The immateriality of Space is critical for any theory of Matter and the tremendous challenge in conceiving Matter is that Matter cannot be accounted for or constructed out of anything that is itself material and if anything material is to be employed in the determination of matter this is a mere circular run-around whereby it is taking for granted what is in required of an account and somehow Matter must be specifiable using completely immaterial resources and Hegel’s determination of Space provides the first pillar for the immaterial account of Matter and Hegel's aim is to provide such an account by specifying Matter in terms of Space and Time y which means he does not fall back upon the empty identification of extension and Matter with which Descartes handicapped his theory of Nature. Rather Hegel will demonstrate how relations of Space and Time provide for something material that is irreducible to either.
For starters there is Space and Space has a very minimal determinacy, Space is a totality very much as Kant describes space in the 'Critique of Pure Reason' where Space and Time are identified as pure intuitions rather than concepts because they are totalities in the sense of containing within themselves all particular spaces and times respectively and for Kant concepts inhere in particulars that have other distinguishing features not contained in the inhering concept for otherwise nothing would differentiate the particulars from what they hold in common yet by contrast Space and Time completely contain all places and moments within their respective wholes. Albeit Hegel in his philosophy of Mind will allow that Space and Time figure psychologically as forms of sensible intuition he sidesteps Kant’s subjective idealism by addressing Space and Time in their own right as elementary factors of Nature and Space and Time are very much formal yet not just by being forms of intuition though intuition may indeed involve spatial and temporal orderings of the contents of sensations but Space and Time are themselves elementary immaterial determinations of Nature within which Mind itself has its reality as a worldly embodied self that is not merely reducible to something purely physiological.
Space is a totality encompassing all of its particular instances completely within itself but it is a wholly abstract totality, Space has the character of being external to itself and this self-externality has a logical character that must be defined without invoking spatial relations, Space is self-external in that it renders itself other to itself but not to anything else since every other factor falls within its bounds, Space falls apart from itself ever extending beyond itself in an unbroken continuity, Space has this uninterrupted continuity because there is nothing about the way that Space is external to itself that involves any kind of qualitative real differences, each part of Space as such is indistinguishable from every other, even though they fall asunder, every aspect of space always has more of itself outside itself.
The most minimal distinction of Space is a point, it comprises the most elementary non-space or negation of space and all by itself the point exhibits the same kind of self-externality that applies to everything spatial, a point cannot help but have other points adjacent to it and hence every point is immediately other to itself terminating in another negation of Space that is indistinguishable from itself and each point has another lying immediately beyond itself without any intervening gap and in virtue of every point having another in continuity with itself the point cannot help but form a line consisting of the continuous self-externality of otherwise indistinguishable points.
'Spatial difference is however essentially determinate and qualitative. As such it is (1) in the first instance the point, i.e. the negation of the immediate and undifferentiated selfexternality of space itself. (2) The negation is however the negation of space, and is therefore itself spatial. In that this relation is essential to the point, the point is self-sublating and constitutes the line, which is the primary otherness or spatial being of the point. (3) The truth of otherness is however the negation of negation, and the line therefore passes over into the plane. Although one aspect of the plane is that it constitutes surface in general, in that it is a determinateness opposed to line and point, it also has the aspect of being the transcended negation of space, or the reinstatement of that spatial totality which now has the negative moment within it. It is therefore an enclosing surface, which divides off and separates a distinct part of space'.
- 'The Philosophy of Nature'
Yet a line cannot help but be self-external in addition for at its edge there cannot fail to be another line which has another line beside it involving the same self-externality and so just as the point cannot escape generating the line the line cannot help but generate a plane but the plane has another adjacent to it generating a seamless series of planes comprising a volume of three dimensional space and if that volume is in any manner limited it also cannot help but have other volumes extending beyond itself without end and in each case the successive aspects of Space have beyond them something that is other from them but equally no different generating the ever extending continuity of the totality of space and in this way Space as self-external comprises a totality in continuity with its own negations or externalities.
'It is because of their Notion that the line does not consist of points nor the plane of lines, the line being rather the self-externality of the point in that is relates itself to space and is self-sublating, and the plane likewise, being the transcended self-externality of the line. The point is here presented as that which is primary and positive, and it is from this that a beginning is made. The contrary is also true however, for space may be considered as that which is positive, the plane as the first negation of space, and the line as the second negation, which, because it is the second, is in truth the self-relating negation of the point. The necessity of this transition is the same as it was in the first case. The necessity of this transition is not realized when the point and the line etc. are grasped and defined in an external manner; the former kind of transition is however grasped, as something contingent, when a manner of definition is used in which the line is said to arise from the movement of the point etc. The other figurations of space treated in geometry are further qualitative limitations of an abstract division of space, of the plane, or of a bounded spatial unit. Moments of necessity also occur here; in the triangle for example, which is the primary rectilinear figure, to which, with the square, all other figures must be reduced if they are to be determined etc. The principle of these constructions is the identity of the understanding, which determines the figurations into regularity and so establishes the relations hip s by which they may be understood'.
- 'The Philosophy of Nature'
A question arises as to what this continuous totality signifies for determinate spatial locations or places and what here can be as opposed to there, for here is immediately different from there yet they are distinguishable, in some way, what is there is not here but what is not here is also a here different from other heres or theres and on its own Space provides nothing that allows one to distinguish one here from another and every location is equally here and there in respect to other theres and heres and such a convergence of the difference and identity of every abstract spatial location leads Hegel to discourse upon Space as being in itself absolute rather than relative and absolute Space is only the abstraction of Space.
'To ask whether space by itself is real, or whether it is only a property of things, is to ask one of the most well-worn of all metaphysical questions. If one says that it is something inherently substantial, then it must resemble a box, which, even if there is nothing in it, is still something subsisting within itself. Space is absolutely yielding and utterly devoid of opposition however; and if something is real, it is necessary that it should be incompatible with something else. One cannot point to a part of space which is space for itself, for space is always filled, and no part of it is separated from that which fills it. It is therefore a non-sensuous sensibility and a sensuous insensibility. The things of nature are in space, and as nature is subject to the condition of externality, space remains the foundation of nature. If one says, as Leibnitz did, that space is an order of things which does not concern the noumena, and which has its substrata in things, we assume that if one removes the things which fill space, the spatial relationships between them still persist independently. It may certainly be said that space is an order, for it is of course an external determination, but it is much more than a merely external determination, it is externality itself'.
- 'The Philosophy of Nature'
Relative Space is a more concrete spatial determination in which distinguishable frameworks of moving objects stand in relation to one another and these involve further specifications that are not provided by the mere self-externality of space and its generation of extension, and Space by itself without yet involving Time never mind Motion and Matter cannot be anything other than absolute because it lacks any concrete filling that could provide for the contrast of different determinate spatial contexts, such as inertial frames of reference or material Gaussian co-ordinate systems those things that Albert Einstein, (1879 – 1955), invoked as the fundamental contexts of his general theory of relativity.
The absolute character of formal Space is very much different from what Aristotle asserted to be the absolute nature of Place for he saw that considered abstractly right and left could be considered relative since if one changed one’s vantage point what was right could become left and vice versa yet if one considers what is up and down Aristotle maintains that one encounters an absolute spatial distinction and this difference is rooted in natural Place which is connected to the specific nature of material substances and reference to the unmoved mover may give no more absolute direction than the eternal orbit of celestial motion yet the active form of natural things directs them to a specific place whose location is thereby absolutely grounded in the causal principle of nature, that which is earth tends to move down in an absolute sense just as that which is fire tends to move up in an absolute sense and these are not relative directions because they are tied to the unequivocal place to which things of a certain kind gravitate and without that connection there would be no way to distinguish one direction from another in any unqualified absolute manner and Kant eliminates all such connection through understanding natural necessity to be restricted to material laws indifferent to the specific form of things an as far as Kant conceives the Space of Nature with reference to moveable bodies Space is relative, together with the motion that proceeds within it.
Discourse upon the relativity of Space typically invokes inertial frames of reference where spatial relations refer to the motion of a body in relation to some physical background involving moveable and/or moving bodies of its own and in this concrete framework of a plurality of bodies in motion relative to one another it is arbitrary which frame of reference is regarded as stationary and there seems to be no objective means of determining whether any particular body is in motion or whether its background is moving in the opposite direction while it remains stationary for both scenarios appear equivalent just as do all the numberless intermediate schemes in which the bodies move in opposite directions at various speeds and accelerations while retaining the same difference in speed. Albeit Hegel was very much cognisant of this relativity of spatial relationships in the concrete setting of bodies in motion he maintained that Space in itself is absolute, Space without further qualification that is to say Space still unqualified by Time, Matter and Motion permits of no relativity in virtue of the fact that it lacks what is necessary for there to be determinate spatial frames of reference and the self-externality of Space that generates lines from points, planes from lines, and volumes from planes has nothing to which it can be relative and Space on its own provides no basis for establishing any determinate differences that make room if I may so put it for distinct spatial frameworks.
Hegel rather demonstrates that Space gives rise to Time and what is truly a breakthrough in Hegel’s account of the transition from Space to Time is the twofold insight that Time presupposes Space and that Space cannot help but yield itself to Time and there cannot be Time apart from Space and Space cannot fail to engender Time a situation in no need for supernatural powers to be called upon to save the day if I may use a temporal metaphor to account for the space-time continuum and Nature can have no more indeterminate rudimentary factor than Space and Space is sufficient to provide for the emergence of Time. This does raise the question as to what exactly is the basic minimal determination of Time and whether it needs to be characterized in respect to Space and Hegel maintains that Time is what Space becomes which then raises the question as to how Space becomes Time and how Time be thought of in terms of Space.
'Space is the immediate determinate being of quantity, in which everything remains subsistent, and even limit has the form of a subsistence. This is its deficiency. Space is a contradiction, for the negation within it disintegrates into indifferent subsistence. As space is merely this inner negation of itself, its truth is the self-transcendence of its moments. It is precisely the existence of this perpetual self-transcendence which constitutes time. In time therefore the point has actuality. Through the generation of difference within it, space ceases to be mere indifference, and through all its changes, is no longer paralysed, but is for itself This pure quantity, as: difference existing for itself, is that which is implicitly negative, i.e. time; it is the negation of the negation, or self-relating negation. Negation in space is negation relative to another; in space therefore the negative does not yet come into its own. In space the plane is certainly negation of the negation, but in its truth it is different from space. The truth of space is time, so that space becomes time; our transition to time is not subjective, space itself makes the transition. Space and time are generally taken to be poles apart: space is there, and then we also have time. Philosophy calls this 'also' in question'.
- 'The Philosophy of Nature'
'Equilibrio Spaziale', 1925/26, Giacomo Balla
And the further question as to whether or not every stage in the development of Space from point to line to plane to volume is a moment in Time for the development at issue is not merely a logical succession of categories of thought. Point, line, plane, and volume are real spatial determinations and they are non-logical albeit they are immaterial and the yet further question arises as to whether their succession is a passage in time and thereby a generation of Time. In each case the move from one spatial determinacy to another is immediate without any intervening intermediary stage and further there is no separate persisting backdrop against which these developments proceed and they comprise differentiations of and within the totality of Space by which its self-externality unfolds.
They are simply spatial differences without any temporal distinction and the continuity of points, lines, and planes is a continuity of spatial distinctions and not of moments in Time for something extra must be supplied to provide for any differences that can count as temporal, for there to be any Time then non-logical differences must no longer simply fall within Space as negations internal to its self-externality but rather Time as non-spatial must involve a negation or becoming other to spatial determinacy as a whole and Hegel provides an elementary solution to the challenge which is to say Time is the totality of Space being external to itself and instead of setting a part of Space such as a point, a line, a plane, or a determinate volume external to some other spatial factor, Time sets Space other to or outside itself in its entirety and the question arises as to how Space can be self-external in its totality. By being Space now, which becomes other to Space before.
The succession of Time is none other than the continuous othering of the totality of Space whereby Space is external to itself as a whole and each moment in Time is the totality of Space as supplanting its own totality and immediately giving way to its own totality once more and so on and whereas Space was external to itself in a spatial manner in the development from point to line to plane to volume the self-externality of Space in its totality involves a development that can no longer be spatial in character. The self-externality basic to Space pushes Space beyond itself, for once Space has exhausted the intra-spatial options provided by the negations of point, line, plane, and volume, the defining character of Space pushes it beyond itself a beyond that consists in nothing more than the continuous self-externalization of Space in its entirety, and this involves no other resources than Space itself provides and it is generated by nothing other than the self-externality intrinsic to Space.
The totality of Space can be outside itself only from one moment to the next and the passage of Time is nothing but the ongoing differentiation of Space in its totality and here the totality of Space is negated and Time is that in which Space becomes its own non-being. The now is immediately Space that is no longer, that has passed into the past, now is that which the future will be in that the now becomes the past making the future present and there is no other resource ready to hand for distinguishing the past from the present other than the totality of Space being external to itself and any other natural factor presupposes Space and Time and hence cannot be employed in constituting time, Time is the self-externality of Space as a whole where Space is continually set in an external relationship to itself and the present, past, and future cannot be distinguished by anything other than the non-being of the totality of Space that is just as much the totality of Space as external to itself while (if I may use that term) the present is immediately past and the future is immediately present insofar as Space as a whole is self-external and this self-externality is Time. Such distinctions of the ever succeeding otherings or self-negations of the totality of Space are just as equivalent as the differences in Space itself, just as every point, line, and plane is identical in character to every other, so there is no way of distinguishing any now from any other now in terms of time itself.
'The present, future, and past, the dimensions of time, constitute the becoming of externality as such, and its dissolution into the differences of being as passing over into nothing, and of nothing as passing over into being. The immediate disappearance of these differences into individuality is the present as now, which, as it excludes individuality and is at the same time simply continuous in the other moments, is itself merely this disappearance of its being into nothing, and of nothing into its being'.
- 'The Philosophy of Nature'
Every now emerges from the past and is pregnant with the future and the spatial totality that has replaced what has slipped into the past is no different from its predecessor or successor and only more concrete determinations of Nature involving bodies in motion, can provide for any real contrasts, but matter and motion themselves presuppose space and time and their seamless continuities. In and of themselves, the temporally distinguished totalities of space contain nothing that can concretely distinguish them from one another. Each moment of time, each distinction of past, present, and future, presents the same self-external spatial totality. The now is Space that is other than Space that was and Space that will be but that otherness is completely devoid of any further content and this difference that is no difference is what allows Kant to designate the now the same thing as eternity and the now may instantaneously slip into the past but another now no different from it just as instantaneously replaces it to be instantaneously replaced by another now without end indeed the very character of the now is such that it keeps on returning to itself in slipping into the past and giving way to the future.
The resulting continuity of Time has a totally abstract determination yet it is more concrete than that of Space in particular in virtue of the flow of time containing Space in its totality with a further qualification and that qualification is that Time encompasses Space together with the process by which the totality of Space becomes external to itself taking on the additional character of being now extending across past and future and the totality of Space has become poised between these temporal dimensions into which it is endlessly drawn perpetually reverting to the same timely situation and the dimensions of Time are just as abstract as the dimensions of Space. In the same way that depth, height, and width have no abiding difference so every moment of Time is just as much present, past, and future and the past was the future and the present, the future became present only to fall into the past, and the present becomes past and takes on the future, and like the dimensions of Space so the dimensions of Time finish up having equivalent specifications.
Space and time demonstrate themselves to have an intrinsic relationship to one another, Space is the minimal threshold of what can be considered natural and Space cannot help but give rise to time which incorporates Space within its process and the emergence of Time from Space is not a temporal event for there is no Time prior to Time and there cannot be a Time when there was Space without Time yet upon Time emerging and encompassing Space in temporality Space is in a position to become more concretely determined that is to say with Space and Time at hand Place can both be and be conceived which can be demonstrated by outlining how Place issues from a unity of Space and Time and once there is Time setting the totality of Space external to itself the totally abstract spatial location of a point can take on a more determinate character making possible the distinguishing of Place which raises the question as to what is the concrete character that is suitable to identify with Place, Place cannot be characterized by making reference to Matter for Matter cannot be invoked for Matter itself will incorporate Place in its own constitution and we are left wondering what Place can be if all it involves is Space and Time.
The issue is whether Motion determines Space and Time as Place or Motion like Matter presupposes Place and Aristotle apparently characterizes Place in reference to natural substances and the motion to which they tend by nature and yet the primary motion comprising locomotion is change of place so Motion takes Place for granted and Place must hence be determinable prior to locomotion and moving substance and with Motion and Matter excluded from the determination of Place one might regard Place as something merely spatial in character yet Place is not just here for here is assignable to every point without exception yet place is a determinate location and so the question arises as to what Space and Time have to offer that permits Place to be more determinate than here.
Well, because of Time and its encompassing of Space Place can be both here and now, Place combines Space and Time, it is spatiotemporal location and Place is a here that is mediated by Time and a now that is mediated by Space and Place is still relatively abstract but it is more concrete than either here or now in virtue of nothing other than uniting them both. By itself here has no temporal determination yet Time does encompass Space, nevertheless the present like the past and future involves reference to only the totality of Space not to any particular here. Now therefore has no specific spatial connection and Place provides the elementary juncture of Space and Time, of here and now, doing so in virtue of nothing but what is contained in the ongoing process of space-time.
Motion depends upon Place just as does Matter if Matter requires a dynamic account involving moving forces and Motion understood as locomotion involves change of Place that is to say a change of spatiotemporal location from one here and now to another here and now and Motion involves the succession of time exhibiting itself in spatial determinations and the change of location exhibiting itself in the passage of Time. And the question arises concerning from whence such a dual process of Motion arises and the bare process in question is formal, since it does not involve Matter and any of the real differentiations of Place that material bodies in motion provide and this is what Kant addresses in his discussion of phoronomy, what leads Place to generate Motion is the same self-externality that leads points to generate lines, lines to generate planes, planes to generate volumes, and spatial totality to generate Time and since each here and now is indistinguishable from every other in a seamless continuity the same continuity applies to each space-time unity.
Each place is in continuity with others since none retains any abiding distinction from what it has outside and before and after itself and the self-externality of Place is Motion and the transition of each particular place into others separated yet adjacent in both Space and Time and the issue is then about what must be added to formal motion to provide for Matter for two deficits must be overcome, first if something occupied merely a point in space time we have to ask if there is any way of distinguishing between its presence and its absence and the infinitesimal spatial punctuality of a point precludes any material actuality that could hold itself apart from the void, and likewise, if something were just now at hand for a mere moment of Time we further need to know if there could be any way of distinguishing between its presence and its absence, any material actuality would be instantaneously cancelled as the present moment immediately passes away and so for anything material to be it must both endure and occupy a determinate volume and Matter must have an extended as well as a persisting presence. Any actual body must occupy a bounded volume and endure for some time otherwise there is nothing material and so as to what the minimal specification of Matter must involve Matter will combine Space and Time comprising a here that is now and a now that is here yet Matter must be more than the here and now of Place or the formal motion of points in space-time. Matter must lay hold of some extended Space over Time and do so in a way that distinguishes its enduring occupancy from that of empty space-time and by itself Place offers nothing to prevent one place from passing over into another.
What is other to Place is merely a not-here-and-now which cannot hold itself apart from any other not-here-and-now, every not-now is another now just as every not-here is another here and every not here-now is a here-now and every other place is a place as well. And so there is no way of preventing Place from becoming other than it is, Place cannot help being identical with other places.
'Initially, the place which is thus the posited identity of space and time is also the posited contradiction set up by the mutual exclusiveness of space and time. Place is spatial and therefore indifferent singularity, and is this only as the spatial now, or time. As this place, it is therefore in a condition of immediate indifference to itself; it is external to itself, the negation of itself, and constitutes another place. This passing away and self-regeneration of space in time and time in space, in which time posits itself spatially as place, while this indifferent spatiality is likewise posited immediately in a temporal manner, constitutes motion. To an equal extent however, this becoming is itself the internal collapse of its contradiction, it is therefore the immediately identical and existent unity of place and motion, i.e. matter'.
- 'The Philosophy of Nature'
Place becomes other places and in so doing Place gives rise to Motion in a completely formal way and he motion is completely formal because all it comprises is how the passage of Time becomes a change of Place and alternately how change in Place becomes a change through Time. Kant develops this formal motion in his discussion of phoronomy as if it somehow applied to Matter as moveable with abstraction made of every material feature except for quantity, thinking of matter just as a point moving through Space and Kant presents the formal account of Matter as paving the way for the dynamic constitution of Matter and Hegel follows him in this only so far as to present the formal specification of Motion as giving rise to the minimal specification of Matter and Matter will once more be intrinsically connected to Motion, and upon such a foundation aspects of the dynamic discussion that Kant forged ae renewed but it is to be done in a significantly different way.
'Spessori di spazio', c. 1913, Giacomo Balla
My muse is doing such an excellent job she merits a pay rise, i.e., more love, but when one's love is infinite that is not possible, although apparently, and this is not my area of expertise, according to mathematician Georg Cantor, (1845 – 1918), infinity comes in different sizes, and so my infinite love for my muse is infinity of the largest sort.
Long awaited darkness falls
Casting shadows on the walls
In the twilight hour, I am alone
Sitting near the fireplace
Dying embers warm my face
In this peaceful solitude
All the outside world subdued
Everything comes back to me again
In the gloom
Like an angel passing through my room
Half awake and half in dreams
Seeing long forgotten scenes
So the present runs into the past
Now and then become entwined
Playing games within my mind
Like the embers, as they die
Love was one prolonged goodbye
And it all comes back to me tonight
In the gloom
Like an angel passing through my room
I close my eyes
And my twilight images go by
All too soon
Like an angel passing through my room
Abba: 'Like An Angel Passing Through My Room':
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Coming up next:
Another Time. Another Place.
To be continued ..