SPACE AND TIME _ By Marsigit

SPACE AND TIME

By Marsigit, Yogyakarta State University

Email: marsigitina@yahoo.com

Subjective Conditions of Sensation

Ross, K.L., 2001, exposed that Kant proposes that space and time do not really exist outside of us but are "forms of intuition," i.e. conditions of perception, imposed by our own minds. This enables him to reconcile Newton and Leibniz: agreeing with Newton that space is absolute and real for objects in experience, i.e. for phenomenal objects open to science, but agreeing with Leibniz that space is really nothing in terms of objects as they exist apart from us, i.e. with things in themselves. The bulk of Kant's exposition on time and space in relation to sensory perception can be found in the opening pages of The Critique of Pure Reason (1781) (Gottfried, P., 1987). He said that in the first part of the Critique, the "Transcendental Aesthetic," for the most detailed treatment of time and space as the a priori condition for cognition; in this section Kant examines time and space as universal forms of intuition that help render sensory impressions intelligible to the human mind.

Gottfried, P., 1987 noted from Kant that although the forms of time and space are "subjective conditions of sensation" and depend for their appearance on perceptual activity, they are nonetheless characterized as being a priori: antecedent to the specific sensations for which they provide a conceptual frame.  He elaborated that Kant intended the Critique to furnish a "transcendental" analysis of the structure and operation of the mind as revealed in sensory and other judgmental activities; since he was exploring the subjective, but non empirical basis of perception, his "transcendental" analysis treated the mental apparatus underlying sensory consciousness. He then stated that space and time seemed to be part of it, and Kant offered several arguments for each one to prove that its cognitive role was both constant and universal.

Werke, [1]referred to Kant stated that time existed as a "subjective condition" of perception, "not for itself or as an objective quality in things"; to conceive of time as something objective would require its presence in things which were not objects of perception; however, since time and space were only knowable as the a priori forms of intuition, any other assumption about them, apart from this context, could not be substantiated. Further, Gottfried, P., (1987) explained, based on Kant’s views,  that “time” was also "the form of our inner sense, of our intuition of ourselves and of our own inner situation; belonging neither to any pattern nor place, it determined the relationship of perceptions within our inner situation. He excerpted Werke,, " Because this "inner intuition" as such assumed no shaper, it had to be imagined "by analogy… by positing succession through a line extending ad infinitum in which sensory impressions form a uni-dimensional sequence and by generalizing from the attributes of this line to those of time itself."; and it was concluded that time was to be seen "as the formal a priori condition for all appearance."; whereas space remained the "pure form of al outward intuition," time supplied the subject with an inward orientation essential for perceptual relations.

Shabel, L., 2003, further noted that Kant argues that the structure for the a posteriori representations we receive from sensation must itself be a priori; this leads him to the science of a priori sensibility, which suggests that our capacity to receive representations of objects includes a capacity to receive representations of the a priori form of objects. Accordingly, since space is one of two such a priori forms, a priori sensibility includes a capacity to receive pure representations of space. She elaborated that Kant's claim that our concept of space contains a pure intuition in itself... [and thus] can be constructed': the concept of space provides us with a `principle' for performing constructions in pure intuition, in particular, a priori constructions of basic spatial regions that exhibit particular basic spatial concepts.

Werke, 4:33 in Gottfried, P., (1987) stated that Kant denied to time, as well as to space, an "absolute reality," maintaining that outside of its cognitive function "time is nothing."; unlike Dinge an sich (things in themselves) that might exist independently of man's apparatus of perception, both time and space could be evoked only "in relation to appearance:" that is, only in relation to the world as it appeared to our senses. Further, he concluded that the "objective validity" of time and space was limited to the regularity of their relationship to sensation, yet within this limited framework their activity was constant and predictable. Therefore, he ultimately stated that  "The reality of space and time," wrote Kant, "leaves the certainty of sensory knowledge unchallenged; for we can be equally sure of it whether forms inhere in things in themselves or in the intuitions of those things; on the other hand, those who assert the absolute reality of space and time, whether they are posited as coexisting or inherent, are at variance with the principles of experience".

Kant delivered his explanation to clarify distinction between appearance and illusion, a verworrene Vorstellung (confused representation) of reality (Gottfried, P., 1987)[2] as:

“When I say that in space and time intuition represents both external objects and the self-intuition of the mind, as it affects our senses and as it appears, that does not man that such objects are a mere illusion; for in appearance objects, along with the situations assigned to them, are always seen as truly given, providing that their situation depends upon the subject's mode of intuition: providing that the object as appearance is distinguished from an object in itself. Thus I need not say that body simply seems to be outside of me…. when I assert that the quality space and time… lies in my mode of intuition and not in objects in themselves”

Metaphysical Exposition of the Concept of Space

According to Kant, a pure concept of space warrants and constrains intuitions of finite regions of space; that is, an a priori conceptual representation of space provides a governing principle for all spatial construction, which is necessary for mathematical demonstration as Kant understood it (Shabel, L., 2003). She, then  remembered that from a partial account of the task of Kant's `Metaphysical Exposition of the Concept of Space', which is itself the first task of the Transcendental Aesthetic; and therefore, as already noted, the Aesthetic is meant to constitute, from Kant `a science of all principles of a priori sensibility', and begins with an investigation of space, which Kant rather unhelpfully identifies as one of `two pure forms of sensible intuition as principles of a priori cognition'.[3] On these suppositions, the concept of space would be indistinguishable from what Kant calls `the general concept of spaces in general', presumably that concept `which is common to a foot as well as an ell'. But Kant explicitly states that such a general concept itself rests on limitations of space  and cannot itself be the source of the boundlessness of space .

Thus, an exposition of such a `general concept of spaces in general' could not be expected to satisfy Kant's goals in the Transcendental Aesthetic (Shabel, L., 2003). She concerned with Kant's identification of a concept of space that is strictly identical neither to a general concept of spaces in general, nor to any particular intuition.[4]  Gottfried, P., 1987 also indicated that, as Kant submitted, space could not be an "empirical concept," since its representation was necessary, based on Werke, 58 claims,   "to relate impressions to something outside of me (to some point other than where I stand), and to perceive them not separately but actually in different places"; moreover, unlike a concept that simply restricted associations, space admitted of an unlimited possibility of application (an unendliche gegebene Grosse, of "infinite given magnitude).[5] 

According to Kant, concepts are not singular, nor can they contain infinitely many parts; thus, space is represented in intuition and it seems equally impossible to intuit a single infinitely large object. Therefore, according to Kant's, this would require that we be able to form an immediate (unmediated) representation of an infinite spatial magnitude, that we grasp its infinitude in a single `glance', as it were (Shabel, L., 2003). So, Kant uses the Metaphysical Exposition, at least in part, to describe the pure spatial intuition that underlies any and all geometric procedures, but he does not use properly geometric procedures to describe that intuition. While cognition of the `axioms' of geometry depends, in some sense, on our having a capacity for pure spatial intuition, that capacity cannot itself be described as a capacity for geometric reasoning. So, our capacity for pure spatial intuition, described in the Metaphysical Exposition, is pre-geometric in the sense that it is independent of and presupposed by Euclidean reasoning.

Schematism

Kant claimed that there is only one way in which a mediating element can be discovered, that is, by examining the single element which is present in all appearances, but at the same time is capable of being conceptualized that is “time”. According to him, we must therefore discover various ways of thinking of time, and if we can discover the ways in which this must be done, we can say that they both conform to the conditions of thought and are present in all appearances. Kant calls these conceptualizations of time "schemata"; he then found four fundamental modes of thinking time, one corresponding to each of the basic divisions of categories that are time-series, time-content, time-order, and the scope of time.[6]

Kant claimed that as a one-dimensional object, time is essentially successive that is one moment follows another; and in order to think time as a succession,  we must generate the time-series that is we must think one moment as following another. Kant suggested that at each point of the series up to that point; therefore, we always think time as a magnitude. Accordingly, since the categories of quantity are those of unity, plurality and totality, we can say that they apply to appearances in that all appearances must be thought as existing within a specific time- span which can be thought as momentary that is as a series of time spans or as the completion of a series of time spans. On the other hand, Kant insisted that we can think of a given time as either empty or full; in order to represent objects in time we must resort to sensation, so that in thinking a time we must always ask whether that time is filled up. Thus the schema of quality is the filling of time; it would be natural to assume that the question whether-a time is full admits of a simple answer of yes or no. However, Kant claimed that reality and negation must be conceived as two extremes or limits, between which exist infinitely many degrees; he called these degrees as "intensive magnitudes"[7]

Kant also claimed that schemata for the categories of relation are treated separately because the relational categories treat them in respect to one another and that time considered of it-self is successive but not simultaneous, and space is simultaneous but not successive. Kant, therefore noted to think objects in a time-order: as enduring through a number of times that is that of the permanence of substance, as "abiding while all else changes"; as in one state of affairs which succeeds another that is we think the states of substances as occupying a succession of times, in accordance with a rule; and as co-existing that is the schema of reciprocity or mutual simultaneous interaction.[8]

Meanwhile, Kant insisted that time is supposed to relate objects, not to one another, but to the understanding that is, we can think an object in one of three ways: as occupying some time or other, without specifying what part of time that is the schema of possibility in which we can think an object as possible in so far as we can think it as occupying some time or other, whether or not it actually occupies it; as existing in some definite time that is the schema of actuality in which we think an object as actual when we claim that it exists in some specific part of time; and as existing at all times that is the schema of necessity in which an object is thought as being necessary if it is something which we must represent as occupying all times, in other words, that we could not think of a time which does not contain that object.[9]

Kant’s Antinomies of Space and Time

Kant's Antinomies are intended to show that contradictory metaphysical absolutes can be argued and justified with equal force, meaning that neither can actually be proven. It can be argued however, that Einstein answered Kant by proposing a non-Euclidean (Riemannian) universe that is finite but unbounded (i.e. without an edge).

KANT’S CONCEPTS OF SPACE AND TIME

Kant's Antinomy of Space and Time is the first of Kant’s four Antinomies.

Thesis	Antithesis
The world has a beginning in time, and is also limited as regards space.	The world has no beginning, and no limits in space; it is infinite as regards both time and space.
Proof	Proof
If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in that world an infinite series of successive states of things. Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away, and that a beginning of the world is therefore a necessary condition of the world's existence. This was the first point that called for proof. As regards the second point, let us again assume the opposite, namely, that the world is an infinite given whole of co-existing things. Now the magnitude of a quantum which is not given in intuition [i.e. perception] as within certain limits, can be thought only through the synthesis of its parts, and the totality of such a quantum only through a synthesis that is brought to completion through repeated addition of unit to unit. In order, therefore, to think, as a whole, the world which fills all spaces, the successive synthesis of the parts of an infinite world must be viewed as completed, that is, an infinite time must be viewed as having elapsed in the enumeration of all co-existing things. This, however, is impossible. An infinite aggregate of actual things cannot therefore be viewed as a given whole, nor consequently as simultaneously given. The world is, therefore, as regards extension in space, not infinite, but is enclosed within limits. This was the second point in dispute.	For let us assume that it has a beginning. Since the beginning is an existence which is preceded by a time in which the thing is not, there must have been a preceding time in which the world was not, i.e. an empty time. Now no coming to be of a thing is possible in an empty time, because no part of such a time possesses, as compared with any other, a distinguishing condition of existence rather than of non-existence; and this applies whether the thing is supposed to arise of itself or through some other cause. In the world many series of things can, indeed, begin; but the world itself cannot have a beginning, and is therefore infinite in respect of past time. As regards the second point, let us start by assuming the opposite, namely, that the world in space is finite and limited, and consequently exists in an empty space which is unlimited. Things will therefore not only be related in space but also related to space. Now since the world is an absolute whole beyond which there is no object of intuition, and therefore no correlate with which the world stands in relation, the relation of the world to empty space would be a relation of it to no object. But such a relation, and consequently the limitation of the world by empty space, is nothing. The world cannot, therefore, be limited in space; that is, it is infinite in respect of extension.
These proofs really only use one argument, that an infinite series cannot be completed ("synthesized") either in thought, perception, or imagination. That was roughly Aristotle's argument against infinite space.	There are two arguments here: First, that there is no reason for the universe to come to be at one time rather than another, where all points in an empty time are alike. Second, that objects can only be spatially related to each other, not to empty space, which is not an object.

Source: Ross, K.L., 2001

Note:

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1.       See Gottfried, P., 1987, Kantian Time And Space Reconsidered

2.       As it was elaborate by Werke

3.       As it was cited by Shabel, l., 2003, Kant insisted that we will expound the concept of space first. I understand by exposition (expositio) the distinct (even if not complete) representation of that which belongs to a concept; but the exposition is metaphysical when it contains that which exhibits the concept as given a priori.

4.       Ibid, in the course of his first argument for the intuitive nature of our representation of space, Kant stated that one can only represent a single space, and if one speaks of many spaces, one understands by that only parts of one and the same unique space. And these parts cannot as it were precede the single all-encompassing space as its components (from which its composition would be possible), but rather are only thought in it. It is essentially single; the manifold in it, thus also the general concept of spaces in general, rests merely on limitations.

5.       Ibid, Kant’s argued that space is represented as an infinite given magnitude. but no concept, as such, can be thought as if it contained an infinite set of representations within itself. Nevertheless space is so thought (for all the parts of space, even to infinity, are simultaneous). If there were not boundlessness in the progress of intuition, no concept of relations could bring with it a principle of their infinity.

6.       See Mattey, G.J., 2004, Kant Lexicon, G. J. Mattey's Kant Home Page, http://www-philosophy.ucdavis.edu/kant/Kant.htm

7.       ibid

8.       ibid

9.       ibid