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“Things in themselves” and noumena are similar in Kantian metaphysics (Critique of Pure Reason, mostly) and interchangeable much of the time. The phenomena/noumena divide is integral to Kantian metaphysics, so it is natural to wonder where “things in themselves” fall.

The Stanford Encyclopedia of Philosophy has a useful section discussing this (Things in themselves, noumena, and the transcendental object) where noumena are divided into “noumena in a positive sense” (positive noumena) and “noumena in a negative sense” (negative noumena). Then it is argued “things in themselves” are a subclass of negative noumena.

However, this provokes the question “What is the difference between positive noumena and negative noumena?”. The entry is difficult to understand on this matter.

Other natural questions are “Are there negative noumena that are not things in themselves? If so, what are they? What are some examples?”.

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    Negative (this is not-p) and positive (this is q) determination of a thing play a role here: negative noumena are defined by "this thing, but not as we conceive it" - negatively, while positive noumena are defined by "conceived by intellectual intuition". One may object that intellectual intuition is only negatively defined as "not representing sensual objects", but that's not true: It is an intuition that realises (makes real) the things it conceives by conceiving it (§75 CoPJ, IIRC).
    – Philip Klöcking
    Sep 2, 2021 at 15:36
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    Pace SEP, noumena, negative ones especially, are not things in themselves, at least not in intension. They are abstract posits of the intellect, while the thing in itself is intended to be something ontological they aim at. There is a detailed study of fine distinctions b/w noumena, transcendental objects and things in themselves (and phenomena and appearances) that flow from the interplay of empirical and transcendental perspectives in Palmquist, Two Perspectives on the Object of Knowledge (from his book Kant’s System of Perspectives).
    – Conifold
    Sep 2, 2021 at 20:07
  • I guess mathematical things would be in the positive noumena class, as defined by the intuition we have of them?
    – CriglCragl
    Sep 2, 2021 at 23:18
  • @CriglCragl While Kant was sympathetic towards mathematics as a pure, a priori science, things generally are objects of experience, and that is what he means here. An intuition means specifically that which is the touching point between intellect and the world, as it were.
    – Philip Klöcking
    Sep 3, 2021 at 19:27
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    Thinking about it strictly within Kantian thought, it is also important to think of it as a limiting concept (Grenzbegriff) of our understanding. We can do without negative noumenon if we talk about the set of possible knowledge (Erkenntnis) only, but not if we are talking about the limits of possible knowledge since then it is an important concept determining these limits.
    – Philip Klöcking
    Sep 12, 2021 at 21:16

3 Answers 3

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Since Kant holds that, "Space is 3-dimensional," and, "Time is 1-dimensional," are synthetical, he leaves the door open to conceiving, but not visualizing (imagining), higher-dimensional space/time. But these representations are then noumenal without being representations of ding an sich, because if our space/time sensibility were equipped with the capacity for higher-dimensional imagination, yet it would still be sensibility and not intellectual intuition. (We might also ask about using e.g. imaginary numbers as signatures of dimensionality, I suppose, which would make for even more exotic noumena...)

There are also relatively positive moral representations ("perfect duty," "the type of the law," "ends in themselves," "proper respect," etc.) that fall enough on the side of noumenal representation (per the moral resolution of the Third Antinomy), or there is even the representation of the transcendental ideal, the ens realissimum, as a sum or focus for all positive properties in general. As for the use to which these are put: they are more regulative and less constitutive as principles, so there is a limitative quality to them, hence something negative (but we should be able to speak of noumena that are both positively and negatively functional, as representations, like how we say that zero itself is positive and negative).

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First, I don’t know the technical answer. I am not a Kant expert or a detail expert.

Whatever old metaphysics was, that’s what the things in themselves are. Loosely speaking a necessary structure. I would use the same word as Hegel. A Logic. Hegel’s Logic is said to be Ontological. It’s the grand logical movements of Being that tie it all together and proceeds along, things like that. Even though I have always thought of Hegel as sort of open ended “until reason prevails” (my words).

You see the logical connections, purposes and ends especially with Aristotle and Aquinas. Hegel then is the new Aristotle-Aquinas-with Spinoza thrown in. Something like that.

Unmoved mover (Aristotle) sets it going because logically it has to do so, and there is a purpose to things. Or God (Aquinas) sets it going with ends in mind. Everything is connected.

What is NOT merely empirical. The big necessary logical narrative we arrive at through intuition as Klocking says. Philip helps me a lot with his discussion of intuition.

Kant gave us a restricted OS and software. Gauss and Einstein changed at least the Trans Aesthetic software. In other words these are software updates to Kant. Kant can be fixed with a mere software update perhaps, updating us with non-Euclidean geometry etc. Kant was a genius but he really was the end of “real” Philosophy. He knew this. He tipped his hat respectfully to things in themselves. Out of respect.

(The idea of making a kind of update to Kant was very generally E. Cassier’s idea)

Now we have philosophy as the mere handmaid to science.

Whereas the only real Philosophy is true, “logically required” metaphysics that we can know and discuss. You don’t just give a software update to a logically necessary Metaphysics.

Kant seems to say we can’t know big metaphysics, so Philosophers can’t discuss it. Then Hegel discusses it like crazy. Which of course changes the world (Marx etc) and makes Popper furious.

People are very wrong when they say we can just ignore Kant’s things in themselves. Kant was a brilliant by insisting on things in themselves. He retained that. He gives a kind of peculiar beacon of hope. A Hopeless hope and he showed respect.

Kant threw down the gauntlet, and Hegel eagerly picked it up. Maybe too eagerly. But Kant DID throw down the gauntlet, and we have to love him for it.

PS. The OP’s question seems to be an academic question within Kantian studies and I don’t know enough to answer it. I’m more interested in what the next major philosopher (Hegel) made of Kant’s project. Here is a review from Telos journal.

On Hegel’s Critique of the Noumenal in Kant Link https://www.telospress.com/on-hegels-critique-of-the-noumenal-in-kant/

Taking off from the above link:

There is no “One” that can stand apart. Meaning, in general, no Descartes. Which means we use Spinoza. Illustrated by Engels:

· Oct 27 "Labor is the source of all wealth, the political economists assert... But it is even infinitely more than this. It is the prime basic condition for all human existence, ... in a sense, we have to say that labor created man himself" Friedrich Engels.

Ie our dialectical struggle with the world. Meaning real struggle. We can’t stand apart and consider our own cognition because it is built from an evolving (dialectical) encounter with the world. With Engels, “labor” We are immeshed in the process.

Another Engels quote: Quote: "So do you think", I asked, "old Spinoza was right when he said that thought and extension are nothing but two attributes of one and same substance?" "Of course", Engels replied, "old Spinoza was quite right". Conversation, Plekhanov and Engels.

And and also from the Telos review of Booth:

Kant preserved the “many” which man collapsed into one. Copernican Revolution Whereas in Hegel the many is already Forced into the One when man comes upon it. Concept of Force. “Hegel’s force overcomes the Kantian antinomy of the phenomenal and noumenal reality,”. See quote from Jean Hyppolite here:

When we envisage the fall of a body in space, we posit the same being twice: as reality, the motion is a juxtaposition that can be broken down into parts . . . but we can consider the “whole of the motion,” the integral of which it is the realization. We then have force, the content of which is identical to its manifestation, but which formally differs from that manifestation.[4] Telos Hyppolite

PPS. Instead of Labor struggle, Hegel would suggest probably a Bildung of the Spirit. But it would still be a school of hard knocks.

The Telos article doesn’t use Engels, rather it features Adorno, Heidegger and Jean Hyppolite (Hegel Scholar) When I speak of Labor struggle here, I do not mean a struggle against Capital. But literally a struggle to survive in the world. Popularly speaking, evolutionary struggle.

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Kant must define noumena as a thing that is thought but not sensed. He cannot give a positive definition of noumena without contradicting the position that we cannot know anything about noumena through speculative reason.

Noumena is therefore an epistemological designation, not an ontological designation like thing-in-itself. Mathematical objects are things that are negative noumena (not sensed but thought), but aren't things-in-themselves bc they are merely formal entities (their objective reality consists of their formal reality - or the thing is merely its definition).

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  • Mathematical objects are synthetic a priori, that is, pure objects that don't come from experience, and are produced subjectively. That's out of the scope of sensible objects, which are perceived empirically by the senses, where the domain of the noumenon and phenomena correspond. Mathematical objects are NOT noumena.
    – RodolfoAP
    Oct 3, 2021 at 9:43
  • here is the problem with that. how do we do physics and engineering if mathematical objects dont relate to sense at all? they are not absolutely pure in the sense nothing related to sense but actually derived from according to kant from the sensible form of intuition of space just like the categories of substance, cause, and community are from the sensible intuition of time. My definition of negative noumena is what is not sensed but thought, positive noumena would be freedom and the moral law. You can think that noumena are physical objects, they dont even carry with them the idea of unity. Oct 4, 2021 at 22:50
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    @ Vishnu: that position fits better to empiricism, where mathematical objects are not pure, or Aristotelian Form and Matter, where forms do physically exist in nature hidden to our senses, but both are contrary to what Kant proposes.
    – RodolfoAP
    Oct 5, 2021 at 5:57
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    I get ur 2nd idea; math objects aren't "out there" in the physical reality since they are only formal. However, i dont understand why Kant can't empiricist at all? he did want to combine the two thoughts: rationalism and empiricism. I wouldnt say empiricism is "contrary" to Kants project. Oct 6, 2021 at 15:06

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