According to Kant our empirical experience is synthesized from sensations through categories. Apparently, unconscious "productive ability of imagination" mediates the process using the schemes of space and time. Curiously, Kant's examples of this (mental) synthesis come from scientific reconstructions, such as Euclidean geometry or Newtonian mechanics. So it seems that Kant identifies mental synthesis of knowledge with its reconstruction in sciences, where indeed some mathematical structures are a priori necessary to make empirical claims meaningful (like notions of geometry and calculus in mechanics).

In hindsight, Kant's identification was clearly wrong, but could he still be right about the mental part? Our spatial intuition is still entirely Euclidean, so it would seem that "mental a priori" are Euclidean as well. In science, on the other hand, the mathematical structures (according to Cohen, Cassirer, Reichenbach, etc.) are only relatively a priori, they evolve over time. But if science can evolve, and the unconscious mental synthesis can not, there is a problem.

QUESTION: Was Kant right that our minds use space and time to synthesize perceptions, if so is that space Euclidean? If empirical experience is synthesized according to a priori schemes how do we manage to extract something from it that does not conform to these schemes?

This is not specific to space and time or Kant, whatever mental schemes or categories are used to synthesize perceptions they can not keep up with evolving scientific descriptions. If categories are "conditions of the possibility of knowledge" how is it possible that scientific knowledge eventually violates conditions of its possibility?

EDIT: jobermark's answer gives a nice example of a priori in color perception, which should not be controversial. But this highlights the issue: neither color nor space perception evolved since ancient Greeks, or even since prehistorical tribes, while science did. If Kant was right about mental a priori then he had to be wrong about something else, like the acquisition of knowledge. Perhaps, reason can take from perceptions more than it put there itself after all. That would require a mechanism for forming new schemes/categories, which are not hard wired (and listed in Kant's table), but are extracted from perceptions somehow.

If we do have such a faculty how does it work?

  • Reflective function of the power of judgement. It is building concepts through which we perceive all the time. It is unclear how the genenesis of the twelve categories works, since all he is saying is that they are necessary conditions of the possibility of perceiving determinate objects (and only therefore for knowledge as well), not that they are "hardwired". Sensibility (or imagination) does not materially go beyond Euclidian space, and science does so only formally. Nobody is able to imagine a representation of objects in non-Euclidean space. They all use analogies or formulisation.
    – Philip Klöcking
    Commented Jun 28, 2017 at 14:31
  • Kantian schemas are used by knowledge acquisition in a synthetic a priori way and both of them are mostly fine so far in respect of synthetic a priori, it’s just the fact that since Kant scientific progress brought us tremendously more knowledges in the synthetic a posterior way which actually affects very little in above Kantian transcendental ideal intuitionism, if any at all… Commented Oct 3, 2023 at 7:36

6 Answers 6


You made the question clearer, but my other answer was already too long. Sorry to be kind of rude in giving another answer before anyone else has.

Going back to color, I think I can give at least one answer. By applying another a priori model, that of linear order, to color, we have the model of the spectrum as an alternate representation, and one that transcends our own perspective and allows us to unify it with that of other animals. It also hints at a non-circular view of color and points the way toward radio waves and gamma-rays.

So categories can modify our understanding of other categories in ways that are not implicit in their original forms.

Likewise, we have taken the notion of dimension implicit in space, and the notions that come from higher numbers, and defined 11-dimension manifolds. We have taken notions of continuity and infinite subdivision to realize that we can have dimensions that are too small for anything real to travel through them. So the stuff behind String Theory does not involve the creation or discovery of new categories, only the rearrangement of existing intuitions in bizarre and unexpected ways.

In "Metamagical Themas", Douglas Hofstadter calls this notion of creativity his 'knobs' theory. The idea is that there are so many potential intersections already implicit in the categories we already experience that simply combining them in different ways, 'turning up or down the X knob on Y' can account for even highly creative discoveries in retrospect.

So we can take away more than we put into an intuition by fruitfully combining it in new and interesting ways with other intuitions, even if there is not a continual supply of truly new modes coming from anywhere.

  • Very interesting. Frankly, I am puzzled that Kant came out so strongly about it no matter how much he believed in geometry and physics: "experience itself is a kind of cognition requiring the understanding, whose rule I have to presuppose in myself before any object is given to me, hence a priori, which rule is expressed in concepts a priori, to which all objects of experience must therefore necessarily conform, and with which they must agree".
    – Conifold
    Commented Nov 5, 2014 at 2:59
  • How much of Kant's philosophy can be 'saved' if the question of mental a priori is merely empirical, not transcendental, and their significance is merely psychological because our mind can create new categories whose "rule" we don't need to "presuppose"?
    – Conifold
    Commented Nov 5, 2014 at 3:01
  • Kant would probably be horrified by this kind of reinterpretation. Rescuing his insights does not rescue the philosophy behind them. A lot of his real thinking is about protecting idealism from materialism, and harmonizing the concepts, as they seemed destined to destroy one another. I don't have this fear, because of this (possibly quirky) bias of my own -- I think the development of physics has proven physicalism an undecidable proposition, every time we crossed the boundary of what is acceptably 'pysical' it has just retreated. So both will survive.
    – user9166
    Commented Nov 5, 2014 at 14:32
  • But from the thoroughly psychological point of view, we are discovering more and more that this is how it works, we have evolved biases that are basically impossible to see past, except insofar as we use a different part of the mind the subvert them. Even then, they are very unstable. I think that is a powerful insight that many of us need to pay more attention to. But I don't believe the process is a perfect closed circle. Your quote almost takes us back to Socrates drawing in the sand and saying 'so, you remember!' It is too circular to account for any variation in intuition.
    – user9166
    Commented Nov 5, 2014 at 16:29

It might make sense to back off from something as basic as space and time to color. Clearly, we do not perceive color in a way that clearly maps to any thing other than our own evolved senses. Outside of the realm of human beings, the primary colors are not the same, and there are not always three of them.

Our eyes seek certain colors and isolate them, but not for some philosophical or hard-physics reason. We have a three-primary color wheel because it is inborn. By certain theories, we evolved from apes that ate fruit, so we have sensors primarily for water and unripe and ripe fruit. We would not have this model of color if we did not impose it.

But basically, there is a continuum of wavelengths, and different animals have evolved different peak sensors that fit their more specific goals. Dogs see mostly blue and a very fine gradation of browns and tans -- presumably because water (which reflects the sky) is important, and so is the exact marking of various forms of small animal fur...

There is a lot of evidence we are equally aggressive about our construction of space: the timing of the ways we process 3D objects; the way we construct object constancy when fooled; the fact that we imagine we have full and constant coverage of our perceptual space even though a lot of the information we make it up of is very stale, and there are two big blind spots right near the middle of it, etc. (enter groupie mode) Daniel Dennett collects a lot of it, in Consciousness, Explained. (exit groupie mode) This -- https://www.youtube.com/watch?v=dSopiOvWhMQ -- captures some of the highlights.

So I would say that our model of space is as inborn as our model of color, and that Euclidean space is the model we project. But it is evolved, and it can continue to evolve, if a better model eventually really offers breeding advantages.

(Warning, this is a very idiosyncratic answer, and my favorite topic...)

Time is more of a question in general. But it is clear to me. Memory is achieved via an exothermic chemical process. So if time moved backward, in the sense that entropy locally decreased in a fine-grained and uniform way, we could never remember it.

I would suggest that what we perceive as quantum indeterminacy is, in fact, time flowing backward often, but by a very small amount, in an way constrained locally by the wave 'shapes' of the particles involved. If this happened too much, we would perceive way-too-much of the universe as random, so we must inhabit a 'timeline' where time progresses forward in general, away from some point of very low entropy. But the pressure that makes it do so could be imperfect, and allow for temporal eddies to arise constantly. (This model is basically Boltzmann's theory of the universe as a deep entropy well, favoring the second law of thermodynamics as a trend rather than a rule.)

Edit -- (more groupie mode)

At the risk of just going on forever. I think it is also a marker of Kant's clarity that in each case there is a physically real underlying thing, of which our evolved model is a loose wrapper, in echo of the idea that behind he 'real underlying thing' there is theoretically another 'underlying thing' that is real in a different sense. And he reached this conclusion before we realized our actual inborn model of space or time had any difficulties at all.

  • +1 for the top part. I also like how you specify which part is your view in the bottom part. I'm not sure about your bottom view, because of the way I understand entropy to work, viz., it takes a lot of energy to put things in order -- always more than the amount of order it generates.
    – virmaior
    Commented Nov 4, 2014 at 4:57
  • From Boltzmann's point of view, it takes a lot of energy to resist the trend in entropy. He theorized that there would be parts of the universe/timeline where entropy was the rule and not the exception, and in those parts it would take a lot of energy to create entropy. (The fact the two really did not seem related, logically, but always were, implied to him there was something else, more local, going on.)
    – user9166
    Commented Nov 4, 2014 at 14:29
  • That means there are large parts of the universe beyond our detectable universe, either too far away, or far in the past or future, where our physics would just make no sense, because our ways of measuring time would not accord with the actual action of time. It gave others the idea for the current 'competing universes' models in physics.
    – user9166
    Commented Nov 4, 2014 at 14:38
  • I guess I should have marked those, so retroactively @virmaior on those last two comments.
    – user9166
    Commented Nov 4, 2014 at 20:06
  • 1
    @jobermark - Given that there exists a Big Bang of some sort, the fluctuation theorem specifies that time flows away from it. "Why is there a Big Bang instead of everything being in equilibrium" is another question that I personally am much less interested in due to doubts that we have any way to make progress on it. (Also, a heck of a lot of macroscopic systems get dragged along through time like we do, so calling it "human" is kind of presumptuous.)
    – Rex Kerr
    Commented Nov 4, 2014 at 20:54

Yes Kant was right about space and time (and no he was not wrong about knowledge) where being right about space and time and not being wrong about knowledge are epistemological claims.

Critique of Pure Reason is a response to radical skepticism. It offers the comfort of legitimizing the existence of facts in regard to empirical phenomena. The price is that the these facts are always subject to the caveat that they are mediated through and limited by the natural limits of human experience.

We can talk as if the results of an experiment confirm facts about space and time, but we're simply committed to a convenience. Humans can wonder What is it Like to Be a Bat, but it is an error to assume there exists some bat so Nagely as to wonder what it is like to be a human. There is no legitimate basis for a claim that bats can wonder at all.

To say that "Kant was clearly wrong" is to misunderstand the problem he was tackling. For millenia, the best philosophical responses to radical skepticism required Descarte's gods and proofs thereof. After Kant, it was still about two hundred years until G.E. Moore's offered a simple god free response to radical skepticism. However, the horrible price for Moore's stance is any claim to being clever.

  • I think Critique is concerned with apparent universal validity of some theoretical claims rather than empirical facts. Since then we learned that this validity is far from universal in the first place. So historically, Kant's solution was a superb one as his influence even today indicates. But with the benefit of hindsight it is easy to see that some parts of it can not work. I think it's a testament to his insight though that there were good reasons for him to suggest them, and replacing them is not at all easy.
    – Conifold
    Commented Nov 5, 2014 at 18:46

If Kant is to be saved, then the categories of space and time must be more abstract than is the case in either Euclidean or non-euclidean geometries, such as would contain implicitly all possible geometries. Schopenhauer identified the principle of sufficient reason as being at the root of all knowledge relations, whether logical, geometric, temporal, or causal. If Schopenhauer, a neo-kantian of sorts, is correct in this identification, then neokantianism has an explanation for how scientific/mathematical models can be extended beyond the scope of any one form of the principle of sufficient reason (where temporal, geometric, logical, and causal relations are the four forms of of the principle) by mixing up the forms in various ways, say deriving geometric axioms such as those in a given non-euclidean system, from the geometric category and using the category of logic to derive implications that themselves wouldn't result from the strict rendering explicit of geometric relations.


I think that the answer to Molyneux's problem was a conclusive "No", which means that individuals likely do not have an in-born sense of geometry of space, and certainly not a Euclidean one. i.e./ Project Prakash did research on individuals suffering from near blindness, and found they could not distinguish between objects by their shape at first, despite years of 'knowing' what those shapes were by touch.


  • This is missing the point. The question is about the form of sensual and particularly visual intuition [given there is sensual input], not about whether the representations given by different senses can intuitively be brought in correspondence. The interesting thing highlighted here may be that touch seems to represent things inherently different from sight.
    – Philip Klöcking
    Commented Jan 16, 2018 at 19:54

The question has it that 'Kant's identification was clearly wrong', but not about anything in particular -- what is 'scientific reconstructions, such as Euclidean geometry or Newtonian mechanics'? Kant doesn't mention 'Euclidean geometry', for example, in so many words. This proceeds with something about how 'Our spatial intuition is still entirely Euclidean, so it would seem that "mental a priori" are Euclidean as well.' I find this rather loosely stated for the purpose -- 'Our spatial intuition' seemingly means nothing in particular, and would mean nothing in particular, I suppose, to Kant. I think the word 'intuition' seems ripe for equivocation here. Is it the ability to understand something immediately? Is it a thing that one knows or considers likely from instinctive feeling rather than conscious reasoning? I figure these are usages of the term 'intuition', but not that it gets us very close to Kant. I know that I'm quibbling about something that may seem a trivial distinction -- does 'intuition' mean 'unexplained feelings that something is true'? Does 'intuition' mean 'going with our gut instincts can help guide us to faster, more accurate decisions'? I would emphasize that if we are seriously considering what Kant says, then okay, what is it in so many words, that Kant says?

While I am quibbling, I see this: 'If Kant is to be saved, then the categories of space and time must be more abstract than is the case in either Euclidean or non-euclidean geometries, such as would contain implicitly all possible geometries.' Well, space and time are not 'categories', Kant has a list of 12 categories. Gotcha. There is a point here too, about 'all possible geometries', fine. A related point is that we can invent new ideas in mathematics and call them discoveries. So, mathematics is an interesting science, what are these scientific methods? It's a question, whether you read Kant or not.


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