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Primairly according to Kant space is a priory form that 'causes' that we can experience things in 3d. He argues this as follow:

"In the transcendental exposition, Kant refers back to his metaphysical exposition in order to show that the sciences would be impossible if space and time were not kinds of pure a priori intuitions. He asks the reader to take the proposition, "two straight lines can neither contain any space nor, consequently, form a figure", and then to try to derive this proposition from the concepts of a straight line and the number two.

He concludes that it is simply impossible. Thus, since this information cannot be obtained from analytic reasoning, it must be obtained through synthetic reasoning, i.e., a synthesis of concepts (in this case two and straightness) with the pure (a priori) intuition of space.

In this case, however, it was not experience that furnished the third term; otherwise, the necessary and universal character of geometry would be lost. Only space, which is a pure a priori form of intuition, can make this synthetic judgment, thus it must then be a priori. If geometry does not serve this pure a priori intuition, it is empirical, and would be an experimental science, but geometry does not proceed by measurements—it proceeds by demonstrations."

But is it excluded that space can be experienced or that it could be something in itself or a noumenon? Perhaps Kant himself doesn't say anything about this but could it be derived from his theory that it is possible or at least open?

Fe if you walk you experience distance and things has an extension what you can see, so why should it be a form a priori?

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    The question is not very specific as it seems to presuppose that there is only one sense of 'space' Kant uses. There is the form of our intuitions, pure intuition, the idea of absolute space and the experience of relative spaces. You should specify which works you want considered... – Philip Klöcking Feb 27 '16 at 17:06
  • I didn't know Kant had already so many interpretations, but when I have to chose I think the absolute space would be a candidate. Perhaps he considered that as a abstract negative thing in it self (or noumenon?)?? – Marijn Feb 27 '16 at 17:12
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    Can you indicate where you are quoting from? – virmaior Feb 27 '16 at 23:10
  • This appears to be quotations from wikipedia – virmaior Feb 28 '16 at 2:51
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    Kant clearly says in the Transcendental Aesthetic that space and time are intuitions which make other objects possible. They are the condition for the representation of any objects. – Kyle Feb 29 '16 at 3:34
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According to the Trancendental Aesthetics of Kant's Critique of Pure Reason space and time are the two kinds of human intuition. I.e. the two basic dimensions to classify the input from our senses, step one of mental information processing.

The second step is the information processing by means of the categories. The output of both steps is named experience.

Quite different is the contemporary concept of space and time according to current physics. Here the best elaborated theory is the Theory of General Relativit. It combines space and time as two components of 4-dimensional spacetime. Both component have only a relative meaning, relative to a given observer and his system of coordinates.

But more: Spacetime is a physical quantity. It is affected by other physical quantities like masses. The first confirmation of the resulting curvature of spacetime was the observed bending of light when passing near big masses like the sun. An actual confirmation would be the observation of gravitational waves (LIGO experiment). They are oscillation of spacetime due to the radiation of gravitational energy by the merge of two black holes.

According to the General Theory of Relativity spacetime is an objective physical quantity "existing in itself", i.e. independent from the observer. This view is different from Kant's concept of space and time.

During the history of physics before Einstein many different concepts of space or time were proposed, e.g. by Newton, Leibniz, Mach.

Added. If the question is, whether Kant considers space a noumenon, my answer is "no". Space is an intuition, i.e. one of our means to classify the input from senses. On the opposite, noumena are hypothetical objects in the outer world, which create the input for our senses.

  • But do you think that space could exists also in itself following the theory of Kant or did he exclude it explicite because it is only a human intuition a priori which forms our experiences? – Marijn Feb 27 '16 at 21:06
  • You talk about physical quantity for spacetime, but isn't it more a coordinate system or a mathematical primer or just something in our head: astronomy.stackexchange.com/questions/13526/… Perhaps it could be in that case more a negative noumenon as it is so abstract en.wikipedia.org/wiki/Noumenon#Positive_and_negative_noumena – Marijn Feb 27 '16 at 21:11
  • @Marijn I do not agree with the statement that spacetime is "merely a [...] coordinate system" from one of the linked answers. Spacetime is a physical quantity like other quantities, e.g., energy, momentum, velocity, charge. Because spacetime affects and is affected itself by other objects; example: it determines the geodesics, it's curvature is determined by masses. Spacetime with its metric and curvature is independent for the observer, while coordiate systems are means for our orientiation in spacetime. They depend on the observer. – Jo Wehler Feb 27 '16 at 21:31
  • @Marijn One great step of Einstein behind the space conception of Ernst Mach was the idea, that spacetime is more than just a container. - Kant's concept of a noumenon as a thing-in-itself is the base of every constructivist epistemology. When you accept a constructivist point of view then all things of the real world are noumena, not only spacetime. – Jo Wehler Feb 27 '16 at 21:32
  • This is a physical model of the space that we actually live in, but it is not the space and time Kant is talking about. It is not an intution, and it is surely not apriori. We interpret four-dimensional space-time by extrapolating from an internal intuition of three-dimensional space that is natural to us and the ability to add dimensions to that space by a mathematical process of product formation, largely trained into us by modeling time. We never experience anything as being in four-dimensional spacetime. – jobermark Feb 29 '16 at 20:08
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Space cannot be a "thing in itself" because is not a "thing." It does not have an unknowable, noumenal "side," so to speak, like the dark side of the moon, because it is not an object. It is the necessary mode of perceiving objects, though this is not exactly Kant's terminology.

Space is a necessary, unifying form of any and all experience. It cannot be experienced, yet one cannot have any experience without it. An analogy might be light, which we can never "see" in itself, yet without which no objects can be seen. Space is the "dimensionality" that makes any and all appearances possible.

When you think of walking along and "experiencing" space, you are measuring time intervals between apparent objects. Yet with no perceptions you would have no such intervals, no way to measure "space itself" apart from what is located by means of "timed" perceptions.

And since, for Kant, mathematics is synthetic a priori, you cannot resort to conceiving of space in some "pure mathematical" way, because you require perceptible geometric "lines" and other "objects" to do so. You need to draw a line, if only in imagination, to "know" that it must conform to certain rules.

Nothing, not even space, "gets started" without some experience. Yet once experiences can be compared reason can then infer transcendentally the a priori functions that made them possible and are "already" contained in them. But this does not mean that anything real, such as space, is "left over" if we somehow subtract all possible experience.

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Kant seems to have held that space cannot be a real thing in-itself.

First, Kant's conception of space is analogous to the long-held view that colors, smells and such are subjective, "phenomenal", and do not exist independently of us (in modern philosophy, this view is often attributed to John Locke). Kant thought of space, then, in the same way that a physicist thinks of colors. To think that space really existed would be analogous to thinking that colors existed physically, in addition to particles, waves and such.

That without calling in question the existence of external things, it may be said of a number of their predicates that they do not belong to the things in themselves, but only to their phenomena, and have no self-existence outside our presentation, is what had been generally accepted and admitted long before Locke’s time, but more than ever since then. To these belong heat, colour, taste, &c. No one can adduce the least ground for saying that it is inadmissible on my part, when for important reasons I count in addition the remaining qualities of bodies called primarias, such as extension, place, and more especially space, together with what is dependent thereon (impenetrability or materiality, figure, &c.) amongst the number of these phenomena. (Prolegomena §13)

Second, Kant held that attempts to regard "phenomena", such as space, as things-in-themselves, would lead to logical contradictions. The first antinomy is held to demonstrate, that attempting to rule whether time, or space, are finite or infinite, would result in contradiction.

When I speak of objects in time and space, I do not speak of things in themselves, because of these I know nothing, but only of things in the phenomenon, in other words, of experience, as the special mode of the cognition of objects, which is alone vouchsafed to man. I must not say that what I think in space or in time exists in itself in space and time apart from this my thought; for I should then contradict myself, because space and time, together with the phenomena in them, are nothing existing in themselves and apart from my presentations, but are themselves only modes of presentations, and it is obviously contradictory to say that a mere mode of our presentation exists outside our presentation. The objects of sense exist then only in experience; and to give them a special substantive existence for themselves, apart from or before the latter, is equivalent to imagining that experience can be present without or before experience. Now, when I inquire as to the size of the world in space and time, it is for all my conceptions just as impossible to say, it is infinite, as it is finite. For neither of them can be contained in experience. (Prolegomena §52c)

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Short answer: Maybe, but we cannot know.

I will quote three parts of the Phoronomy (first chapter of the Metaphysical Foundations of Natural Science from 1786). This book as a whole and this chapter in particular have to be read as a completion of the Critique of Pure Reason (regarding the reasons see e.g. Förster's The 25 Years of Philosophy, chapter 2 and 3).

First a quote about how the following concepts have to be understood (Ak. 4:480.6-10):

I call something ‘material’ if and only if it is movable in space. Any space that is movable is what we call ‘mate- rial’ or ‘relative’ space. What we think of as the space in which all motion occurs—space that is therefore absolutely immovable—is called ‘pure’ space or ‘absolute’ space.

Here it is helpful to keep in mind that he clarifies in which sense the space is movable/material. He explains that taking a point that moves relative to a related system (a relative space), we could never determine wether the point is the one moving within the system or the system around the point.

Second a quote about space that can be experienced (Ak. 4:481.12-21):

In all experience something must be sensed, and this is the real component in sensible intuition. So the space in which we are to set up experience concerning motions must also be perceptible, i.e. must be indicated by what is perceptible; and this space the sum-total [Inbegriff] of all objects of experience, and itself an object of experience is called empirical space. Now, if such a space is material, it is itself movable. But a movable space, if its motion is to be perceptible, presupposes a larger material space for it to move in, this enlarged space presupposes one larger still, and so on to infinity.

Here we have two aspects: First, the empirical space is only perceptible and constituted by objects ("indicated by what is perceptible"), i.e. it is not really perceptible itself. Therefore, it is a necessary condition for our experience, but not in the sense noumena are, because they are thought to be necessary in the sense that there has to be something affecting our senses. Second, as the relative spaces always are thought to be movable, there has to be a larger space they are able to move in, which leads us to even larger spaces and so on.

Therefore, for preventing infinite regress, there is the idea of an absolute space (Ak. 4:481.28-33):

An absolute space—i.e. a space that isn’t material because it isn’t movable—is something we assume because it is required for the possibility of experience. But in doing this we are assuming something that can’t be perceived in itself or in its consequences. Furthermore, although we need this assumption for the possibility of experience, we never have any experience in which absolute space plays a part. So absolute space is in itself nothing; it’s not any kind of object.

As you can see, THE space can never be perceived and isn't even an object. As not being an object and not having any corresponding intuition, it also cannot be a thing-in-itself in the classical sense (at least we cannot prove its reality). It is a purely ideal space.

  • I read from your quotes that Kant introduces the following types of spaces: 1) movable space 2) empirical space 3) absolute space. ad 1) I do not understand the definition. What does it mean to move space? Kant jumps from "movable in space" to "movable space". ad 2) I see a slight similarity between Einstein's spacetime and Kant's empirical space. Because also the former is perceptible by its curvature. ad 3) I do not see the necessity for a further type of space (absolute space), required for the possibility of experience. All non-quantum events are events in Einstein's spacetime. – Jo Wehler Feb 27 '16 at 23:51
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    @Nelson Alexander If you don't know the book already I would like to address your attention to Greene, Brian: The Fabric of the Cosmos (2014). Greene starts with recalling the different conceptions of space due to Newton, Mach, and Einstein. Chapter 2 is entitled "The Universe and the Bucket". But in the light of General Relativity I consider all other conceptions of spacetime outdated. And Kant's three different space concepts - not invented by a working physicist - seem to me a bit overengineered. Do you really understand what "moving space" means and what this term explains? – Jo Wehler Feb 28 '16 at 18:29
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    @Nelson Alexander According to General Relativity there is only one spacetime with its metric and curvature. What moves relative to each other in Galilei's ship example, are the observers and their preferred coordinate systems - not certain spaces. The Galilei-transformation allows to convert the coordinates of one inertial system to the other. Velocities transform but accelerations are invariants. - Aside: In his book Greene gives also an introduction to General Relativity :-) – Jo Wehler Feb 28 '16 at 18:55
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    I was just trying to describe what the Kant excerpts seem to be saying. And I believe Kant was an able "physicist" in his day, though not an experimentalist, of course. As to the reality, by the time I get a feel for GR, it may no longer completely prevail, having now read Smollin and others on the "reality of time" or Susskind on "holographic principle." My God! People who know basically nothing, like me, can only wait for the cosmological dust to settle. – Nelson Alexander Feb 28 '16 at 19:04
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    @alexander: Rovelli, in this interview, 'you ask about a way of overcoming this separation [between physics and philosophy]. A good start would be physicists stop talking down philosophy; for centuries, physicists were cultured people, who knew the main philosophical ideas of the past ..'; – Mozibur Ullah Feb 29 '16 at 12:31
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It is a priori in the sense that it is a "condition" of experience. Walking and measuring distances is empirical... but space (and time) is what makes these experiences possible according to Kant.

It is true that it is only a posteriori that we even get the idea of space. Meaning if we didn't have experiences we wouldn't even get the idea of space. But by analyzing our a posteriori experiences (experiencing things in space and time), we find necessary pre-conditions for any sensory experience. So we get a priori information by analyzing our a posteriori experiences.

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    The technical term would be a posteriori, not post-priori. And adding references would very much improve this answer, as well as an actual covering of the actual question. – Philip Klöcking Feb 28 '16 at 18:31
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    "Post-priori" reminds me of those grocery stores in the U.S. called "Superettes"... might turn out to be a useful Kantian term. – Nelson Alexander Feb 28 '16 at 19:09

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