One of Kant's example of a priori synthetic knowledge is the knowledge of geometry, that is of space itself. It is a priori as it cannot be otherwise - it is independent of experience because it is a condition of experience. How would I experience the world if I was not aware of space first?

But space is definitely out there. So it must be synthetic; that is, it must rely on experience. It is definitely not analytic in that it is determined by its form or grammar.

How is this possible, since 'a priori' means independent of all possible experience? Can this mean all possible experience of that particular individual, but perhaps not of all possible experiences of his ancestors, as they are not his own experiences.

Hence a possible answer to this, and I do not know if Kant alludes to this, is that we carry all the experiences of our ancestors within us. That we know of space is because our ancestors through their own experience developed over time an intuition from their direct perception of space.

One of my ancestors is a single-celled protozoa like animal. Does it know of space? Another is a ape-like animal, does it know? And if they both do know, is the quality of one in some indefinable way better?

Essentially I'm positing an evolutionary argument for this problem.

Does this make any sense? Does Kant make this argument; and if he does, does he dismiss it out of hand for some other explanation?

  • 1
    Related Quotation: "Why is synthetic a priori knowledge necessary?" - Nietzsche
    – commando
    May 27, 2013 at 16:49
  • I'm personally having a hard time with why we must have a priori knowledge of space. You say it's because that is a condition of experience. I say it is the first consequence of experience. Just as understanding language is not the condition, but rather the consequence, of hearing it, so too is knowing space not the condition, but rather the consequence, of experiencing it.
    – commando
    May 27, 2013 at 16:57
  • @Commando: experience require space and time for it to happen. Can you imagine experience without a temporal or spatial quality to it? Perhaps if you close your eyes and attempt to get around the space around you - but are you surprised by that? May 27, 2013 at 18:15
  • @Commando: another answer may go from the biological and evolutionary. Look at a deer when it is born. It struggles to its feet. In those few seconds are you saying that it has learnt what space and time is, it has learnt how to use its limbs to move around? May 27, 2013 at 18:17
  • I am indeed saying that we instantly learn what space is. Not in any complex terms, but simply "there is this thing space, in which my experiences are located". If I was born a disembodied thought with no physical experience, I would not know what space is because I have had no experience from which to derive that knowledge. As for the deer, I would grant the evolutionary perspective, but simultaneously argue that this makes it technically a posteriori, since at its roots such instinct comes from experience. Even if knowledge of space was similarly evolutionary, it would be a posteriori.
    – commando
    May 27, 2013 at 18:30

5 Answers 5


According to Kant, space is not definitely "out there." We have no way of perceiving the things as they are in themselves (the noumena), because all perception is mediated by the mind and our senses. Therefore to say that space is out there is to make an assumption that we have no way to verify. Space and time, according to Kant, are the forms of intuition, the way that our perceptions may be determined. So rather than thinking of space as something out there, it is the way our mental equipment represents the things we perceive (the phenomena):

"Thus, if I take away from our representation of a body all that the understanding thinks as belonging to it, as substance, force, divisibility, etc., and also whatever belongs to sensation, as impenetrability, hardness, colour, etc.; yet there is still something left us from this empirical intuition, namely, extension and shape. These belong to pure intuition, which exists a priori in the mind, as a mere form of sensibility, and without any real object of the senses or any sensation." (A21/B35)

"Space is nothing else than the form of all phenomena of the external sense, that is, the subjective condition of the sensibility, under which alone external intuition is possible." (A26/B41)

Kant specifically denies that space is a property or relation of things as they are in themselves:

"Space does not represent any property of objects as things in themselves, nor does it represent them in their relations to each other; in other words, space does not represent to us any determination of objects such as attaches to the objects themselves, and would remain, even though all subjective conditions of the intuition were abstracted." (A26/B41)

Secondly, a priori knowledge could in no way come from experience, not even as an inheritance from our ancestors. Otherwise, Kant's Critique would have been a total failure, because his whole purpose was to find justification for metaphysical principles such that they could be known with necessary certainty. If a priori knowledge did have its origin in experience, it could never rise above the level of contingency, because experience could at some point provide evidence to disprove it. John Locke made the mistake of thinking that he could derive such principles from experience:

"... we have to thank the celebrated Locke for having first opened the way for this inquiry. But a deduction of the pure a priori conceptions of course never can be made in this way, seeing that, in regard to their future employment, which must be entirely independent of experience, they must have a far different certificate of birth to show from that of a descent from experience." (A85/B118)

David Hume, on the other hand, didn't fall into the same error. However, even though he recognized that such principles had to originate in the understanding independently from experience, he failed to see how such principles could be applied to experience:

"David Hume perceived that, to render this possible, it was necessary that the conceptions should have an a priori origin. But as he could not explain how it was possible that conceptions which are not connected with each other in the understanding must nevertheless be thought as necessarily connected in the object..." (A93/B125)

So to answer your question specifically, there is no evolutionary argument for the problem, because it would still be rooted in the contingent uncertainty of possible experience. The most experience can do is provide us with undetermined intuitions. Concepts, on the other hand, are abstractions from raw intuitions. In order to understand Kant, it's essential to understand that intuitions don't abstract themselves. There's nothing in intuitions that suggests the possibility of concepts or knowledge. It's the difference between seeing a mix of colored paint on a canvas and seeing what the painting is depicting. It's difficult to explain, because we tend to take too much for granted. Understanding these things requires some careful reflection.

Take Descartes, for instance, when he said "I think, therefore I am." In that affirmation, he found the kind of certainty that experience can't provide, and from that he had something to build upon to develop his philosophy about the world. Kant also took the same starting point, but he went in the opposite direction. Instead of simply regarding it as foundational, he sought to understand what foundation such certainty has:

"But this representation, 'I think,' is an act of spontaneity; that is to say, it cannot be regarded as belonging to mere sensibility. I call it pure apperception, in order to distinguish it from empirical; or primitive apperception, because it is self-consciousness which, whilst it gives birth to the representation 'I think,' must necessarily be capable of accompanying all our representations." (B131)

"For the manifold representations... must conform to the condition under which alone they can exist together in a common self-consciousness, because otherwise they would not all without exception belong to me." (B131)

Notice that he's saying here that representations could not exist in a common self-consciousness, i.e., the "I think" wouldn't be possible, unless certain conditions are met. To discover those foundational conditions, he had to treat "I think" as a conclusion to be derived from principles that are even more fundamental. In other words, he was digging deeper than Descartes in order to discover the conditions that make thinking possible; when you do this, then what you find is: you can never get past the foundational elements of knowledge, such as concepts, to discover some basis in experience, as if raw intuition could themselves provide the possibility of knowledge. Multiplicity, for example, doesn't itself suggest the idea of possible unity. A whole doesn't suggest the possibility of parts. Those are abstract concepts which presuppose the ability to abstract. For that reason, Kant concluded that a priori knowledge is rooted in the understanding itself:

"[T]he concepts met with in metaphysics are not to be sought in the senses but in the very nature of the pure understanding, and that not as innate concepts but as concepts abstracted from the laws inherent in the mind (by attending to its actions on the occasion of experience), and therefore as acquired concepts. To this genus belong possibility, existence, necessity, substance, cause, etc., together with their opposites or correlates. Such concepts never enter into any sensory representations as parts, and thus they could not be abstracted from such a representation in anyway at all." (Inaugural Dissertation, sec. 8)


My understanding is as follows. Being 'a priori' does not mean independent of all possible experience. It means a proposition that can be be understood independently of experience. "Can" is the key word here. There's nothing stopping an a priori proposition from also being known empirically. Consider the cliche, but lucid, bachelor example, "All bachelors are unmarried". This is a priori as it can be known without the need to investigate the world. By understanding the concept of a bachelor and what must be true if one is a bachelor you can infer that the statement must be true. However you could also know this empirically by going and checking that all bachelors are, indeed, unmarried. In Saul Kripke's "Naming and Necessity" he uses the example of a computer checking for primes. If you ask a computer if 7 is a prime number then it will tell you. You have discovered this empirically, based on your understanding that the computer is a reliable source. However you can also discover this independently of worldly experience by checking that it meets the requirements for a prime number.

I might be misunderstanding but it sounds like you're making a fallacy of equivocation by using the word "space" to mean different concepts. There is a distinction between physical space and and and theoretical, geometric space.

[Source]: "In short, we ought to distinguish (1) the space described by a mathematical theory, from (2) the space of experience and physics, from (3) the space of human intuition —even if under some theories these are intimately related to one another."

Kant makes that distinction, if a little indirectly by pointing out that some geometrical concepts that are true (in the general sense of the word, not the philosophical sense), are not necessarily true in physical space.

"there is no contradiction in the concept of a figure which is enclosed within two straight lines....The impossibility arises not from the concept in itself, but...from the conditions of space and of its determination."

Saying "we know of space" is too unspecific a statement to be usefully analysed. What type of "space" are you referring to?

Again, apologies if this is just me misunderstanding your argument but "So it must be synthetic. That is it must rely on experience." sounds like you're saying that being synthetic means it relies on empirical experience. Being synthetic doesn't inherently mean that it is a posteriori (empirical). To be synthetic merely means that it can not be known purely based on the concepts expressed by the words. Basically it's anything that isn't analytic.


My original question related to theorems of euclidean geometry 'learned' in secondary school which all seemed to me so obvious that I could 'see' immediately how to prove them. Reading philosophy at university later, it seemed likely to me that this was an example of a priori knowledge. I had not decided whether it was synthetic.

It being a priori was because there was no reference to space as such, made by the drawings on the blackboard.

Thinking about it now - many years later - I'm 73yrs old - I wish to say those propositions are synthetic a priori.


I am sorry for Kant but there is no such thing as a priori knowledge - he couldn't know since he lived before Darwin and modern neuroscience. Everything we "know" has to be learned and there are three levels on which we "learn" what he might consider a priori knowledge:

  1. Over hundreds of years and thousands of generations we, the humans had to "learn" what senses are useful to us, in what space they should be encoded and what the building blocks for a smart sensory evaluation are (neurons). A plant for instance does not "know" space.
  2. During our development as individuals, our nervous system had to learn how to relate sensory input and structure it. If you close the eyes of an animal while it grows up, it will stay blind even if you open them when it is grown up. This is because it's nervous system did not learn how to relate the spacial information (connectivity of primary visual cortex). A blind person for instance has a different notion of space than a seeing person especially for two-dimensional spaces.
  3. During the evolution of our culture as mankind, we had to learn how to communicate and how to come up with concepts such as vision and space that allow us to describe the world. If nobody ever told us that we have a notion of space, we would not realize. A feral child for instance is not aware of the concept of space because it never got introduced to a culture with the according words and concept.

I think to answer this question, it is very important to realize that even though Kant was a brilliant thinker, he might have introduced concepts and ideas that are obsolete. I claim the idea of a prioi knowledge is one of them and the findings of the last hundred years in neuroscience and biology support me in this claim.

  • Couldn't evolved instinctual "knowledge", like a newborn colt's ability to walk, be considered a priori? Some distinction between generational learning (human syntax inclination) and lifetime learning (semantics) is useful.
    – obelia
    Sep 7, 2013 at 17:15
  • A distinction between these two processes definitely makes sense. But in the case of the brain development it is very hard to distinguish them. The idea that genetics regulates the brain development of the fetus and as soon as it is born, it starts to learn, is a misconception. Even the nerves in the foals motor areas need to learn the right mapping during it's development in the mother (you can see them moving in the mare). Neurons don't wire correctly if they do not get activated - so a nervous system does a priori (before activation / experiences) not know anything.
    – Brandli
    Sep 8, 2013 at 18:49
  • The information supplied by science is empirical, a posteriori. The epistomological basis for a priori knowledge is by definition independent from empirical knowledge, so the idea that science could render it obsolete doesn't even make sense.
    – user3017
    Jan 7, 2014 at 15:09

The notion of analytic a priori, is one of the biggest myths in philosophy, because once a premise contained within a statement is realized, the conclusion can no longer be a priori. Synthetic a priori (as intution), is closer to being baseless, but that still falls short. The only true form of a priori is sensual information

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