The term is generally used in contrast with, or in relation to, "phenomenon" (plural: phenomena), which refers to appearances, or objects of the senses. A phenomenon can be an exceptional, unusual, or abnormal thing or event -- but it must be perceptible through the senses; A noumenon cannot be the actual object that emits the phenomenon in question. Noumena are objects or events known only to the imagination - independent of the senses.
Roughly, a noumenon may be distinguished from the following concepts, although it has been argued they are actually synonymous:
- Thing-in-itself, an actual object and its properties independent of any observer.
- The Absolute]], the totality of things; all that is, whether it has been discovered or not.
"Noumenon" is the neuter form of the present passive participle of Greek "νοείν (noein)", which in turn originates from "nous" (roughly, "mind"). Noumenon is linguistically unrelated to "numinous," a term coined by Rudolf Otto and based on the Latin numen (deity).
Noumenon came into its modern usage through Immanuel Kant. The etymology of the word derives from the Greek nooúmenon (thought-of) and ultimately reflects nous (mind). Noumena is the plural form. Noumenon (Kant used the term "Ding an sich", or "thing-in-itself") is distinguished from phenomenon ("Erscheinung"), the latter being an observable event or physical manifestation capable of being observed by one or more of the five human senses. The two words serve as interrelated technical terms in Kant's philosophy. As expressed in Kant's Critique of Pure Reason, human understanding is structured by "concepts of the understanding", or innate categories that the mind uses in order to make sense of raw unstructured experience.
By Kant's account, when we employ a concept of some type to describe or categorize noumena (the objects of inquiry, investigation or analysis of the workings of the world), we are in fact merely employing a way of describing or categorizing phenomena (the observable manifestations of those objects of inquiry, investigation or analysis). Kant posited a number of methods by which human beings make sense out of the interrelationships among phenomena: the concepts of the transcendental aesthetic, as well as that of the transcendental analytic, transcendental logic and transcendental deduction. Taken together, these "categories of understanding" are Kant's description of the sum of human reasoning that can be brought to bear in attempting to understand the world in which we exist (that is, to understand, or attempt to understand, "things in themselves"). In each instance the word "transcendental" refers to the process that the human mind uses to increasingly understand or grasp the form of, and order among, phenomena. Kant was asserting that to "transcend" a direct observation or experience is to use reason and classifications to strive to correlate with the phenomena that are observed. By Kant's view, humans can make sense out of phenomena in these various ways, but can never directly know the noumena, the "things-in-themselves," the actual objects and dynamics of the natural world. In other words, by Kant's Critique, our minds may attempt to correlate in useful ways, perhaps even closely accurate ways, with the structure and order of the various aspects of the universe, but cannot know these "things-in-themselves" (noumena) directly. Rather, we must infer the extent to which thoughts correspond with things-in-themselves by our observations of the manifestations of those things that can be seen, heard, touched, smelled and/or tasted, that is, of phenomena.
According to Kant, objects of which we are sensibly cognizant are merely representations of unknown somethings—what Kant refers to as the transcendental object—as interpreted through the a priori or categories of the understanding. These unknown somethings are manifested within the noumenon—although we can never know how or why as our perceptions of these unknown somethings are bound by the limitations of the categories of the understanding and we are therefore never able to fully know the "thing-in-itself". Kant was arguing, in part, that the categories of the understanding are required for our sensible understanding of things-in-themselves, the pre-existence of which is a requisite for the function of these categories.
Noumenon and the thing-in-itself
Many accounts of Kant's philosophy treat "noumenon" and "thing-in-itself" as synonymous. However,"noumenon" and "thing-in-itself" are only loosely synonymous inasmuch as they represent the same thing but viewed from two different perspectives  Thing in itself: an object considered transcendentally apart from all the conditions under which a subject can gain knowledge of it. Hence the thing in itself is, by definition, unknowable. Sometimes used loosely as a synonym of noumenon. (Cf. appearance.)" -
"...though we cannot know these objects as things in themselves, we must yet be in a position at least to think them as things in themselves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears."
..but is much more doubtful about noumena:
"But in that case a noumenon is not for our understanding a special [kind of] object, namely, an intelligible object; the [sort of] understanding to which it might belong is itself a problem. For we cannot in the least represent to ourselves the possibility of an understanding which should know its object, not discursively through categories, but intuitively in a non-sensible intuition".
A crucial difference between the noumenon and the thing in itself is that to call something a noumenon is to claim some kind of knowledge, whereas Kant insisted that the thing in itself is unknowable. Interpreters have debated whether the latter claim makes sense: it seems to imply that we know at least one thing about the thing in itself (i.e., that it is unknowable). But Stephen Palmquist explains that this is part of Kant's definition of the term, to the extent that anyone who claims to have found a way of making the thing in itself knowable must be adopting a non-Kantian position.
Positive and negative noumena
Kant also makes a distinction between positive and negative noumena 
"If by 'noumenon' we mean a thing so far as it is not an object of our sensible intuition, and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term".
"But if we understand by it an object of a non-sensible intuition, we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. This would be 'noumenon' in the positive sense of the term."
The positive noumena, if they existed, would roughly correspond with Plato's Forms or Idea — immaterial entities which can only be apprehended by a special, non-sensory, faculty: "intellectual intuition".
Kant doubts that we have such a faculty, because for him intellectual intuition would mean that thinking of an entity, and its being represented, would be the same. He argues that humans have no way to apprehend the meaning of positive noumena:
Since, however, such a type of intuition, intellectual intuition, forms no part whatsoever of our faculty of knowledge, it follows that the employment of the categories can never extend further than to the objects of experience. Doubtless, indeed, there are intelligible entities corresponding to the sensible entities; there may also be intelligible entities to which our sensible faculty of intuition has no relation whatsoever; but our concepts of understanding, being mere forms of thought for our sensible intuition, could not in the least apply to them. That, therefore, which we entitle 'noumenon' must be understood as being such only in a negative sense.
The noumenon as a limiting concept
Even if noumena are unknowable, they are still needed as a limiting concept , Kant tells us. Without them, there would be only phenomena, and since we have complete knowledge of our phenomena, we would in a sense know everything. In his own words:
"Further, the concept of a noumenon is necessary, to prevent sensible intuition from being extended to things in themselves, and thus to limit the objective validity of sensible knowledge".
"What our understanding acquires through this concept of a noumenon, is a negative extension; that is to say, understanding is not limited through sensibility; on the contrary, it itself limits sensibility by applying the term noumena to things in themselves (things not regarded as appearances). But in so doing it at the same time sets limits to itself, recognising that it cannot know these noumena through any of the categories, and that it must therefore think them only under the title of an unknown something".
Furthermore, for Kant, the existence of a noumenal world limits reason to what he perceives to be its proper bounds, making many questions of traditional metaphysics, such as the existence of God, the soul, and free will unanswerable by reason. Kant derives this from his definition of knowledge as "the determination of given representations to an object." As there are no appearances of these entities in the phenomenal, Kant is able to make the claim that they cannot be known to a mind that works upon "such knowledge that has to do only with appearances." These questions are ultimately the "proper object of faith, but not of reason."
Criticisms of Kant's noumenon
Pre Kantian critique
Though the term Noumenon did not come into common usage until Kant, the idea that undergirds it, that matter has an absolute existence which causes it to emanate certain phenomenon, had historically been subjected to criticism. George Berkeley, who pre-dated Kant, asserted that matter, independent of an observant mind, was metaphysically impossible. Qualities associated with matter, such as shape, color, smell, texture, weight, temperature, and sound were all dependent on minds, which allowed only for relative perception, not absolute perception. The complete absence of such minds (and more importantly an omnipotent mind) would render those same qualities unobservable and even unimaginable. Berkeley called this philosophy immaterialism. Essentially there could be no such thing as matter without a mind.
"But it was just this difference between abstract knowledge and knowledge of perception, entirely overlooked by Kant, which the ancient philosophers denoted by noumena and phenomena. (See Sextus Empiricus, Outlines of Pyrrhonism, Book I, Chapter 13, ' What is thought (noumena) is opposed to what appears or is perceived (phenomena).' ) This contrast and utter disproportion greatly occupied these philosophers in the philosophemes of the Eleatics, in Plato's doctrine of the Ideas, in the dialectic of the Megarics, and later the scholastics in the dispute between nominalism and realism, whose seed, so late in developing, was already contained in the opposite mental tendencies of Plato and Aristotle. But Kant who, in an unwarrantable manner, entirely neglected the thing for the expression of which those words phenomena and noumena had already been taken, now takes possession of the words, as if they were still unclaimed, in order to denote by them his things-in-themselves and his phenomena."
The Noumenon's original meaning of "that which is thought" is not compatible with the "thing–in–itself," which signifies things as they exist apart from being images in the mind of an observer.
A "thing-in-itself" (or "ding an sich") in Kant's understanding is, for example, our Sun. The Sun existed, before any of our babies was born. Hence and therefore, the Sun is a thing-in-itself or "ding an sich" in regard to any of the babies, since: the baby needs the Sun to come into life (like all life on Earth does), but the Sun did not need a baby (or anything similar) to exist. What Kant claimed (and he did not claim more) was, there was matter before there was a so called "geist", the human mind. No more can you read out of Kantian's definition of the thing-in-itself in all of his writings. Kant did simply say: The Sun existed long before than there was some living creature to make any notice of the Sun.
Nietzsche, having been profoundly influenced by Schopenhauer's work, went on to criticise Kant's noumenon on slightly different grounds. He later similarly criticised Schopenhauer's work. Nietzsche found fault in the noumenon's lack of definite properties and its complete inability to interact with other things. He argued that a thing in itself would necessarily be outside of any causal chain since it cannot interact with any other things without demonstrating other properties than being the "ground of being". Nietzsche and later philosophers argued that the noumenon is of an utterly indeterminate nature and that any discussion that does not treat it as such cannot, in fact, be a discussion of the noumenon. In demonstrating any definite properties, the noumenon would cease to be so. Nietzscheanistic criticism of the noumenon found, for example, in his Beyond Good and Evil.
Nietzsche provided increasingly sophisticated accounts of the noumenon throughout the body of his work by explaining its numerous influences and connections with other ideas. An example of such comment can be found in his criticisms of materialistic atomism and what he called "soul-atomism", which follows Nietzsche's belief that synthetic judgments a priori are impossible in the first chapter of Beyond Good and Evil:
"[I]t is high time to replace the Kantian question, 'How are synthetic judgments a PRIORI possible?' by another question, 'Why is belief in such judgments necessary?'--in effect, it is high time that we should understand that such judgments must be believed to be true, for the sake of the preservation of creatures like ourselves; though they still might naturally be false judgments! Or, more plainly spoken, [...] synthetic judgments a priori should not "be possible" at all [...]"
Nietzsche then asserts that "the atomism of the soul" is connected with a belief in the existence of the thing in itself. He then attempts precisely to define that particular type of atomism:
"Let it be permitted to designate by [the atomism of the soul] the belief which regards the soul as something indestructible, eternal, indivisible, as a monad, as an atomon: this belief ought to be expelled from science!".
In arguing that the concept of the noumenon negatively influenced other ideas in specific ways, Nietzsche specifically characterized it in those ways.
Though Nietzsche was critical of theories concerning what could not be observed, he believed that theories ought to be capable of being falsified: while arguing against what he held to be the negative influence of the Kantian noumenon in the philosophy and science of his day, Nietzsche roughly approximated the scientific philosopher Karl Popper's assertion that falsifiability was the basis of scientific knowledge:
"One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability."
Nietzsche wrote in the eighteenth section of the first chapter of Beyond Good and Evil that
"It is certainly not the least charm of a theory that it is refutable; it is precisely thereby that it attracts the more subtle minds."
- Stanford Encyclopedia of Philosophy on Kant's metaphysics.
- Glossary of Kant's technical terms by Stephen Palmquist
- Overview of various scholar's interpretations of Kant
- Article from undergraduate journal Noesis
- Lecture notes by G.J Mattey
- Kant's System of Perspectives (Lanham: University Press of America, 1993) by Stephen Palmquist