend and treat the elements of an empirical envisagement (where the elements now consist of the objects themselves [earlier conceived and recognized], e.g., the relationship of the table to the floor, i.e., that the top is parallel to the floor and holds items at a height convenient for adults when seated) in an equally synthesizing way such that new predicates are attached to the concept with a force of mind equal to that which binds the spectral elements originally in the object by means of the concept; and thus providing a necessitation of the multiplicity and examples for exemplification just as did the original synthesis of the spectral elements via an object. [Here, with the experience, the necessitation, since it is empirical, means only that violations are deviations and must be explained, and not that the necessity is apodictical (a prerogative reserved by Kant for the category, and which will be discussed later).]

[* This also makes possible the analytic judgments, i.e., saying something about an object without having to look at the object, e.g., that a table has a top. Curiously Kant makes no mention in the TDA that he is also describing there the source of these analytic statements through the formulation of the concept of the object. That this is the case, however, is clear from a comparison of the comments regarding bodies, which are found in TDA II.3.6, TDB 19.2 and Part IV of the Introduction to the Critique of Pure Reason.]

It may be helpful to pause for a moment in this development and seek a perspective on Kant's thinking as expressed thus far. In the Dissertation Kant imagined the human, firstly, intuiting objects which, while they existed as objects on their own (and had to be in order to be intuited), were only seen in space and time, i.e., merely as appearances; and, secondly, providing a necessitation to the relationships of these objects amongst one another by means of the intellect in prescribing laws (which were to represent the essential, interactive constitution of these objects). This approach was unacceptable to Hume who argued irrefutably that since objects were things on their own and entirely dissimilar to the intellect, the latter had no warrant for prescribing laws regarding them.* Kant, momentarily staggered by this argument, finally changed (or rather expanded) the scope of his thinking, though retaining its form. Thus in Pure Reason he abolished the (supposedly intuited) objects and left in their place the sheer elements of which they were comprised, i.e., specters, and then showed that Hume's objects of experience could not arise to be recognized except by means of a unification of these specters in accordance with universal connections which, in the case of the objects themselves, were called concepts and, with regard to the relationship amongst the (thusly constructed) objects, laws (of experience).** Thus an experience in the Dissertation consisted of combining already existing objects via laws; and this notion of experience (as a combination via laws) was not only retained in Pure Reason but even expanded to include the objects themselves, such that the objects of experience are themselves now conceived to be assembled from spectral elements by means of concepts, which are universalizing expressions analogous to laws. In this way, by providing an indispensable role for the intellect in making these objects possible as objects of experience, Kant also achieves a justification for the action of the intellect with regard to experience and thereby remedies a deficiency of the Dissertation. Finally, to add the "icing to the cake," Kant so formulated the notion of perception (the empirical apprehension which I shall shortly introduce as the "second look") that even it could not take place except in accordance with, and pursuit of, a connection (formulated by the productive imagination) in conformity with the categories. The categories thusly become the supreme law of laws (of nature) by means of which we were empowered and prompted to look for empirical connections, those being either concepts or laws, such as Hume's law of association or Newton's law of the mutual attraction of bodies.***

[* And indeed who went so far as to suggest that these laws merely mirrored and summarized the perceived behavior of the objects through an exposure to them.]

[** This consideration provides additional support for the writer's contention that the usage of "intuition" for Anschauung is not well advised, for it implies the existence of the objects of experience as things on their own which is diametrically opposed to Kant's thesis in Pure Reason (though not entirely so to that of the Dissertation where objects existed as such on their own). The only way we come to recognize these things on their own is by virtue of a synthesis of spectral data (our sole source of empirical information) by means of a concept which is the object such that what is perceived (actually only specters) is always considered only a view. The force of the independence of the object is made possible by the determined, i.e., the concept-driven, envisagement. Thus I see the table before my eyes (even though I admit that what I actually see is merely a view of that table, and not the table itself), and hence obviously the table exists as a thing on its own (empirically speaking [and only so]).]

[*** The details of Kant's argument for the subjugation of perception to the category are given below, and so this assertion is really only a promise at this point in the article.]

Returning now to the TDA (and beginning with II.3.7) we learn that the concept unifying the elements of the envisagement into an object not only provides (1) necessity to the multiplicity and (2) a determination to an envisagement (example of the object), it also represents a unified consciousness. And furthermore since the object of experience is not a thing on its own, but rather a mental provision to the spectral data for the purpose of encompassing or embodying that data, and since experience with this object must of necessity await the appearance of the object, this unified consciousness must actually precede the object and indeed provide it to the specters in order that they might be transformed from things on their own into examples and views of objects, with which then experiments can be undertaken, and concerning which experience becomes possible. This preceding unity of consciousness is called the original apperception, and it is the means utilized by Kant to provide a pervasive unity to all possible recognitions, and to which we now turn our attention.

Often times I will lock a door while mentally preoccupied and then shortly thereafter not be able to remember whether I had actually done so or not. In order to be sure I must make sure, i.e., I must return to the door and try it. The first situation, that of preoccupation, is indicative of a state of consciousness in which I do or see something without what we might call a mental "registration," i.e., as soon as a new impression arises, any former impression has completely vanished; a condition also expressed as "out of sight, out of mind!"* Much, perhaps most, of our lives can be characterized by this vague, dispersed sort of consciousness which Kant includes under the denomination of "unconscious depictions."**

[* This does not describe a depiction but rather merely a sequence of mental states whereupon A, B arises (as in the alphabet), and upon B, C arises, and in each case the preceding vanishes. It also describes association, where A does not depict or represent B but rather is replaced by it in a rather mechanical way. A depiction (Vorstellung) denotes an awareness of a "standing for" or "in place of," and thus of A and B together in a certain relationship called denotation. This will be discussed below in a more appropriate context.]

[** Which, at first glance, seems an obvious contradiction, for one of the marks of any depiction is that it is formulated consciously (TDA III.3.3). But once formulated, it can arise without consciousness as in the example just cited of locking the door. Indeed one of the most common instances of this phenomenon has probably already been experienced by the reader of this article, namely a realization that every word in a given paragraph was read and nothing at all registered or retained due to some mental preoccupation, and that the paragraph had to be read again with consciousness.]

The second state, checking the lock to make sure, is a clear and focused consciousness. It is sometimes described as "presence of mind" and often admonished by "watch (or think about) what you are doing." This same consciousness is represented by the "double take" (caricaturized by the slapstick comic) which we might call the "making sure" consciousness, or the "second look." This second look (when its content is empirical) is also an expression of what Kant calls a perception (Wahrnehmung or "careful taking").* **

[* Hence perception is a careful and deliberate look which is directed toward making sure of the data and which is always empircial. Accordingly the apprehension of the elements of the pantomimic circle was not a perception, but only because the data was pure (even if sensitive) and not empirical, and thus had to be apprehended on the "first look."]

[** I am indebted to Werner Pluhar for suggesting the "care" or "caution" rendering for the German "Wahr" rather than the more obvious (and technically less accurate) "true". I observe merely that the reason we might think "true taking" is due to the care that is actually taken in making sure. In any case the validity of the perception is to be understood as based on the careful input of data.]

This latter consciousness Kant calls the transcendental apperception, and it is that consciousness which can and does precede experience and indeed all objects (subjectively speaking), and by means of which both the experience and the objects of experience are made possible as depictions. It is that state of mind, for example, which precedes the sighting of the pantomimic circle as we pay attention to the movement of the finger in the expectation of discerning something which is neither obvious nor immediately (empirically) present.

Kant conceived of this apperception as an edifice of interrelated and component parts which together make up an integrated system; but originally, before any exposure to specters and their synthesis has taken place, it is merely a capacity for, and form of, a system. The actual contents of a given individual's consciousness will be gleaned from that person's exposure to specters through the envisagement and then by the treatment (synthesis) of the apprehension of those specters by the person's productive imagination, all of which finally results in a recognition of an object or an experience with that object (as was described above regarding the table). The synthesis by the productive imagination is undertaken in light of the form of the apperception; and recognitions arise only when a synthesis has been achieved which accords (1) with the specters and (2) with the form of apperceptual unity, i.e., the category; which together constitute Kant's two-prong touchstone of truth. The process of integration into consciousness is itself a conscious activity which, since there is no object provided by the senses which might be looked at in the cursory sort of way of the first state of consciousness described above (other than a sheer specter like Hume's "ballooning" table [which expands as we approach it]), calls for a deliberate awareness in order to "find" (actually to place mentally) the object in the specter.

The form of apperceptual unity (by means of the category) might be described as a system of universals and laws. All recognitions are conceived of as universal expressions or as modifications of universals. I never learn that a specific specter is this or that, but only that objects are this or that. When, for example, I perceive that a piece of iron sinks in water, and even though I do have certified data (a fact) for the productive imagination, I have not made a net addition to my consciousness, nor will I, until I can recognize that iron sinks, i.e., all iron;* barring that I have a perception (of data) but not a recognition (comprehension).** [This will be covered more completely in a subsequent example. Presently we imagine a consciousness which is a formal unity, i.e., preceeding even the first perception and the first recognition, and where this unity, upon the receipt of data, is expressed empirically in terms of universals, and which merely preserves itself as a complete unity as perceptions are introduced (via specters) and recognitions attained.]

[* Although, since the object is empirical, this universalized experience is still contingent, and I will later learn that not all iron sinks (or rather that iron does not always sink) and the equally important and modifying lesson that the shape of the material is one of the determinants as to whether it will float or not, e.g., iron floats when in the shape of a vessel.]

[** This is quite different from the mental edifices of Leibniz and the rationalists. They pictured the mind as actually and preceedingly possessing concepts of individual classes of objects, e.g., iron, boats, tables, which were then prompted to the mental forefront (a form of remembrance) upon the sighting of some (more or less) correspondence in the impressions (which constituted a "confused" rendering of the object). Kant hypotheses instead merely a capacity for universalizing (= concepts and laws) such that the specters become the content, with the object being the conceived form; hence without any preconception of specifics. This universalization is either the concept of the object itself, such that all tables, for example, have tops; or else it is some law concerning the behavior of the object, e.g., that a table falls when the legs are removed, or that air expands when heated.]

[Concerning the consciousness of self, Kant observes that the a priori and transcendental (i.e., recognition-enabling) apperception is merely a capacity for recognitions and does not per se itself provide any sense of self. Like empirical objects, the self must reveal itself as a specter (via envisagement) in order to be recognized. Thus a synthesis of spectral data into some object will be necessary in order for the self to arise to view as a something which engages in synthesis. Once some synthesis has been achieved, there is a something, an actual (empirically) unified consciousness, which then in turn can be noticed and then denominated the self.

[In this consideration (which is found [albeit dimly] in TDA II.3.7.1-10.3) there is already a hint of Kant's ultimate intention with regard to the TDA, namely the subjugation of perception to the category. For since the self can only be aware of its own self by means of a preceeding synthesis, and since the synthesis must consist of the provision of an object to the specters, and since there is no indication in advance as to which specters are to represent an object (as examples or views) such that the apprehension described with the pantomimic circle (or Hume's table) might ensue, it follows that there must be an a priori principle that all specters are subject to the conditions of apperceptual unity in order then that any specter be subjected to the synthesis which alone leads to an object whereupon then the self incidentally provides a material, as it were (i.e., its own synthesizing results), for self recognition and empirical self awareness.*]

[* This consideration is interesting and is remotely analogous to the thinking of the founder of the 18th Century Methodist movement, John Wesley, an Anglican priest. He experienced what he considered to be a new attitude which, if authentic, could only come from God and would represent a real and present communion with God, but which, according to John Calvin's doctrine of a limitation to the scope of God's love and a constant (time-independent) status before God (and therefore: "damned at death; then always damned") might only be a self delusion which would not be discerned until later, and therefore his supposed transformation could not be certified unless also experienced at the point of death. In order for an assurance of salvation to arise before one's deathbed and therefore for the promise of the Christian gospel to be meaningful, Wesley felt compelled to assert the universal love of God whereby then his experience (which was already authenticated subjectively by an inspection of the sincere desire of his heart) was objectively validated as the work of an all-loving and all-pursuing God. Furthermore any given person might now be prompted by this principle to expect (anticipate) and hence to look for such a transformation and thereby have a real basis for the faith which was called saving, and which, according to Wesley, was necessary in order for this work of God to have any effect. In a like manner, Kant asserts that the only way that a connection might be sought in any given case were for connectability (associability) to be in fact preceedingly assumed for all cases.]

We are now poised at TDA II.3.10.4 where we begin the descent to the category by a final consideration of the object of depictions. A depiction is a consciousness which refers to something else, its object.* The term "table" refers to the concept of table which, in turn, may refer to a specter, e.g., this (present view of a) table, or to a pure envisagement (a line drawing or a pantomimic description of a table), and may in turn for its part also be the object of (example for) the concept of furniture, and that in turn of article, etc. The specter is the only object which is given to us immediately and to which we may stand passively. The object we actually see is a product of the envisagement as in the case of the finger we considered earlier where it could be anything from the number one, to a length, to a pointer. But in all of this there is one pervasive and fundamental outlook regarding the specter which is profound in its implications, namely: we know that the specter is not a thing on its own but rather refers to, i.e., stands for, an object which cannot itself be seen (for only individual specters are ever open to sensing); this object is called the Transcendental Object = X (TO=X). [This consideration will facilitate an understanding of the deduction of the valid application of the category to specters, for the proof will hinge upon whether the specter is considered to represent an object of human experience or be a thing on its own; if the latter, there will be no use for the category, but if the former, then the category is not only useful but indeed indispensable for the provision of the object which the specter is to exemplify (even as any given specter of the table exemplified the table to Hume from a given perspective in space and time, i.e., as its look).]

[* A depiction or representation is always a signification that one thing is to have for another, e.g., the word "red" stands for a color, and thus requires at least the possibility of having in mind at once both the term and the sensation. This is different from what may pass for representation among the animals which is a form of association where one state, A, prompts another, B, but then vanishes upon the awareness of B, much as the preceeding letter is forgotten upon the recitation of the following one of the alphabet. This is a subtle, though critical, distinction which underscores a certain, necessary role of the apperception in the apprehension and integration of spectral data, i.e., perception and then recognition. (Incidentally, if I hear the whirl of an electric fan, for example, while feeling the touch of a pen in my hand, then as I concentrate on either, the awareness of the other recedes and even vanishes; and thus only one can be in mind [vividly] at any one time.)]

Now (TDA II.3.11) since the concept of this TO=X is general and encompasses all specters whatsoever (those which are eventually assigned to bodies, those which are found to be internal states, e.g., memories and thoughts, and those which, like the rainbow, remain mere specters), it does not direct the production or identification of any envisagement (in contrast to the empirical concept/object), but rather serves merely to require and insure a uniformity and consistency among all recognitions about any given object, e.g., the size of a table, its color, its position, its strength.*

[* And insures that our recognitions are not arbitrary or sheer fancy per TDA II.3.4.]

Now since (1) this TO=X is the only object ever possible for us, to the extent that the specter is thought to be merely the representation of an object (and not a thing on its own),* and since (2) this concept of something = X is the means whereby the specter is found merely to depict an object (for the object [the empirical concept] is a production of the apperception [by means of the productive imagination as constrained by the form of the apperception]),** it follows that this TO=X will require that the data entering into the makeup of the object (the original concept of any specific object, by means of which analytic statements may be made) as well as the data to be used subsequently for making judgments about the object (synthetic judgments through experience) be apprehended in accordance with a principle which insures complete uniformity of the empirical consciousness which is the entire and ever consistent edifice erected by means of the a priori and transcendental apperception (the understanding itself) with the materials provided by the senses including, of course, the form of the sensitivity, i.e., space and time.

[* The reader is reminded that any specter can be called an object in a grammatical sense when, for example, I say that the specter of Hume's diminishing table is an object of our discussion. The German for object (Gegenstand) also means subject matter. But if we take the specter (as it appears to us) for the object of experience, then we treat the specter as a thing on its own, at which point inquiry ceases and we are faced merely with trying to memorize and second guess the antics of this thing, whatever it might be.]

[** This form, as we shall discover below, means a dependence of the apperception upon the category for a "fit" of the data into a unified, empirical consciousness.]

We are now gradually approaching Kant's primary thesis that the specter, though given independently of the intellectual, connective concepts of the apperception, is nonetheless subject to these concepts. As a preface to an examination of Kant's presentation and proof of this thesis in TDA II.4, which constitutes the heart of the Deduction, I wish to speculate briefly on an experience, the results (though not the details) of which are described by Hume in the following passage from the Enquiry:

"When a child has felt the sensation of pain from touching the flame of a candle, he will be careful not to put his hand near any candle; but will expect a similar effect from a cause which is similar in its sensible qualities and appearance."*

[* Section IV, paragraph 33(b).]

I will imagine a grown person capable of rational thought, but without experience, somewhat as Hume did with the figure of Adam in the Enquiry.* I assume that this Adam has already had sufficient exposure to lighted candles to conceive of an object, i.e., a flame, as a bright, dancing and even curious and enticing topping or "hat" to some candles. This concept and the recognition of the flame provide him with the capacity to make analytic statements about flaming candles in general, i.e., without having to take a look at any particular one, e.g., that it is bright. But now Adam is about to embark upon an experiment with these flames (based perhaps on sheer curiosity), namely the determination that the flame is not only bright, but also hot; and so Adam reaches out to touch the flame.

[* Section IV., subsection 23.]

Upon noticing the painful heat coincident with the touch, Adam will indeed reflexively withdraw his finger, but then will wonder: did the heat come from the flame, or did that just happen at the same time (= a fluke, i.e., a sheer coincidence)? In order to make sure, and at some point in time, Adam, in full awareness, will carefully and slowly let his hand approach the flame again (and indeed will move it back and forth more than once) and will notice the increase in heat as his hand draws nearer to the flame, i.e., he will notice the correlation of the rise in heat with the reduction of distance and that the change in the heat happens only in this way (in the experiment). It is this "second look" which first constitutes a perception, properly speaking, i.e., a careful look at, and apprehension of, empirical data for the purpose of the assembly and certification of facts, i.e., that whereof we are certain.*

[* Incidentally, we can see from this theoretical example that the perception, as the so-called second look, is obviously predicated upon the principle that the future resembles the past, which therefore is not derived from experience but rather precedes it and makes it possible by making the perception possible. The difference between a pure envisagement (like the pantomimic) and an empirical one (which, when carefully apprehended, is called a perception) lies in the necessity of this principle for the latter, for it is certainly not needed when the multiplicity is purely given.]

Upon consideration of the elements, the bright flame and the correlation of heat and distance, Adam will at some point spontaneously conceive of an explanation, i.e., a necessitation to make be (universally so, i.e., a recognition) what he has just found in this specific case to be (a perception); namely that

1. the flame itself is hot, i.e., on its own, and hence always so; and, of equal importance,

2. the reason that it does not always feel hot is due to its distance from Adam, thus the intensity of the feeling is in inverse proportion to the distance of the hand from the flame, i.e., the greater the distance, the less the heat.

This latter fact is actually an empirical law, a universal expression which is necessary for the explanation of the present phenomenon, but also which Adam will express eventually as a law of dissipation of qualities in general, e.g., sounds, heat, light, etc.* Thus Adam is not satisfied in knowing that this particular flame is hot,** for that was given to him by the perception (the determination of the facts), but rather insists (per the nature of his apperception) to speak universally, and has now established (through the conception of a law [essentially a figment of his productive imagination]) that all flames are hot, whereby then this particular flame/heat relationship can be derived from (necessitated by) that general law.*** This is the completion of the experience: a new predicate is attached synthetically to the concept, namely the flaming candle is not only bright (an analytic statement),# but also hot (a synthetic statement), and while the empirical data (the heat) is a posteriori, the form of the experience (the deliberate and directed search for a cause, which is called a perception) is a priori. The general object that is presupposed (a sheer depiction invented by Adam's mind) is that of nature, i.e., an orderly arrangement of, and actual interaction among, the objects of the world (and merely represented by the specters), which is independent of the perceiver, and which, therefore, can be observed and replicated and expressed.

[* His productive imagination will very likely have fashioned, suddenly, a corollary schematic, e.g., a series of concentric circles or spheres with a common center. And to this mental diagram, he will think: the flame is the center and the figures are the feelings of heat in inverse proportion to their size, i.e., the larger is the weaker, and thus express the form of an empirical envisagement to which the present case corresponds and which can be used in the future to determine other envisagements and thus provide additional examples of this law of dissipation.]

[** Which would most surely have required at least one confirmatory replication with another candle (and thus again presupposing the replicability of the experiments).]

[*** This concept of experience was first expressed in the Dissertation, namely the positioning of the sensa in time and space (observation of the spatial and qualitative [warmth] correlations) on the one hand, and then the binding or connecting of the positioning via laws on the other. In the Critique Kant expands the concept to bind the spectral elements into objects and simultaneously warrants the utilization of laws of the intellect through making both the objects of experience and the laws of their interaction (their nature) possible by means of these contributions of the intellect (called the categories) which then in turn guarantee thereby the pervasive unity of the empirical consciousness.]

[# Taken from the original concept itself, though which was originally conceived (synthetically) in order to provide an object such that certain spectral data might be unified and singularized (if I might be permitted that term).]

It is worth a moment to remind ourselves that the necessity attaching to the relationship of heat and candle flame is empirical, and thus, unlike the necessity provided via the category (which is inviolable and will be discussed shortly), situations may arise where no heat is found with the candle, in which case Adam will discover, perhaps, that a cold glass has just been place around the candle, or that it is a fake candle or a mirrored image of the candle (both of the latter being very difficult concepts for the strict empiricist). Thus deviations will occur, but which are nothing more than prompts for the discovery of an explanation (which is presupposed through the concept of a nature).

In order to support the reasonableness of this speculation, I will present some details of an actual and personal experience with a motorbike. For several days after purchasing my new motorbike it did not perform properly (I had already long ago gone from treating some view of the bike as a thing on its own to the concept of the bike, and thus to the bike as an empirical thing on its own, i.e., under empirical necessitation whereby then I knew [according to a method very similar to that utilized by Adam] that a certain performance was called for). I observed that the bike hesitated and faltered in cool weather and drove very well in hot weather. The facts of this perception also constituted an aggravating (and intriguing) problem until one hot afternoon I heard a loud hissing sound while removing the gas tank cap to check the fuel level. Before I could even think the words I "saw" the object:* the gravity-fed fuel system (the fuel tank sits above the engine) was unvented (a faulty cap, I learned later). Gasoline is highly elastic and contracts in cold weather (and thus a vacuum would form and the engine would falter due to the lack of fuel being able to descend into the engine) and expands when heated (and thus would be forced into the engine for outstanding performance during warm weather). That was the cause of the hissing sound: the gasoline had expanded under the afternoon sun and the tank was pressurized. My sudden grasp of the situation was expressed by an instantaneous, schematic production of my imagination: a straight line descending from a circular sort of figure, the former representing the descending fuel line and the figure the tank. To this schematic I was able to think what I just explained above (although, at the time, I did not think that expressly, but was merely conscious of an ability to do so).** [The production of this schematic as the means for directing and ordering the reproductive imagination (and thereby distinguishing the subjective apprehension from the objective]*** and as the sensitive correspondence (and thus also application) of the category, can often be discerned upon introspection when facing a problem calling for a solution. There is frequently a "trial and error" approach on the part of the productive imagination in putting the spectral elements together.]

[* Which, psychologically, is very much like suddenly seeing a face in a cloud that others have been pointing to but which you had not yet been able to make out.]

[** This schematic is for Kant the sensitive object itself, a very interesting concept which is described in the next part of the Critique, dealing with the Schema. He calls it the phenomenon and, in a sense, it provides continuing (though modified) validity to the earlier Dissertation which dealt with the observation and connection of phenomena in space and time, for experience consists in this very connection. But it is in the Critique that he first describes how it is that these phenomena (objects of experience) arise out of spectral data, namely by the phenomenon (a schematic [image provider] of the concept) being the empirical thing on its own and the basis for the recognition of the object through the spectral data. The phenomenon or empirical thing on its own is also a representation of the TO=X (as a specific object) and is provided entirely gratis by the mind in order to have an object which the specters then represent empirically as views.]

[*** To be enunciated below.]

By way of comparison of these two experiences, Adam and I both had already developed concepts of our respective objects and had already earlier recognized them. Thus for the two of us they existed as things on their own (which is the way we describe the object [empirically] and the result of our recognitions of them). The flame, as a(n empirical) thing on its own, neither included or excluded the further concept of heat; but the bike, in contrast, did already include the further predicate of a certain performance which had been added to it earlier in the same way that the predicate of heat was added by Adam to the concept of the flame. Thus while the heat originally associated with the flame offered no conflict with the concept of the flame, the performance of the bike was a contradiction of the empirical necessity supplied through the concept of the bike and of its subsequently added predicate (but which, though appended later, still supplies the same necessity [subsequently] as the concept of the object does [originally] to the components of the object, e.g., the brightness of the flame and the parts of the motor bike engine). Thus (and in an effort to make clear a rather subtle point) while the object is provided synthetically to the spectral data (the flame, the motorbike itself), it does not cease to be spectral, although, for the purposes of our human understanding, the recognition of the object, which is supplied by the mind transcendentally (for the sake of producing a recognition), means that we look upon the object as a thing on its own, pre-existing and which needed merely to be sighted, in an exact parallel to seeing the face in the cloud, except in the latter case, even though the impression of the sighting is that the face was always there and that we had not looked properly earlier, we know that it was not (that it is a sheer envisagement), and we make this distinction by contrasting the face in the cloud, as sheer specter, from the face on a human head which, for us and relatively speaking, is there on its own (but which originally is a result of a prior conception of a something, the TO=X, which denotes an existence independently of our own viewing). Thus the concept of the thing on its own has a proper (and even necessary) meaning as long as we are speaking empirically.

The preliminary point to be made with regard to the details of the two experiences (in anticipation of the forthcoming commentary on TDA II.4) is this: the certification of the faulty performance of the motorbike was a perception, but not a recognition (technically speaking), and thus it was a problem (intellectually speaking) for it was impossible that it might be admitted into a general, empirical consciousness (which, as we will remember, is a system of interrelated components, all of which fit as elements of a unity [one of the most emphatic points of the TDA, and to which end the TO=X serves]). The motor bike was an example of a(n earlier developed) concept which included necessity, i.e., it had to function in a certain way (per a preceding synthesis). The perception of the circumstances of the actual, erratic performance, i.e., cool weather/bad and hot weather/good, was merely the establishment of the facts in pursuit of a solution (a recognition) and not the end supposed by the empiricists. The law of the expansion of fluids provided a means of explaining the apparent failure of another law, namely that of the natural descent of fluids (in a gravity system), and did so in a manner which was entirely consistent with both laws.

One other point concerning the two experiments will be important before we return to the TDA. The recognition necessitates the details of the empirical apprehension (perception), and does so by distinguishing the objective apprehension from the subjective, and thus denotes the object's independence from the perceiver. As I accumulated data I may have noticed the engine's hesitation before noticing the coolness of the weather on any given morning or evening, and likewise may have simply accepted the good performance as a welcomed part of a nice (warm!) day; but upon discovery of the object (the sealed tank), I saw that the factors of the perception were merely subjectively valid, e.g., that I merely happened to notice the cool weather after sensing the hesitation, and that in fact the cool weather preceded the hesitation and indeed necessarily so, i.e., as its cause, and could have been so noticed.*

[* This consideration is actually an anticipation of Kant's discussion of the Second Analogy from the Critique of Pure Reason.]

We turn now to TDA II.4 and will utilize these experiences to fathom Kant's logic. His goal here is to show that even though the specters are given independently of the understanding and intellect, still, by virtue of the fact that the apprehension of an object is dependent upon the perceiving subject and is undertaken for the sole purpose of discerning an object (supplied by the productive imagination) in and among the specters (so that they not be things on their own), and the fact that the apprehension of empirical data is merely another word for perception, we will find that all specters and all perceptions are subject to the conditions of apperceptual unity, and that those conditions will be expressed via the productive imagination in putting specters together in various ways (via a schematic) which is a search for an objective apprehension (a recognition) from which the subjective (actual) apprehension (the perception) might be derived,* and that a recognition arises then (and only then) when the schematic corresponds to a category of pure thought. (We will follow Kant's argument in TDA II.4 by paragraph).

[* In the case of the motorbike, the objective apprehension (recognition) arose upon the discovery of the sealed tank, whereby then, in conjunction with the law of the expansion of liquids, the perception of hot weather/good performance and cold weather/bad performance could be derived. Regarding the candle, the recognition that the candle was hot (the objective apprehension being first the hot candle and then the feeling of heat) was based on a law, formulated at that moment, concerning the dissipation of qualities over space. From this the subjective apprehension of: first no heat (hand at a great distance from the candle) and gradual increase in heat (hand approaching), could be derived and explained.]

Paragraph 1. There is only a single, thoroughly inclusive and pervasive experience, and its components are the perceptions (which, in the vernacular, are themselves called experiences). These perceptions are connected in an all-encompassing, mental edifice called the empirical consciousness and form thereby a profound unity by means of connective and synthesizing concepts such as mutual causation where, for example, the parts of an engine must interact in such a way that a certain effect (called performance) is rendered. This unity reflects the notion of the TO=X, the function of which is to insure such unity not only with regard to all judgments about a given object, but also (by virtue of the depiction of nature itself as an object) with regard to all (empirical) judgments in general, i.e., about all objects.*

[* The use here of the parts of an engine to exemplify the category of reciprocity or mutual effect also serves, incidentally, as an analogy for the empirical consciousness (experience), which is an assembly of perceptions (interrelated parts) which together constitute a (mutually supportive and interlocking) whole, i.e., more than a mere conglomeration; a thesis which hearkens back to the Dissertation (II 390-391).]

Paragraph 2. These connecting concepts cannot be empirical, for, as we have established, there is always the possibility of a deviation from an empirical concept (even though it must be explained), e.g., even though the motor bike must function in a certain way, it did not on one occasion (due to a faulty tank). In other words, the empirical necessity is such that deviations can occur (although the necessity is still valid in that an explanation must be provided); but this means that the basis of this empirical necessity (that which provides this [albeit only empirical] necessity) cannot itself be empirical, for that would mean that deviations could arise and be permitted for which no explanation were required, i.e., a deviation from necessity itself (= no necessity).*

[* This is similar to Wesley's argument against Calvin alluded in an earlier footnote. If God could exclude even one person from his love, that one might be Wesley and thus Wesley's experience of a transformed heart would lose its certitude because it could then constitute a self-delusion. Thus for Wesley's certitude regarding his own relationship to God, it was necessary that the universal love of God be a first principle in his theological system.]

Paragraph 3. The means of the connection necessary to produce the comprehensive unity of empirical consciousness is the category and it serves as well for experience as for the objects of experience. Thus the objects of experience themselves are unified (from spectral data) by the same set of categories which makes possible the necessary connection (of the thusly assembled objects) which characterizes experience and which we have seen in the case of the heat of the candle flame and the gravity-fed, motorbike gas tank.

Paragraph 4. The unity of apperception, as an empirical (and self discernible) phenomenon itself, can only arise to view ("prove itself") when there is a necessitation of depictions, and this in turn is a function of a synthesis of specters in and through various modes of time. The concept of causation, for example, indicates a connection through time such that two or more depictions are unified and together make up or represent a single span of time whereby not only does each denote the other necessarily but then also in a certain order or temporal direction whereby one precedes and the other follows, i.e., it provides a universally valid determination of time.* Thus the concept of a vacuum and the law of the expansion of fluids served to necessitate the erratic performance of the motorbike, an otherwise inexplicable phenomenon in light of the general experience with bikes and engines; and this understanding in turn means that the good performance had to follow upon the hot weather, and the poor upon the cold. It was for this reason alone that the psychological "click" took place which is called a recognition, much as that which arises upon the sighting of the face in the cloud, especially after a bit of searching and trying. Thus upon the removal of the universal and absolute form of connection (through time, and which is here called causation), we would have nothing more than the (otherwise inexplicable) perception of the balky bike.** Indeed, as Kant indicates in what it is either sheer hyperbole or possibly the most provocative and profound statement in the entire Critique: without the category our lives as understanding beings would be less orderly even than a dream.

[* Such a determination of time is called an objective apprehension in contrast to the perception which is merely subjectively valid. Indeed, as we have already noted, the point of the objective apprehension is to provide a derivation for the subjective apprehension, and is what we call a recognition.]

[** Stated so here only for the sake of argument and contrast, for, as we shall shortly see, even this perception can only arise in pursuit of, and therefore as an anticipatory function of, the TO=X, and hence of the category as the means for insuring a priori the pervasive consistency called for by the concept of this object (X).]

[It might be helpful momentarily to interrupt Kant's argument in TDA II.4 and consider this statement regarding dreams. This final sentence of TDA II.4.4 actually hearkens back to TDA II.2, which is otherwise a very strange passage, even for Kant. There we are told that the law of association explains mental phenomena (much as the law of the expansion of fluids explains many physical phenomena, including the balky bike). But then, Kant goes on to say, this law is predicated on the specters actually relating in a regular sort of fashion, without which there would not be any basis for the reproductive imagination to picture something else as a result of the prompt of some object. But this object does not exist on its own, but merely as a result of a synthesis. Therefore the synthesis precedes, etc. Now (I say) without that synthesis we would presumably be in the same state as the animals. With them (again presumably) there would be no association with consciousness, i.e., where one thing stands for or represents another (= a depiction), but rather merely the substitution of one mental state by another, i.e., when A arises, then B not only follows but also annihilates A, etc., much as the common recitation of the ABC's demonstrates.* Thus there must be a preceeding consciousness, for a retention of elements and a synthesis into objects, before the possibility of a recognition of the law of association as an explanation of mental phenomena can arise, and with it any experience with that phenomenon. And thus it is that without a connective possibility for the perceptions, they would never depict objects and thus never be anything more than dispersed and independent sequences; (indeed not even that, for a sequence, i.e., the awareness of that, requires a retention which is made possible by the apperception in search of recognition [and which therefore is category-driven]); and therefore the actual sightings of which would not be nearly as orderly as dreams which are based on objects of experience.**]

Which is essentially the now proverbial situation where each of ten persons possesses (only) a different one of the ten words of a sentence, i.e., there is no unified consciousness, and thus, according to Kant, no consciousness of self.]

[** Our dreams, while often "crazy," are never wild (at least not with memory). In one of my dreams I am having trouble starting my motor bike and then notice that the tire is flat whereupon a "light goes on" and I "see" why the engine failed to start; an absurd conclusion (given an experience with a bike), but which exemplifies the surrealist state of dreams. But still I am dealing with objects even if they exhibit the sort of behavior more consistent with Alice's Wonderland. In a world of non-objects, on the other hand, where faces and smiles and whatnot appeared randomly and disjointedly, then the world becomes truly insane (per our present, rational perspective) for we would take sheer specters as things on their own, e.g., letting the size and shape of Hume's table hold as things on their own. (See the footnote on B 69.)]

Paragraph 5. Now since the category, e.g., that of causation (as our current focus), is necessary in order that there even be a (self-)discernible, empirical consciousness, which can only arise through the necessary connection of perceptions into components of objects (which are provided via the original and transcendental [though, as such, originally not discernible] apperception), and therefore since the categories are necessary for objects ever to come into view (be recognized) in and through the specters (particularly as we distinguish internal objects, e.g., imagination, from external objects, e.g., bodies),* it is obviously inane to seek the origin of the categories in any exposure to objects.

[* We must certainly imagine (via the TO=X) and then recognize an independent, external world in order ever to recognize even the least aspect of ourselves, e.g., that we sleep or daydream or overlook things, i.e., that a sought object was in a place I had surveyed earlier and I had simply not seen it during my search. See Kant's Refutation of Idealism beginning with B 274.]

But given that, still Hume raises a critical challenge: if the categories originate independently of experience and even though they may be necessary for experience to arise, by what authority can we say that all specters are subject to human experience (law making) and thus can be included (= must be includable) in that universal edifice of consciousness called experience? for it could well be that (all or, at least, some) specters might abound without being subject to assembly into objects of human recognition, i.e., objects of experience.

The categories relating to experience are applied to specters by means of rules of empirical association. One of these rules reflects causation and directs us to look in the past in order to necessitate the present.* This rule of association, which directed my search in anticipation of an explanation for the hesitation of the bike, was premised on the so-called affinity of the specters, namely that the specters were subject to laws (and were not independent things on their own) and that they (the hesitations) could be reproduced and therefore experiments and observations undertaken (such as restarting the motor bike with an eye to a careful perusal of its performance and the circumstances surrounding that, which is the very meaning of perception, i.e., that careful, perusing look which can only occur a priori, even though the data is empirical and provided a posteriori).

[* After originally perceiving a faltering of the motorbike, I racked my brain for clues as to what the problem might be. I had just filled the tank and therefore (I say, based on the empirical rule of association) I wondered if perhaps the fuel had been contaminated. I noticed the bike faltered once upon climbing a hill; could that be it? Etc. This empirical rule of association, an empirical manifestation of the category of causation, directed me in my search. Random depictions were dismissed as I looked for something which had come about such that the faltering of the bike could be associated with it for a possible connection. For example, although I will have noticed traffic control signs, still, consistent with the rule, I will have ignored them, for they would be present during good and bad performance. Thus the rule (reflecting causation) helped me decide what to consider and what to ignore, and this (relatively) a priori. This is discussed at length in the Second Analogy. Another rule of empirical association reflects community and reciprocity and is discussed in the Third Analogy.**]

[** Incidentally, it is easy and confusing to identify Hume's law of association with Kant's rule of association, the former explaining mental phenomena in the same sort of way that Newton's law of gravity explains physical phenomena, while the latter is a rule which directs investigation in search of an explanation. Thus Hume's law (as well as Newton's) would have been originally conceived as a result of an investigation utilizing Kant's rule.]

But how can such a judgment be made in advance of the data, i.e., that the specters are joined in an affinity such that there are laws of nature (making experimentation and replication possible), and that the perception in search of factors is relevant and meaningful? This is, of course, the great question of Pure Reason; Kant's answer is given in the next paragraph.

Paragraph 6. All specters, to the extent they are to represent something, i.e., to the extent that they are thought not to be things on their own, are subject to an incorporation into a single, numerically identical consciousness (for there is no other way that they might depict something [as opposed merely to being what they are, sensations, which would, at most, provide unconscious associations, i.e., upon mental state A, mental state B arises to, and A vanishes from, consciousness]). As such their apprehension is subject to the requirements of the synthesis of the unifying and incorporating apperception. This means they must be integrated into that single, empirical consciousness in accordance with the categories, for, as was established in TDA II.4.4, the category is the means of a universal time determination or connection (such that the concept of a single, all encompassing span of time arises to include all spectral existence, and which represents objective reality). And therefore and in this way the specters are subject to the categories as the conditions of an integrated and singular, empirical consciousness, i.e., to laws which are sought out by the productive imagination (under the auspices, as it were, of these categories) in order to provide a universality to connection, e.g., the law of association or the law of the expansion of fluids, for it is only by means of laws that the objective apprehension and universal time determination can be expressed, from which the perception is then derived (= explained as occurring under subjectively valid conditions), which is the very hallmark of recognition, e.g., due to the law of the elasticity of fluids and the happenstance of the sealed fuel tank, the hesitation of the bike in cool weather (a perception) was inevitable, and thus explained.

What would be the situation if I did not preceedingly insist upon an integration of the specters with my empirical consciousness (as a systematic edifice)?* If I did not preceedingly insist upon a reason (explanation) for the hesitation of the bike, then I would accept its hesitation into the same general and empirical consciousness with a preceding recognition concerning the nature of motorbikes, namely that they function in a certain way. And this would constitute a conflict in my consciousness, namely that bikes must perform in a certain way and that this bike does not perform in that way.** This would be similar to a situation where my consciousness were composed of fight songs of two competing ball teams which were in present conflict, and upon hearing either team's song begin, I would join in lustily and not be conscious of singing in conflict with what I had just sung earlier. Or suppose the expression "log floats" brought to mind images of floating logs, and the expression "log sinks" produced the memory of a (waterlogged) log on the bottom of a lake, and I would assert the validity of each expression alternatingly and without any appreciation of a conflict. Such a state would constitute complete, intellectual fragmentation much, perhaps, as some who are called mentally limited and who can focus on one thing, but not relate it to something else; hence, a complete lack of even the possibility of any mental conflict.** Such a split consciousness is a thorough contradiction because the only way that the "my" can arise to be a part of a meaningful "my perception" is for there to be a thoroughly unified and singular consciousness.

[* This question is actually treated in this fashion only in TDA III.7-11.]

[** Or, and especially originally before any recognition, I would assemble its inexplicable behavior with equally inexplicable behaviors of other specters in disjointed memories.]

The consequence of this a priori insistence upon associability (connectability) is exemplified by what did in fact happen with me in the case of the hesitating bike, for there the perceptions (of the hesitation and surrounding circumstances) were considered merely a problem awaiting a solution (which is patently predicated on the concept of an orderly world, i.e., one which makes sense, which is an expression of the TO=X applied to a global object [= nature]); but in no case was there any even apparent integration of a sheer perception into an empirical consciousness (composed of recognitions).* And thusly are all specters subject to the category, i.e., by being withheld from integration into the general consciousness, called experience, until such a necessitation (and universal connection) is discovered, i.e., until the objective apprehension is discerned, which therefore is presupposed (as a possibility) and to the discovery of which the perception is originally undertaken and directed, and therefore to which it is subject.**

[* Indeed, the first awareness of a possibility of a problem was thought to be possibly a fluke (happenstance) and called for a careful focus on the subsequent performance of the bike, in which case the perception of the problem, as I (a being of understanding) actually must consider it, first arose.]

[** The fact that the actual performance of the bike conflicted with the (conceptually) required performance should not be allowed to obscure the role of the category. Its function is original and efficacious even before a perception is seen as a problem, i.e., before recognitions have been established such that a possible conflict might then arise; for a perception is still not a recognition until it has been subsumed under a category such that a unified (TO=X mandated and schematically expressed) time is attained. Thus the unity is original (albeit only formal) and merely maintained (empirically).]

Paragraph 7. The lynch pin to all this is the realization that the specter is not a thing on its own but merely a play of the depictionary capacity of the mind. Thus for any object to arise to view, e.g., Hume's unvarying table or the constantly hot candle or the properly functioning bike, a synthesis is required. Since all specters are considered to manifest objects (and not rather to be things on their own),* there is ultimately only one object, in pursuit of which the human is constantly engaged, namely nature (= universal order, or "everything makes sense"), and it is the attainment of the recognition of this object that the understanding is dedicated (and perceptions, i.e., careful, second looks at data, are sought and are even possible).{FN 70}

[* This statement, I suppose, is the highest in human cognition, for based upon it all specters are to represent some object and thus be subject to the unifying and transcendental role of the apperception (expressed by TDA II.4.6.1), namely that all specters are to be included in the empirical consciousness, i.e., as objects.]

[** Robert Paul Wolff expresses concern (p. 163) that Kant overstates his case by asserting that all specters are connected (an assertion Kant modifies, but retains, in TDA III.11). But this concern is unwarranted, in my opinion, for it is only under such an assumption that I can be certain that any given specter is subject to the affinity and thus to investigation via experimentation (the "Wesley argument"). The envisagement presents all tentative configurations to which then the understanding can be applied if there is any curiosity. To assume that everything is connected does not mean that I set off on a rampage, as it were, to discover the connection of all specters at once.]

And thusly do we have Kant's answer to the question concerning the possibility of judgments in advance of the spectral data which make up the content or material of those judgments: such judgments (as expressions of the category) are necessary in order that even the first perception of the spectral data (the so-called second look) can be made, for the very raison d'être of the perception itself is to facilitate these judgments and to make them possible.

Brief Summary and Overview of the Text of TDA II.4

In TDA II.1 - 3 Kant presents the concept of the object and its (mental) formation and recognition, i.e., the apprehension, retention and unification of a tentative multiplicity which then renders a necessitation of the multiplicity and a determined envisagement (sighting) of the (unifying) object in space and time. In TDA II.4.1 & 2, he gives briefly the concept of experience with the object, i.e., perceptions of diverse objects which are necessitated with the same forcefulness as the "welding" of the pre-object spectral data into objects (as just stated). In TDA II.4.3 Kant identifies the category as the condition for experience with objects as well as the condition for the very objects themselves of experience. In TDA II.4.4 we learn that the category is the only means of providing the universality and necessity which are expressed relative to the objects (by the concept) and to the experience (by means of laws), and which exemplify and represent a universal, cohesive, empirical consciousness, i.e., that the category provides a universal (and thus also necessary) connection such that all objects, e.g., tables, are constituted in a certain way and also behave in a certain way (in accordance with certain laws). In TDA II.4.5 we see that these categories cannot be derived from experience and then, due to that very fact, i.e., that they are independent of experience, we must face Hume's question as to how they then can apply to all objects of the senses (the specters) in advance. The solution to this problem Kant gives in TDA II.4.6: the apprehension of the spectral data is the only means for the incorporation of that data into the (single, unified, empirical) consciousness whereby alone a specter can objectively depict something rather than be a thing on its own; and therefore, since all specters are to be considered as mere depictions (and thereby enabling us to avoid the illusion and absurdities of the alternative [Hume's table itself getting larger and smaller]), all specters must be incorporated (or incorporable) into the consciousness and therefore via the apprehension and hence thereby be subject to the conditions of an objective apprehension (recognition), for the sake of which, and in pursuit of which, the perception first arises as a (merely) preliminary step. Finally, in TDA II.4.7, Kant reiterates that the problem really is how to assign objects to sheer specters, and that the ultimate object for which all perception is directed as means is nature, a systematic edifice (as consciousness) of absolutely cohesive elements (perceptions).

Perspective

In very general terms then (and looking for historical perspective), in the Dissertation Kant conceived of a mental process such that intuited, pre-existent objects were mentally placed in a system (nature) according to laws provided by the intellect and reflecting objective reality. In Pure Reason by having the intellect play the additional and critical part in the very formation of the objects themselves, Kant is able to retain that Dissertation role for the intellect as the agent for placing these objects into a system. In this way Kant established a bond between the intellect and experience (which was lacking in the earlier work) by subjecting all objects of the senses to the combinatory action of the intellect on the specters (the pre-objects [elements] actually given in and through the senses) through which Hume's objects first arose as objects of experience). But in so doing Kant had to eliminate the link between the intellect and that so-called ultimate reality and instead was forced to constrain the intellect to spectral data. Thus in order to establish an intellectual connection with an empirical thing on its own (a necessary aspect of experience and one part of his Dissertation thesis [though inadequately conceived at that time]) Kant had to give up all contact with a transcendental thing on its own (the other part of the Dissertation).

Conclusion

In a final recapitulation I would like to speculate very briefly as to the experiments which Hume's Adam might have undertaken in order to determine that Hume's table does not change size with the changes in the perspective of the viewer. In the first place I note that Adam originally will have been able to see himself as here and the table as there, a spatial envisagement (which is entirely independent of the intellect). He will then have carefully noted the regularity in the change in size and shape of the table per the change in his distance from the table (also an envisagement). [This perception (= consciously apprehended envisagement) is curious and singular, and the capacity for which may belong to the human alone.] To model this situation, i.e., the spatial positions of himself and the table (which thus far are merely a here and a there), Adam will let his two hands stand for that here and there, respectively, in the one, all encompassing space, and then, beginning with the hands outstretched, will slowly bring each in turn to his eye (the other remains outstretched) while being aware of the gradual change in size and the relationship of that change to the distance covered,* and mentally take the place of each in turn as a "viewer" of the other (looking through his fingers of the hand nearest his eye), and will conceive of the object, i.e., the perceiver and the perceived and the perception in space, and the constancy in size of the objects, from which then the specters and perception can be derived. The recognition of this constancy, and indeed even the perception itself leading to this recognition, will have been predicated upon a notion of the TO=X (a figment of the productive imagination of the human), which then is merely depicted or modeled by the specters according to a human world-envisagement/concept, and specifically in this case to the category of substance with its particular schema for the world, namely that the quantity of matter is neither increased nor decreased (the first of Kant's three analogies of experience). The result of the experiment is the concept of an object in space in general which retains its shape and size regardless of the perspective of the viewer and merely looks different depending upon that perspective.**

[* Perhaps Adam will also note the lack of sensation related to the change in (apparent) size, which might be correlated to an earlier experiment in which he noticed the relationship of visual change and difference in feeling related to balling up his hand into a fist and then extending.]

[** David Hume should have no qualms regarding this experiment, for its conclusion is not derived from the cited principle of the constancy of the quantity of matter per se (and thus is not dependent upon any rationalist concept [an anathema to Hume {as well as to Kant}]), but rather is dependent upon that principle only to the extent of the prompt to the experiment (just hypothesized) whereby then the conclusion is achieved experientially.]

[* It would seem then that the two most fundamental recognitions which we humans bring a priori to experience are (1) that the things about us are specters (functions of our own envisagement) and not things on their own; and (2) that all things make sense (that sense being expressed for us via the categories as the form of the apperception and its pervasive unity, and thereby the prompt for experiments and the "second look" perceptions).]

A P P E N D I X

Anyone familiar with Kant's thesis and logic concerning the TO=X and with David Hume's own brilliant insights into the problem of human knowledge, must wonder how it is that the Scotsman did not rather write the Critique of Pure Reason in the place of Kant and instead of turning to skepticism. Kant suggested that the answer is to be found in Hume's particular concept of mathematics. I wonder if, in Kant's opinion, Hume were not too much influenced by the rationalists' notion that mathematics were a purely analytical science when in fact it was dependent upon a pure envisagement, one somewhat like that of the pantomimic circle mentioned earlier in this article. A consideration of this hypothesis may be helpful in understanding the different routes taken, respectively, by Hume and Kant.*

[* This entire section on mathematics has been superceded by a more recent work (on the Object of Mathematics) of an essay entitled Hume's Two Errors; although this appendix may serve in facilitating the Axioms of Envisagement section in Pure Reason.]

In a simplistic way the difference between Hume and Kant with regard to mathematics can be expressed in terms of grammar, namely: does or do 7 and 5 make 12? If the former (Hume's thinking), then 7 and 5 is a singularity and would be expressed algebraically by (7+5). In this case there is no difference between (7+5), (12), (12+0), (-0+12), ((4^2)-4), (7+8-3) and so one without limit. And so then the (12) is neither more nor less significant or meaningful than any other of an infinite count of expressions. Now while this is a rationalist approach, i.e., a system of sheer definitions or synonyms,* it has a certain affinity with the object of the empiricist, and specifically in that mode where a potentially infinite number of mental pictures would be indiscriminately acceptable as illustrations or instances of a given concept or term. For example, the expression "my table" could refer to a host of discrete depictions which we otherwise associate with the term table (my own) and different perspectives of sighting, e.g., close up in bright light, further away in dim light, very far away, etc. In this case, while no contradiction is obvious, it is equally not obvious that these depictions are free of a contradiction, for it might be that some depictions would be illustrations not only of "my table" but of "your table" where these two latter terms are mutually exclusive.**

[* Or where 12 is more or less a nickname for (7+5) or (15-3), etc.]

[** This description of the object of the empiricist, i.e., as a term referring indiscriminately to a host of diverse and discrete pictures, is probably a more accurate representation of the empiricist position regarding concepts than is the notion of the mean or average used in the body of this essay (although the result, from a Kantian standpoint, will be the same).]

Now while mathematics supposedly has an advantage over the empiricist's object, namely that by means of certain definitions, e.g., (11+1), and certain axioms, e.g., (a+b) = (b+a),* any expression, e.g., (22), can be converted into something directly comparable with (12), e.g, (12+10), whereby a determination of equivalency can be made by means of an arbitrarily given rule, i.e., (12) and any expression other than (+0) or (-0) is not (12), still since this is all entirely arbitrary and without the benefit of the focus of an object, the science will have devolved into a semi-metaphysics which is an equally pure "science" made up of sheer definitions and rendering such as, e.g., body and spirit are two, and where it is never certain that a contradiction is not lurking around the next corner or that a mistake in reasoning and calculation has not already been made.**

[* Which is always correct, as opposed to (a-b) = (b-a) which is only correct when a=b.]

[** At the risk of error in speaking beyond my ken, I understand that the non-Euclidian geometries have been proven to be as internally consistent as Euclid's own, but that no proof concerning the internal consistency of the latter has been presented, which was never in question by Kant, for whom there is always an object, space (a pure or sheer envisagement), to which Euclid's geometry is referred and which guarantees its continuing advancement without any contradiction (even if not its unique status as the geometry; but still that upon which any other geometry might be validated).]

With the second understanding of the meaning of 7 and 5, namely as a multiplicity in search of a unification (Kant's position), the matter is considerably different and eased. For now there is an object to which the 7 and the 5 refer as a unity, namely a 12, and this object can be sighted with the same precision as the circle was sighted in the machinations of the pantomimic drawing finger, and indeed in the same way, for the same finger which drew the circle would be seen now differently (a different envisagement), namely as one of the elements making up (or counting to) the five and which are being added to the (mental) seven in order to find and illustrate the object, which is merely called "twelve." And since the twelve is simply a way of looking at the fingers, and indeed at the spatial position assumed by the fingers (and thus merely delineated or pointed to by them), the certification of the twelve occurs by means of a "peek" at the object, to be sure, but not an empirical peek, and thus the object and thereby also mathematics remain entirely free of any "contamination" by empirical data.* **

[* Which is not all that different from Kant's thinking as expressed in the Dissertation. There the senses presented the objects in an intuition which was subsequently cleared of all empirical aspects such that a pure (cleansed) intuition remained, upon which then mathematical machinations might then be based.]

[** For a more recent consideration of the role of the pure envisagement in mathematics see "Seven Plus Five."]

Had Hume possessed this latter view of mathematics, he would not have failed to see that the provision of the object in the case of the twelve for the unification of the seven and the five were no different, conceptually, than the provision of the object (the table) to the diverse specters depicting the table, and that the mind produced both in the same way and indeed for the same purpose, i.e., for the certification of the data and its accuracy by means of a reference to something which were independent of the viewer, namely the object. Thus (as Kant is perhaps contending) due to a lack of a particular understanding and view of mathematics, i.e., because he saw no need for an object, Hume failed to see the connection between mathematics and the empirical sciences and thereby missed the opportunity of being the first to conceive of the Critique of Pure Reason.

In a related matter, the example just given, i.e., of the fingers standing for spaces which, in turn, render an object for the unification of 7 and 5, also illustrates the need for a category for the production of that object (per the Axioms of Envisagement [B 202]). The multiplicity of the object (the 12 spaces) is pure and given entirely a priori, but the prompt to the summation of this multiplicity is provided by the category of total (and an axiom for the accumulation of a homogeneous quantity) in precisely the same way as with the summation of the pure multiplicity (the path) of the pantomimic circle.* Without this we would be left in the position of Hobbes' village idiot who, upon hearing the clock strike three, could only say, though with perfect accuracy, "One, one, one."**

[* In what may seem like a sleight of hand, Kant contends (TDB 26.3) that the recognition of space and time as infinite givens requires an apprehension (and thus the understanding for the determination of the inner sense as in TDA II.1), but not a summation (and thus neither category nor axiom). Presumably the specifics of a given here and there precede as a recognition of spatial positions, and then subsequently are noticed as already being within the all-engulfing space; such that only a connection of the two positions, e.g., a line between them, would require a summation in order for a determined space to arise to view. This seems valid enough: I can see two things in space, or I can also "see" the line joining them as a pantomimic object.]

[** Leviathan, Part I, Chapter IV, Paragraph 10.]

Now we turn to see how our understanding of the TO=X might facilitate a grasp of the Third Antinomy of the Critique of Pure Reason where Kant seeks to show that the concept of nature and that of freedom are not incompatible (without, however, wanting to establish there even the possibility of freedom). Now it is necessary to provide the object to the specters in order to transform specters from things on their own into objects of experience (views and examples of these objects) and thereby to make a real, interactive nature possible. But given this transformation, i.e., this utilization of the TO=X in order to have nature and to have experience within that nature, it follows that it would be impossible for an object that were necessitated according to the laws of nature to be free, i.e., to act according to an internal volition which were independent of the stimulus of the specters, and which is the very hallmark of freedom. Thus a dichotomy of freedom and nature arises. But now we see that since the object of experience (really only a schema invented by our minds for the purpose of having experience) is not a thing on its own but merely a depiction, it is entirely acceptable (particularly when admitting it were merely a fiction) to think of it also--but in a different context--as a thing on its own. Thus a leaf which falls is found to be necessitated according to laws of gravity; and this constitutes an experience with the leaf. But given this, we are still free to think about the leaf differently and to make up a story such that the leaf also wants to fall. And this would be entirely consistent with (though not derivable from) the law of nature, i.e., that whatever nature required, the leaf also happened to want.*

[* This concept is very close to Leibniz's notion of the pre-established harmony where objects did not really impinge upon one another, but rather where each went its own way according to its own internal makeup. This internal constitution was a production of God at the creation of the object (the world) who also insured that the "desires" of any given object would correspond with those of every other object. As an (overly simplified) example, if the leaf happened to want to fall at a certain time, then at the same time the wind would also want to blow and the shadow of the leaf would want to follow a path which, to an external observer, would correspond perfectly to any shadow that were cast by the falling leaf; and if God should decide to annihilate the leaf, a separate act of annihilation would be necessary to eradicate the shadows "cast" by that leaf.**]

[** One of the very interesting aspects of the Leibnizian hypothesis is that it provides alternative ways of thinking about things, and thus a different envisagement, and therefore, finally, that there is no necessity that animals or other beings consider things the same way that humans do (as my dog, for example and per an earlier footnote, may have seen the disciplining newspaper differently than I did). The example here of the shadow is also reminiscent of the storybook character, Peter Pan, whose shadow at one point becomes detached and is found rolled up in a chest of drawers, a predicament which does not at all offend the sensibilities of children of a very young age. (Incidentally the determination of the necessity of one's shadow or mirror reflection is an early experiment which, for some reason, most persons are able to remember, at least vaguely, well into adulthood.)]

Now there is no reason to suppose that a leaf might actually want to do anything; and thus to assert such seriously is to leave oneself open to ridicule (which Leibniz perhaps occasionally did). But with regard to the human this is a different matter, for here we see a capacity of intelligence and of functioning and behaving in accordance with ideas and thereby, occasionally, in opposition to the drives of the sense. Christians, for example, may have an idea of a world which functions according to a law of selfless love and some may consciously weigh all their actions in light of that law (of freedom) and endeavor to act always in accordance with that law (and thereby can consider themselves to be a part of that vastly different world). Thus while all their actions can be ascribed to their nature and how they perceive the world (that they, for example, may be considered by external observers as believing that by their actions and intentions conformable to their idea they will deserve to live in such a world and that there is a moral agent who ultimately renders to each person according to his or her desserts), they also at the same time (according to their internal state and their understanding) function in accordance with sheer ideas and therefore it can be imagined that what they do they do freely (imagined, but not proven, for any proof of this must await Practical Reason).

Now finally, and due to the extreme difficulty that most students have with the notion of the thing on its own (das Ding an sich), I would like to offer a further consideration of this matter. When Ptolemy lifted his eyes to the heavens he saw the same spectral data as did Copernicus, Kepler and Newton. But for his part and for several, weighty reasons Ptolemy recognized an unmoving earth and a moving heavens and that concept (or, more precisely, its schema for empirical application) became the thing on its own, i.e., what (to him) was "really there;" and thus any deviations from that required an explanation. He was hard pressed in this endeavor and invented all sorts of strange objects (movements and paths) to be represented by the spectral data given by Mercury, Mars, etc. Now there was really no difference between the spectacle of the sky as a thing on its own and Hume's table as a thing on its own; in both cases the term is of merely empirical usage and denotes what we recognize to be actual such that the specters we actually have are views of that. The recognition renders (and requires) a thing on its own, empirically speaking, and this thing becomes the basis for our learning about it and the focus for all judgments, for they must cohere since they are made about the identical object (via the TO=X). Thus the night sky is not a transcendental, but rather only an empirical, thing on its own, and therefore was not something that Ptolemy might intuit, but rather was merely that which he dreamed up in order to fix the specters as views.* To this extent then Ptolemy and Copernicus agreed as scientists, namely that the specter was not a thing on its own, and rather only represented a something to a human viewer in space and time. This knowledge was transcendental. In pursuit of this transcendentally predicated thing on its own, they conceived of it differently, and each obtained (or provided) his own, respective, empirical thing on its own whereof the specters became views. So the transcendental object means: the specter is not a thing on its own as it is, but rather that there is an empirical thing on its own whereof the specter is merely a view. And thus we come to common, ordinary speech, e.g., that is the table that I see, only I am looking at it from a distance of ten meters (and hence, strictly speaking, and as everyone knows, it is really only a particular view of the table; or rather we can say: it is the table viewed from ten meters).

[* The Semitic people, it seems, considered the sky as a hard, even metallic dome (firmament) which could conceivably be penetrated by a sufficiently high building (a Tower of Babel), and which covered the plane of the earth and with that made up a large room which could be filled with water (a Great Flood). (See Genesis, The New Oxford Annotated Bible, 1977).]

Kant's Genius

Kant found science caught between two warring sides, the empiricists and the rationalists, but instead of choosing either one of these to champion, he raised a banner which incorporated the standards of each and thus sought reconciliation of both rather than the capitulation of either. All knowledge arises through experience, but not all comes from experience, for the mind itself produces the form of experience as well as that of the object of experience (but not the content of either, which is entirely empirical). Essentially then, in the Critique Kant took his original compromise of the Dissertation (where he attempted a reconciliation of empirical and rational sources of knowledge