From the Kantian perspective, what would be the relationship between our intuitions of space and time (which form the structure of subjective experience and are not things that exist outside of human cognition) and the mathematical models of space and time that are used in theories of physics? Is Kant going to deny that these mathematical models have mind-independent existence and instead say that they are intelligible only through being abstracted from our intuitions of space and time? Do these mathematical models of space and time pose a problem for Kant somehow?

  • Bear in mind that Kant considers compelling shared intuitions like 'autonomy' to be real and mind-independent, despite that they can only be experienced in a mind. Space and time are quite as real as autonomy. So things can be real and independent of individuals, even if they are not aspects of all beings, or of some world totally independent of us. May 28, 2021 at 21:56
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    Transcendental idealism, like idealism in general, is a metaphysical position, meaning that it is about things that are beyond physics. They don't--in general--imply anything about physics that is different from what realist positions imply. There are some differences at the extremes perhaps; for example, an idealist may be more willing to accept the possibility of psychic powers or miracles than a realist, but they don't require such things. It is extremely unlikely that science would ever be able to falsify a metaphysical theory because such theories just don't make observable claims. May 29, 2021 at 0:35
  • Relevant: philosophy.stackexchange.com/a/79471/17209 - don't confuse pure intuitions with concepts of space and time.
    – Philip Klöcking
    May 29, 2021 at 5:28
  • @hide_in_plane_sight What means autonomy to be real? Has space autonomy to be real? Jun 28, 2021 at 7:46
  • @PhilpKlöcking Do you think pure intuition exists? If so then how does it look like? Intuition is always tainted with theory or memory. There is no such thing as pure intuition. Even animals dont have that. Maybe by meditation you can arrive at the point of pure intuition or pure perception. It would be a very disturbing experience. Jun 28, 2021 at 7:51

5 Answers 5


Mathematical models of space and time doesn't pose a problem for Kant according to reference here:

In 1781, Immanuel Kant published the Critique of Pure Reason, one of the most influential works in the history of the philosophy of space and time. He describes time as an a priori notion that, together with other a priori notions such as space, allows us to comprehend sense experience. Kant holds that neither space nor time are substance, entities in themselves, or learned by experience; he holds, rather, that both are elements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantitatively compare the interval between (or duration of) events. Although space and time are held to be transcendentally ideal in this sense, they are also empirically real—that is, not mere illusions.

So clearly Kant is a realist regarding space and time similar to Newton's absolutism of space (he defended Newton in his works), not an idealist such as Leibniz's space relationalism. This is consistent with Kant's famous synthetic a priori position regarding space and time, which are verifiable independent of anyone's experience under this POV. Currently most versions of mainstream physics spacetime notions belong to realistic POV.

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    What the Wikipedia quote says is that space and time are empirically real, that is, true according to a liar.
    – RodolfoAP
    May 29, 2021 at 2:50
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    @RodolfoAP feel similarly, sounds some innate contradiction (fallacy), that's why Kant's synthetic a priori metaphysics trying to bridge empiricism and rationalism has always been controversial... May 29, 2021 at 3:04
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    FYI, he explicitly rejected Newtonian absolute space and argued for relative conceptions in his only work on philosophy of nature.
    – Philip Klöcking
    May 29, 2021 at 5:31

It is a common confusion that the assertion that space and time are merely ideal is the core of Kant's theory of space-time. In any case, this part of his theory is far from contradicting contemporary science in any way, since many scientists today believe our internal spatio-temporal manifolds (let's say, string theorists) don't represent the true nature of the geometry and chronometry of the external world. This is not at all unlike many reinterpretations of Kant's theory by nineteenth-century scientists, like Helmholtz, who claimed that the world can be regarded as infinitely-dimensional and our perception gives us aspect only to a restricted plane of this real space. This is distinct from Kant's own position but remains faithful to its spirit, especially if we go into the more technical details. E.g. Helmholtz also disputed Kant's claims regarding the a priori status of geometry, but, taking seriously Kant's assertion that assuming some geometry is a necessary precondition for possible experience, developed a method for determining which geometry is externally valid without referencing any properties of things as they are (supposedly) in themselves, that is: from a strictly 'internal' standpoint of experience. I'm unsure whether this is as a methodological heuristic, and in what form, is still present in modern-day scientific investigations regarding space and time, but it's importance for the development of many important physiological, philosophical and physical accounts of these notions (like Einstein's theory of relativity) remains unparalleled, even if the relevant authors weren't aware of Kant's influence.


Let's imagine everyone viewed the world, for the sake of argument, through hyperbolic geometry rather than Euclidean geometry. Then our mathematical and physical models of the world would have to begin with that fact because that is the ground of our observations, no matter if later we found that in some way Euclidean geometry was a better fit. It's in this way that our physical and mathematical models are mind dependent.


What you are trying to do with such question is to oppose physics to perception. That is, assuming that space and time would be, from a Kantian perspective, transcendentally ideal, which existence depends absolutely on the mind, but from a scientific/physical perspective, a reality independent of the mind. In such context, you are asking for the relationship between both.

To start, science seeks for empirical truths, not final truths. When we make science, we know that the product (scientific knowledge) will be dependent on our perception, that what we come to learn is not a final truth. In such sense, any scientific approach (or any formal approach from physics) of space and time is assumed to be dependent on the mind. Finally, the physical perspective of time and space has the same basis as the Kantian perspective. So, they are (necessarily) logically coherent:

The scientific and the Kantian views of space and time are essentially the same.

In order to find the relationships between the scientific and intuitive perspectives of space and time, I will use an analogy, comparing the literary and emotional perspectives of a feeling. Both can be equivalent in the sense that they would just be two different forms of an intuition.

So, what are the relationships between the scientific and the Kantian perspectives of space and time? They are the same as the relationships between a feeling and an artistic work expressing such feeling (e.g. the relationships between joy and a poem evoking joy). The description of time and space in physics would be just a formal way to express perceptions of space and time. The only difference is that formal physical descriptions use mathematics to describe experience, and subjective intuitions of space and time are just the product of our subjective experience. But mathematics provides an additional advantage: math is not only a language to communicate concepts, like english, but also a tool that allows analyzing such concepts. So, math provides intuitions of new forms (relativity is essentially a different expression of our intuitions of space and time), like poems can provide feelings of a literary form, which would be essentially different expressions of the same intuition.

So, relativity would be essentially a set of formal conclusions raising from intuitions and empirical concepts, that are the product of a mathematical analysis. Relativity would not be possible without mathematics.

Perhaps you are probably still curious about the effect of the formal, scientific knowledge, over our intuitions. For example, questioning what does the relativistic spacetime curvature implies over my intuition of space and time? In the analogy, how does a poem of joy impact on my intuition of joy?

The answer would be: in nothing. Following the example, there would not be any qualitative change on the effect that a poem of joy evokes on my feelings of joy. In order to know any possible effect, noumenal knowledge would be necessary, so to compare it with phenomenal knowledge, to observe the relationships. Following the example, if joy would be the equivalent of a white light from a noumenal perspective, we could say that the relationship that poems have with feelings is that poems of X specific class have the capability of evoking white light on a phenomenal perspective.

  • Why does svience seek for empirical truth only? Jun 28, 2021 at 7:18
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    @DescheleSchilder Mainly, because science does not enter into metaphysical considerations. Philosophy does. Example: "Induction is the glory of science but the scandal of philosophy". C. D. Broad. (induction is necessary for finding empirical truths, while in philosophy, induction is considered as not necessarily true: plato.stanford.edu/entries/induction-problem). This is not the only conflict between empirical facts and final truths. See Kant's antinomies, for empirical/rational contradictions regarding space, time.
    – RodolfoAP
    Jun 28, 2021 at 7:37
  • @DescheleSchilder I mean science is already aware that our perception is limited so everything that we can follow from that, has that same problem. Like take a ruler and measure and object slightly bigger than the ruler and write down the results. Or pass that ruler to 100 people and ask them to measure that object and you'll not see 1 answer but several answers that ideally revolve around one value. So that value would be our assumption and the spread is our uncertainty and it's physically impossible to get rid of that uncertainty entirely.
    – haxor789
    Jun 23, 2022 at 10:46

Kant's notion of space is a transcendental one. Which means that space has an autonomous existence but it transcends our perception of space, or time, for that matter, as irreversible perceived changes of objects in perceived space. We will never, according to Kant, be able to know the transcendent reality an Sich. Which is a kind of Platonic notion, because Plato thinks the same about mathematical objects, existing in an extramundane mathematical heaven. We can perceive math, like spacetime, while not knowing how the math objects themselves look like.

In his left glove thought experiment, Kant argued that space is not relational as Leibniz stated. The relationships between the parts of a left-handed and right-handed glove are the same and still they are different gloves. So space is not relational. Which doesn't mean that space can be perceived without looking at objects that stand in a relation to other objects. Space and objects in it have a mutual dependence though. Space without objects is a, well, empty notion.

So Kant believed (wrongly, in my opinion) that space refers to something autonomous, independent of creatures, but it isn't space (or time) as we see it. As the porridge in which objects are submerged as dried raisins.

He would have regarded the modern notion of spacetime as a perception referring to an autonomous thing, substance, essence, entity, or whatever you wanna call it. But the perception isn't the real thing, which we will never be able to contemplate as we're bound to perception. Which of course can be questioned. We might perceive a transcendent reality.

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    This is a severe misunderstanding of Kant. In his Phoronomy (Ak. 4:480f) he clearly argues that a) the space we deal with in natural sciences is material, relative space that comes to us through the senses, ie. as a relation between observer and object, b) we cannot know, hence not talk about whether space exists as an as such (an sich), and c) absolute space is, if anything, an idea of reason which has only logical bearing (as idea of an outermost spatial frame of all empirical movement) but no physical/real being whatsoever. Please do not use early writings and sell them as critical.
    – Philip Klöcking
    Jun 24, 2022 at 7:03
  • @PhilipKlöcking Aha!
    – Pathfinder
    Jun 24, 2022 at 8:06
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    I am sorry that this may have come across a bit harsh. The main itch I got about how you wrote it here is that it is everything but clear that there is some "Raum an sich" (space as such). While Kant does argue that there has to be some material/empirical space, this import arguably is a mere function of our form of intuition instead of anything independently affecting us. This is even an important feature when distinguishing Kant from Berkeley. If you got any source for your reading, I'm happy to hear about it.
    – Philip Klöcking
    Jun 24, 2022 at 9:49
  • @PhilipKlöcking No problem. But, for example, what's the difference between a "severe" misunderstanding and a misunderstanding? You misunderstand or not. I notice this use of adjectives a lot here. "Serious", "grave", "unforgivable", "blatant", "severe", etc. Anyhow, the spacetime an Sich can't be known, or at least isn't the perceived spacetime. He might have considered it relational, but not as Leibniz did. That's why he introduced the left-hand glove idea. If no further objects are involved to be in relation with, a left-hand glove is no different from a right hand glove, since all...
    – Pathfinder
    Jun 25, 2022 at 11:33
  • ...relations between the parts are the same. Still the both are different, so space has a non-relational character, and it can exist even when no objects are present. I doubt this myself because space is an aid for objects to interact and you can't have an empty space, as QFT acknowledges. I'm not sure what Kant truly thought. Spacetime is autonomous. Okay. But is it the stuff we see?
    – Pathfinder
    Jun 25, 2022 at 11:39

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