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The noumenon // is a posited object or event that is known (if at all) without the use of the senses. The term is generally used in contrast with, or in relation to "phenomenon", which refers to anything that appears to, or is an object of, the senses. In Platonic philosophy, the noumenal realm was equated with the world of ideas known to the philosophical mind, in contrast to the phenomenal realm, which was equated with the world of sensory reality, known to the uneducated mind. Much of modern philosophy has generally been skeptical of the possibility of knowledge independent of the senses, and Immanuel Kant gave this point of view its classical version, saying that the noumenal world may exist, but it is completely unknowable to humans. In Kantian philosophy the unknowable noumenon is often linked to the unknowable "thing-in-itself" (Ding an sich, which could also be rendered as "thing-as-such" or "thing per se"), although how to characterize the nature of the relationship is a question yet open to some controversy.
The Greek word Noumenon (νοούμενoν), plural noumena (νοούμενα), is the middle-passive present participle of νοεῖν (noein), "I think, I mean", which in turn originates from the word "nous" (from νόος, νοῦς, perception, understanding, mind). A rough equivalent in English would be "something that is thought", or "the object of an act of thought".
Platonic Ideas and Forms are noumena, and phenomena are things displaying themselves to the senses [...] that noumena and the noumenal world are objects of the highest knowledge, truths, and values is Plato's principal legacy to philosophy.—The Oxford Companion to Philosophy 
Noumenon came into its modern usage through Immanuel Kant. Its etymology derives from the Greek nooúmenon (thought-of) and ultimately reflects nous (intuition). Noumena is the plural form. Noumenon is distinguished from phenomenon (Erscheinung), the latter being an observable event or physical manifestation capable of being observed by one or more of the 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 to describe or categorize noumena (the objects of inquiry, investigation or analysis of the workings of the world), we are in fact employing a way of describing or categorizing phenomena (the observable manifestations of those objects of inquiry, investigation or analysis). Kant posited 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, Kant's "categories of understanding" are descriptions 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 increasingly to understand or grasp the form of, and order among, phenomena. Kant asserts 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 sensed, 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".
Many accounts of Kant's philosophy treat "noumenon" and "thing-in-itself" as synonymous, and there is textual evidence for this relationship. However, Stephen Palmquist holds that "noumenon" and "thing-in-itself" are only loosely synonymous in as much as they represent the same thing but viewed from two different perspectives, and other scholars also argue that they are not identical. Schopenhauer criticised Kant for changing the meaning of "noumenon". Opinion is far from unanimous. Kant's writings show points of difference between noumena and things-in-themselves. For instance, he regards things-in-themselves as existing:
"...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 a 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.
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.
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."
Kantian scholars have long debated two contrasting interpretations of the thing-in-itself. One is the dual object view, according to which the thing-in-itself is a distinct entity from the phenomena it gives rise to. The other is the dual aspect view, according to which the thing-in-itself and the thing-as-it-appears to us are two 'sides' of the same thing. This view is supported by the textual fact that "Most occurrences of the phrase "things in themselves" are shorthand for the phrase, 'things considered in themselves' (Dinge an sich selbst betrachten)." Although we cannot see things apart from the way we do in fact see them, we can think them apart from our mode of sensibility (perception); thus making the thing-in-itself a kind of noumenon or object of thought.
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 phenomena, 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.