In Paul Guyer's Kant, section "Space and Time: the pure forms of sensible intuition", Guyer argues that "Kant’s argument for transcendental idealism is incomplete."

For that, he gives two arguments. The first is basically that Kant merely asserts that space is a priori, dismissing some possible alternatives, which I can follow. The second one is a bit more tricky for me - I can see it in a certain logical way, but I can't imagine how things would be if we did not make this assumption. These are Guyer's words:

Second, he is assuming that we can say of any particular object that we perceive in space and time that it necessarily has the spatial and/or temporal properties that we perceive it to have.

I thought that space and time, as a priori intuitions are precisely the "rules" with which we perceive objects. So the alternative path for this assumption would be something like "our perception has rules but its objects don't really conform to them". Could someone clarify this?

In more Kantian terms, I'm guessing that for this to be true we would need to separate

  • the "form of sensibility" that holds the rules which sensations would really conform to, and
  • the "singular intuitions of space and time", a simplification of the form of sensibility.

Would that be correct? What would be the implications of this scenario? Couldn't Kant raise a contention here that in this case the second is not anymore the "singular intuitions of space and time", but "singular intuitions of simplifications of space and time", and that we would necessarily have another "singular intuitions of space and time"?

To be clear, I'm not (only) asking why Kant holds the views he does, but how it could be possible for Guyer to consider the second assumption to be false, and if it were false, what that would imply.

  • Kant could contend that supposed "singular intuitions of space and time" can be misconceived in some cases, but then Guyer's point is how do we know that what we "perceive" in individual instances is, in fact, necessary spatial/temporal properties derived from the a priori forms of sensibility. Kant gives some criteria for a priori properties, the chief ones being necessity and universality, but judgments of necessity and universality are ultimately empirical generalizations. This is not idle concern. Kant surmised that Euclidean geometry is necessary and universal, arguably mistakenly.
    – Conifold
    May 8, 2022 at 8:49

2 Answers 2


Understanding Kant on pure intuition is difficut. And attempting to understand Paul Guyer's interpretation does not make it easier :-)

Second, he is assuming that we can say of any particular object that we perceive in space and time that it necessarily has the spatial and/or temporal properties that we perceive it to have.

In my understanding Kant makes the basic discrimination between a thing-in-itself and the appearance of a thing. We never perceive things-in-themselves. We perceive raw data and construct an appearance. The latter depends to a high degree on our pure intuition of space and time.

According to Kant it is erroneous to carry over the properties of appearances to things-in-themselves. That would be a mistake of categories.

  • My interpretation up until now was that in that quote, Guyer is only talking about objects in appearances, precisely because he makes it very clear that these are objects we perceive in space and time. Would rejecting that assumption lead us to blur the lines between appearances and things-in-themselves? If yes, how? Perhaps this phrase can give some hints on where Guyer wants to go: "he does not seem to have an argument that particular objects necessarily rather than merely contingently conform to the subjective conditions of our intuition of them".
    – gsmafra
    May 4, 2022 at 6:51
  • @gsmafra I apologize. It seems clear to me what Kant means but not what Guyer wants to explain.
    – Jo Wehler
    May 4, 2022 at 10:48

The problem with modern authors lies with the two centuries of disparagement against Kant which serves as the basis of their analyses.

Kant's synthesis of apprehension in the A version of his Transcendental Deduction clearly speaks of two manifolds.

"This act I name the synthesis of apprehension, because it is directed upon intuition, which does indeed offer a manifold, but a manifold which can never be represented as a manifold, and as contained in a single representation, save in virtue of such a synthesis." A99

At issue is that the understanding is only applicable after appearances have been ordered, connected, and brought into relation by "the formal condition of inner sense."

That this had been difficult even for Kant can be seen by his rewriting of this section in the B version. The B version does not mention an unconditioned manifold, although it still declares that given intuitions must be conditioned through time. The B version seems more focused upon how one can know one's own self as a "unity" witnessing intuition.

All he is saying here, however, is that the plurality of appearances in space must be organized into pluralities seemingly witnessed in the same moment. So, we really can have no meaningful distinction between what is static and what is invariant (whence the B version). And we clearly ought not discuss "objects" and "properties of objects" platonistically without stating how we will be speaking of such things in a manner that makes no sense with respect to Kant.

Modern analytical philosophers have been keen on studying some static notion of "truth" in support of "science." All they have managed to do is study truth as possible worlds and spacetime as many universes.

It is, therefore, somewhat disingenuous for modern authors to apply empiricist criticism of Kant. Whatever a spatial or temporal property is for Guyers, if it is beyond what can be known through (surmise from) sensibility, the denial of it is also beyond what can be known through (surmise from) sensibility. This is exactly the nature of undecidable counterfactuality that mathematicians deal with in models if set theory.

I submit that Guyers is misunderstanding his own use of "necessarily." He is writing as if necessity constrains possible properties to only those of sensibility. That is not the meaning of necessity. Properties attached to sensibility are necessary because we do not witness contradictions. What lies "beyond" necessity is modal possibility.

Max Tegmark, anybody?


Please stop regurgitating inaccurate statements about Kant and Euclidean geometry.

With reference to his translation of Kant's "From thoughts on the true estimation of active forces" (1747) William Ewald writes:

"Kant argues that physical space is not necessarily three-dimensional, and that the physical laws of gravitation determine the geometric structure of space; he further contends that a science of the possible kinds of space 'would certainly be the highest geometry that a finite understanding could undertake'. These remarkably prescient ideas were not to resurface until the middle of the next century, in the work of Riemann and Grassman on n-dimensional spaces. This passage is rarely mentioned in discussions of Kant's philosophy of mathematics; but it confutes the common assertion that Kant had no inkling of the possibility of other geometries."

The translation can be found in Volume I of "From Kant to Hilbert."

For what this is worth, I greatly respect your many comments. This one just happens to be inaccurate. But, you can find the translation and decide for yourself.

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