Notice: This page represents a project in development, and perhaps a very slow development at that; and does not yet represent a settled opinion as of 4/12/03. It is more a musing and wondering at this stage. For more current essays see Kant.
5/23/97 Friday 6:41 AM It might be productive to utilize the split finger syndrome in order to exemplify and demonstrate the three conceptions of space, i.e., that of Newton, Leibniz and Kant.
According to Newton, there is a uniform, three-dimensioned space in which all things can be located (problems arise, of course, when speaking of spirits like the soul and God). The sightings of our eye are a distortion of this space.
This is the very common-sense notion of space that all persons grow up with. The distortion of the eyes makes us see further removed objects as smaller, but that is a function of our human make up. Actually they do not get smaller or change size at all.
Now in explaining the spit finger, we must understand that there is a brain in the human which unifies the sensation into a single whole. Thus each eye sees a slightly different view and these two views are molded into one by the brain. Now the spatial point of unification is called the focal point, and anything apart from this point is imperfectly molded. Therefore you can notice that as you look through your finger touching your nose to distance objects, the finger splits and the distance objects are clear; and if you look to the finger, it tends to unify again and the distant objects split into two.
Now Leibniz will not accept this common-sense view for it, in his opinion (and like many phenomena), is an illusion that can capture the unwary and those who leap for the obvious.
The stick appears broken in the water; but it is not. The finger appears split; but it is not.
What happens is this: we notice the things about us and are unable to distinctly cognize them, for while we actually do in fact have a concept of each thing before our eye, the correlation between this concept and the sighting is not definite and so the concept is not clearly in view. In order to express our sightings on a tentative basis we dream up relationships among them which we call space and time. These serve us until we are able to identify the object more definitely, in which case we dispense with the terms entirely. For example, once I know that some object is a table, I can quite speaking of "that thing over there" and instead speak of "the table". Much of our confusion is merely trying to align the codes (languages of a particular group) with the sightings.
The validity of geometry, as a science of space, is tenuous (according to the Leibnizian conception [and will be dependent upon the concept of adequate reason]), for since space is merely an abstracted relationship, dependent as such upon real things, and since these real things cannot be anticipated, except merely to the extent that everything will be rational and follow reasons, we cannot say for sure what the next objects will present to us. For indeed the miracles of God must also be included in the over all conception of the world. Therefore we cannot speak with absolute assurance about the phenomena of the world, although we most surely can of the total existence of all things. I.e., the explanation of the phenomena of the world is dependent upon the conception of the whole, including the souls, God and his miracles, such that the phenomena will be rationally deduced from that conception and therefore what are now seen as miracles will make perfect sense and fit in perfectly.
Space then (and time, too) vanish into imagination, i.e., it is something we dream up in order to explain the diverse pictures that actually do exist like, for example, the split finger. The split finger is a phenomenon and is explained by the merging of two view points by a single soul, to which both viewpoints belongs.
Not only is the split finger an illusion, but all that is spied in space and time is an illusion, i.e., as given, for things do not change as they seem to do when we look at them from different perspectives.
Leibniz considered that a city, for example, existed in such diversity that it could be called infinite. There was not a thing called the city, but merely a myriad count of diverse depictions of the city, from within a house in the city, to the street, to the inside view of the walls to the external view and so on to a distance of one mile and then 100,000,000 miles, etc. All of these views together constitute the city which then is nothing more than all of these views. And so there is nothing called the city on its own at all, and so Newton is totally confused in his thinking. Each point in space can be thought of as a monad, and my own perception of the city, whatever it may be, arises when the soul called Philip arises within a certain monad.
In this way each monad is conceived to contained a view of all the world and all existence, and reflects the diversity in different ways at different times. For example when I go across the room, we are really speaking of a diversity of monads in a pattern such that each one in the line of "my path" successively "broadcasts" or amplifies, as it were, the body and soul of Philip. The consciousness of the "I" called Philip arises in every one of the monads on that path, but successively, so that Philip is aware of moving across as space, although it is really merely through a succession of diverse monads.
The conception is fantastic, but irrefutable (at least it seemed so for a while).
Space and time melt away into nothing and there arises in their place a fantastic world of coordinated monads, all serving to exemplify the glory of God, their creator and "musical" composer and conductor.
Newton's conception then becomes merely a shorthand for dealing with the realities of human perception, but without any more validity than that. That the world seems to be so made up is due entirely to the human mind's tendency to find abbreviations for complex matters. When the individual monad called the soul is finally able to see without the interference of sense organs (with their split fingers and there more and less [all of which are illusions and confusions]), then we shall see that Newton's conception was a toy.
Enter now Immanuel Kant. Kant starts off, of course, as a Newtonian, for this is the way the world looks on a common sense level. But then, under the influence of the metaphysically oriented teachers of the University of Koenigsberg, Kant becomes a Leibnizian. It is far more appealing to the metaphysician in the soul of Kant. But then comes Kant's great discovery of the Achilles' heel of the Leibnizian conception.
Kant's discovery: if space is merely an illusion, as asserted by Leibniz, i.e., an hallucination which will vanish over time, then that means that the totally of spatial relationships will be reduced to relationships among the monads entirely and without exception. But then this means that the description of the left and right hands will draw the identical object in space, i.e., a hand (which will in fact be a left or a right hand, but which will have no contrast in space in order for the difference to arise to view and cognition.) Now Leibniz, as intelligent and creative as he was [and in this regard he is probably the greatest imagination to have come to the human race (at least preceding Kant)], this great man missed this point because he thought that the left and right hands could be distinguished well enough merely as things, i.e., via feelings and coloration, etc. And he did not stop to think of two ideal hands or of two spherical triangles, the parts of each being perfectly interchangeable with the parts of the others, and yet still being incongruent. It is upon this that the Leibnizian conception topples and finally crashes as the mere figment of the human imagination.
Therefore, Kant concludes (a bit hastily), the Newtonian conception is right, for it is only in Newton's space that this distinction, which is most real and veridical, can be noticed.
But then the fertile mind of Kant is only really awakened. He turns now his attention to the Newtonian conception and undertakes an investigation which is quite remarkable and promises to provide the key to the understanding of human reason. He assumes that Newton's conception is right. But then he wonders how we would ever have come to the notion of this conception in that case, for, as it will seem to him, if Newton were correct, then we would never have come to the notion that Hume's table, as that mighty imagination himself confesses, did not change shape and size with the distance from the viewer, for that is the plain and immediate teaching of the senses.
Kant then realizes that for Newton's conception to enter the mind of man, it would have to do so by some sort of an intuition, i.e., an intellectual sighting. But this is lacking, of course, for all our sighting (Anschauung) is sensitive and we have no intuition.
The solution (and this is Kant's theory of human vision) is a sheer envisagement, much as when we spy a face in a cloud or "see" a circle drawn in mid air or project some lines into a 3-dimensioned, spatial object (like the cubes we often draw in our doodlings). We simply dream up an object called space, and we do it by conceiving a space such that our own sighting of space is merely a view point within that space, and thus that the sightings of other persons would also be a viewpoint with in that space, and thereby are able to produce a coordinated world, where it makes sense to distinguish between my right and your right and the right (there the latter is understood as a temporary definition of an area in the space, e.g., when we speak of the window side of a room, or the ocean side of the island).
Given now Kant's conception, it is easy to see why Newton's conception is so appealing, for it is that which we necessarily assume in order that our own sightings be conceived of as in space, i.e., that our sightings be a particular view point in that space, so that now you, at a distance, are not small, but merely look small to me in the same way that I can understand that I look small to you, and likewise while you are to my right, I am too your left (or your right, or your front, etc., depending on how you are "facing").
And likewise, given the Newtonian conception (arising from Kant's conception of the envisagement), it is easy to see why Leibniz would have such a problem with it, for not being aware of Kant's theory, Leibniz can only see that Newton would be confused in thinking as he does, due primarily to the problems with souls and spirits (that was so important to Leibniz but much less so to Newton). Kant's solution will be satisfactory to Leibniz, however, for by relegating space (and time) also to sheer envisagements, the world of the intellect, i.e., that of spirits, is excluded from all inferences from the world of the senses, and so the intellect is free to think things and beings without reference and limitations of space and time.
Following here are earlier drafts on this essay.
5/20/97 Tuesday 5:36 AM Three possibilities concerning the status of space and time: 1. they are real things (Newton); 2. they are merely our imagination abstracted from real things (Leibniz); 3. they are the form of our looking (Kant).
1. Real things. According to Newton then space and time are real things, even though they themselves are nothing, but they serve as "containers" for all real things. The primary difficulty with this conception arises later when we want to think about things on their own and not as objects of human perception, e.g., the locations of the soul, heaven, God. The primary advantage is the certitude we can have of mathematics, especially geometry and mechanics.
2. Abstracted from real things. According to Leibniz, on the other hand, space and time are merely our imagination which we abstract from real things, e.g., that the table is in front of the chair, etc. The primary difficulty lies in the inability to speak universally of geometry, for the plain figures of that science, for example (and since space is merely abstracted from real things, and who can speak in advance of real things), might be drawn in a space where the angles do not sum to 180 degrees. The advantage is when we leave the world of specters (empirical objects of human perception) and soar in the world of the intelligible, e.g., in the moral, we find no problems with regard to space and time, since they are not real on their own at all.
So the two fundamental conceptions: space and time are real things versus: space and time are merely depictions, and nothing on their own at all.
3. Form of human sighting. According to Kant, space and time are merely the way we see things, e.g., the finger which splits when it touches the nose is conceived of as being in a space which is strictly and entirely in the mind but which can also be sighted as a view point in an all encompassing space (and time also). The primary difficulty in this is acceptance of this fact, that space and time are merely envisagements and the form of human envisagement in general, and that what we see before our eyes is not actually in space and time in that way on their own at all, but only in our mind (and which becomes clear only when we utilize some example such as the split finger). The primary advantage is that both of the other two can be explained as human phenomena, i.e., the belief in Newton's space and time (which are the time and space which are conceived to be such that the actually split-finger sort of sightings will make sense and can be derived from that); and the belief in Leibniz's space and time (which are merely a listing of the infinite relationship sighted, e.g., the chair is behind the table, and in front of the wall, and 14 feet away from the tree in the front yard, and 27 miles from downtown, etc. ad infinitum).
5:54 AM Leibniz's system seeks to imagine some sort of relationship between two objects and calls that time and space, e.g., the "old" table and the "new" table are really two objects in a relationship of time where the latter precedes the former, and where, also for example, the table "here" and the table "there" are two objects in a relationship of space, but where neither is earlier than the other, and for which reason (in the Leibniz system) they are called simultaneous. [And so simultaneity is, for Leibniz, merely a relationship which is not successive, whatever that might mean, i.e., there is a real relationship here, but which is not successive, and for lack of a better word we dream up "simultaneous" to equal "not successive, but still real".
6:02 AM Further note: Newton's system seems the more plausible with regard to science and understanding, for the envisagement is such that the objects that are sighted in time and space are really so sighted, but only that the space and time are within the mind and are then conceived of as being viewpoints of the actual, all-encompassing time and space.
In other words, it is easy to see how Newton came to his conception, for it is the common conception of mans everywhere.
With Leibniz the situation is different. He, too, sees things in a space and time which are within the mind. He knows that no space and time can exist in the way sighted, where objects themselves get bigger and smaller as they change their relationship to the viewer, and so he ascribes that to his imagination, i.e., that it is strictly in the mind and that the objects do not really so change. Therefore time and space are a bit illusory, and therefore they are the product of our imagination as it seeks to order things. The ordering is space and time.
It is also easy to see how Leibniz comes to his conception, for it is the view of the metaphysician and not commonplace at all. For the metaphysician time and space are figments of our imagination as we seek to order actual things, and once we fully understand and have order these things, time and space will vanish from our vocabularies as without reference of any kind. The table exists, and the perceiver exists, but the relationship of table and perceiver, e.g., of two feet distance, has not real existence, but is merely imaginary and will not even be conceived of when the objects are fully understood and the world whole grasped.
6:11 AM What then is the struggle with regard to the antinomy? It is between understanding and reasoning within the Newtonian framework (the common place conception), and the solution arises through the Kantian conception.
So we conceive of a Newtonian world and find therein a struggle between understanding and reasoning; and the solution is given via the Kantian conception where time and space are merely sightings whose total validity are limited to things spectral.
The Third Antinomy:
[6:41 AM
7:51 AM Now to tie this back to the original discussion of Leibniz and Newton on space and time, I think that the antinomy arises only for Newton and not for Leibniz, for Leibniz considers the spectral world is somewhat of an illusion (it being merely a viewpoint and not to be taken for a thing on its own), and therefore there is no reason to think that the man is not functioning independently on his own, for, according to my understanding of Leibniz, the monads have no contact with each other anyway and so each is merely reflecting the others in its own way, and so there is no reason why the man is not entirely independent in his actions and therefore responsible for them in their entirety.
So the problem of the antinomy arises only according to the Newtonian view of space and time, namely that all things are in space and time and that therefore all things are determined by space and time. This antinomy is then solved by virtue of the fact that time and space are found to actually be merely envisagements.*
[*The most emphatic and dramatic example of which, perhaps, is the split-finger syndrome, where we clearly see that the space (and time) of our sightings is entirely within us, and that we then actually and actively conceive of a space which is objective (and Newtonian in "feeling") such that what we see is merely a perspective or viewpoint within that space.**
[** Leibniz then, in contrast, sees only the viewpoints and realizes that the space actually conceived of is merely the imagination (a rather bold and insightful play on the part of Leibniz) and that the real space, for all practical purposes, is the subjective (split-finger) space (or really the space/sightings of each eye, which are melded together into an illusionary space {where the split finger actually arises to view}. Thus Leibniz makes a wonderful and (almost) perfect leap over Newton and is left with a single fault: a real space must be presupposed in order to make sense of the terms "left" and "right" with regard to the hands. This is the key discovery that led Kant first to Newton and then finally to transcendental idealism.]
[8:09 AM
To spy a footprint! now that's a task. I am suppose to make a connection between the bottom of a bear's foot, let us say, and a bit of earth. Now that is a difficult connection to make, especially if you cannot first notice the pattern, for that is the give away.
7:30 PM Now what do I have to go on? the color is probably different, and anyway I would want to get stuck on the color.
Suppose a person, in learning what "brown" meant, found himself staring at a brownness as though it were a very thin, but still very real something, much as though he should think that the rainbow were really out in Newton's objective space, for it is not there at all, but rather resides in the ball of each eye, and then is melded into who Leibniz would call an imagination, i.e., as though there really were a world that looked like that, with the split fingers and all that. It is pure illusion (I am sure he would say) and absurd to consider it otherwise.
Newton is absurd, I guess Leibniz is saying, because Newton is imagining something to correspond to that, but that is pure imagination, and it were possible to look at it as a cartoon character might, namely that things really do come into and go out of existence, and that things do indeed get larger and smaller on their own, and the meaning of such things as "distance from you" are simply absurd sounds with no referral, and whereto the student would merely look at you and shake his head in wonderment. That proves that it is an illusion. Leibniz must be telling Newton.
This blows Kant's mind, of course, and Leibniz has seen another way of looking at the identical reality that Newton is looking at, at least to this extent that they both saw themselves as right and the other as wrong. [Thus was Kant so interested in Leibniz's New Essays (a fascinating book) when it finally came out later after Leibniz's death.
Let's see: Leibniz conceives of the envisagement, except he called it imagination, and the objects mere phenomena. So he discovers an alternative to the Newtonian hypothesis.
Kant then takes it a step further. Why not stop at that point for a while? we will find that actually each contains a problem, the Newtonian and the Leibnizian, and that there is solution which explains them both.
We will make space and time into envisagements, i.e., what we spontaneously and universally and suddenly begin to see: the objects are in space (and time). Like seeing a face in a cloud. The impact of the face will be instructive. When we finally see a face in a cloud, we see it as though it were really there the whole time and that we were simply not looking right. And that is precisely the effect that sighting things in space and time have, i.e., it looks like it were there the whole time and that people were merely looking at it wrong the whole time.
So it is an envisagement. Now given that, how shall we derive the Newtonian and the Leibnizian conceptions? The former literally sees things in space and then explains the illusions of the sightings, e.g., the split finger. The other realizes that the only source of space in the first place is that split-finger and that therefore it is far more reasonable to say that space is an illusion itself, and that only the individual sightings, each eye alone, more nearly approach the truth of the matter.
The gains: Newton can speak of geometry, for the same envisagement that arises from our mere looking, that envisagement pictures the things as literally in space, and so what holds for the envisagement holds for the space.
??
Leibniz can distance himself from the senses, the source of all confusion, and head closer into the individual monad, which is only suggested by the single eyes, and their composite sighting (which does not exist like that at all, as everyone will have to admit).
The losses: Newton looses all contact with anything spiritual, for all has been demoted to mere material floating around in space,a and God would have to be so too.
Leibniz looses mathematics into the realm of the never-never land. For its application is now always in jeopardy, since the senses contain only confusion, from which the mind plucks the space in which the math can be demonstrated, and it is merely imagination.
7:46 PM The monad remains real for Leibniz, although all else is merely depictionary. {I don't remember Leibniz remark about Berkeley in New Essays. Leibniz did not go so far as to doubt the existence of real things, but only that their reality was a configuration of the monads, and so that much matter, if you will, actually existed, points of reflection.
7:49 PM