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Incorporeal or uncarnate means without a body. In ancient Greece, a media such as air was said to be incorporeal, as opposed to solid earth, in so far as it offers less hindrance to movement (so as not to presuppose the existence of perfect vacuum). In the problem of universals, universals are separable from any particular embodiment in one sense, while in another, they seem inherent nonetheless. Aristotle offered a hylomorphic account of abstraction in contrast to Plato's world of Forms. In modern philosophy, a distinction between the incorporeal and immaterial is not necessarily maintained: a body may be described as incorporeal if it is not made out of matter. The idea of the immaterial is often used in reference to the Christian God or the Divine.
Whereas modern readers often take "incorporeal" to be equivalent to "nonmaterial," this is not Aristotle's view. Having outlined [in De Anima] various philosophical accounts of the soul, all of which identify it with some kind of stuff, Aristotle concludes: "But all, or almost all, distinguish the soul by three of its attributes, movement, perception, and incorporeality" (I. 2. 405b). In other words, the soul could be incorporeal and still be composed of "stuff". One could believe that the soul should not be called "body" but still understand it as occupying space, as having a "place" (I. 3. 406a). This means that the soul, though neither hyle nor soma, cannot be placed in the Cartesian category of nonmatter, since for Descartes (and for the traditional modern understanding) something is "matter" or "physical" if it occupies space. Furthermore, elements like water and air, taken by Aristotle to be what we would call "matter", are nonetheless "noncorporeal" (On Sense and Sensible Things 5.445a22-23). When Aristotle uses the word hyle, therefore, we misunderstand him if we translate it as anything like the modern term "matter".
But modern scholars seem unable to resist the temptation to read hyle as "matter" (in the modern sense), leading to all kinds of confusion. In one place, for example, where Aristotle is explaining why some theorists take fire to be the stuff of the soul, the English translation by W. S. Hett proceeds, "for this is composed of the lightest constituents, and of all the elements is the nearest to incorporeal" (I. 2. 405a, Loeb edition). The Greek, however, is kai malista ton stoicheion asomaton, more literally translated: "it is the most (or especially) noncorporeal of the elements." Hett's translation implies that Aristotle took fire to be corporeal (that is, material) but almost incorporeal, consisting of very "thin" matter. Aristotle actually seems to be saying that fire is incorporeal—even though he believes that fire is constituted by matter (in the modern sense of the term—that is... "stuff" of some sort). Elsewhere, Aristotle records the opinion of others that the soul is "composed of very light parts." Hett's translation continues: "or as corporeal but less so than any other body" (I. 5. 409b20). Aristotle's Greek, however, is to asomatotaton ton allon: "the most incorporeal of the others" (to translate woodenly). In other words, Aristotle is saying that certain people believe the soul to be composed of very light parts and yet still to be incorporeal. Hett's mistranslation is due to the fact that he reads hyle as "matter" in a Cartesian sense and sees "incorporeality" as belonging to the "immaterial" side of a material/immaterial dichotomy, which does not accurately reflect Aristotle's own categories.—Dale B. Martin, The Corinthian Body
The notion that a causally effective incorporeal body is even coherent requires the belief that something can effect what's material, without physically existing at the point of effect. A ball can directly effect another ball by coming in direct contact with it, and is visible because it reflects the light that directly reaches it. An incorporeal field of influence, or immaterial body could not perform these functions because they have no physical construction with which to perform these functions. Following Newton, it became acceptable to overlook action at a distance as brute fact:
It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.—Isaac Newton, Letters to Bentley, 1692/3
In theology 
As early as Xenophanes (ca. 565-470 BCE)... we find at least a tendency towards monotheism: "One god, greatest among gods and men, in no way similar to mortals either in body or in thought"... [He posits] a god who is the cause of all: "Always he remains in the same place, moving not at all: nor is it fitting for him to go to different places at different times... but without toil he shakes all things by the thought of his mind"...
In Physics VIII,5, [Aristotle] speaks favorably of Anaxagoras' Mind in so far as it is "impassive and unmixed [with the world]"... How can Aristotle have held both that God is immanent and also "impassive and unmixed"? Much of his argument depends on an analogy drawn from geometry. Just as the primary locus of power and influence in a rotating sphere is its central axis, which, although it moves (transitively) the other parts of the sphere, remains quite still, so also the unmoved mover remains majestically impassive even while being the very source of the activity of the universe (Physics VIII,9,265b7-8)... Aristotle rejects the notion that God might think of something other than himself precisely because this would be to diminish his power (Metaphysics XII,9,1074b34). The power that Aristotle is concerned about is the power whereby God has an effect in the world (Metaphysics XII,6,1071b12-32). (In Physics VIII,5, Aristotle also says of Anaxagoras' Mind that "it could only cause motion the way it does being unmoved, and it can only rule being unmixed" -- 256b26-7: emphasis added.) So, we must conceive of God's thoughts about himself as bound up with his immanency (Metaphysics I,2,983a8-10, III,4,1000b3-6). Aristotle offers an explanation of how this works: just as our (internal) intentions are their external objects less their matter, so God thinks himself in the things that depend on him (Metaphysics XII,9,1047b38-a5: also De Anima III,5,430a-19-20). The interpretation of Thomas Aquinas would appear then to be correct, that it is precisely in thinking of himself that God knows—and controls—all other things...—Kevin L. Flannery, "Ancient Philosophical Theology" in A Companion to Philosophy of Religion
In chapter 10 of De ratione animae, Alcuin defines anima (soul) by combining Platonic attributes, including intellect and reason, ceaseless motion and immortality with the Christian tenents of free will and salvation. As a means of interaction with corporeals such as the human body and incorporeals such as God and the Forms, his definition includes traits pertaining to the soul as an incarnate entity within the natural world.
It is one thing to assert that the soul is 'incorporeal' insofar as it is distinct from the human body, and it is quite another thing to espouse the Platonic notion that the soul is utterly incorporeal, or that it is not a body of any kind. Platonic incorporeals differ significantly from the incorporeals of classical Stoicism, which were thought to participate in a diminished form of existence, and from the incorporalia of the grammatical tradition, which were defined on the basis of their imperceptibility to one or more of the five senses... A Platonic incorporeal is necessarily imperceptible to all the senses, and it does not occupy space. Accordingly, Alcuin writes that the soul is 'invisible, incorporeal, without weight, without colour,' although for a reader who already shared Alcuin's Platonic understanding of incorporeals, the mention of invisibility, weightlessness, and colourlessness was redundant. Alcuin also carefully specifies that the soul is circumscribed but nonetheless whole in every part of the body. In other words, the soul is neither diffused throughout the universe as God is or as a world-soul would be, nor is it distributed throughout a space in such a way that it can be divided.
If incorporeality makes the soul imperceptible to the senses, it is even more important that incorporeality allows the soul to apprehend other things that are imperceptible to the senses. The idea that like perceives like goes back to the Greek Presocratics, and in the medieval Latin iterations, it did not have to carry strictly Platonic connotations. Yet principally from Augustine's early dialogues and De Trinitate, Alcuin and other Carolingian thinkers inherited many rational demonstrations of theological doctrines, worked out according to a method of argumentation that combined Neoplatonist metaphysics with Aristotelian logic. Within this mode of discourse, it was exceedingly useful to have recourse to the concept of true incorporeality, and to be able to attribute true incorporeality to the unitary, rational anima, with all of the ontological and epistemological implications that it entails.—Leslie Lockett, "Why Must the Soul Be Incorporeal?" in Anglo-Saxon Psychologies in the Vernacular and Latin Traditions
Traditional forms of Judaism, Christianity, and Islam each conceive of God as an immaterial, nonphysical reality. If "the incorporeality of God" means the denial that God is physical, then all three monotheistic religions accept the incorporeality of God. However, if we follow the etymology of the term and define "incoporeality" as "without body" (from the Latin incorporale), Christianity takes exception to a strict adherence to belief in God's incorporeality when it comes to the Incarnation. According to traditional Christianity, in the Incarnation, the second member of the Trinity... became infleshed (the Latin meaning of incarnatus) and thus, in a sense, came to be "with body." While this pivotal claim about the union of God and man at the heart of Christianity marks a dramatic departure from a radical transcendent theology of God according to which any such union is metaphysically impossible, it does not commit Christians to denying God's immateriality. In traditional Christianity, God the Father, God the Holy Spirit, and God the Son (apart from the Incarnation) are clearly understood as lacking material structure and composition. Because of the shared conviction that God is immaterial, Christians along with Jews and Muslims have historically opposed material conceptions of God or gods such as one finds in Stoicism, according to which God is a vast material being, a world soul or animal, and in polytheism, according to which there are hosts of material deities. God's immaterial reality has also been used to articulate an important difference between monotheism and versions of pantheism... according to which the material world either is God or a part of God. —Charles Taliaferro, "Incorporeality" in A Companion to Philosophy of Religion
See also 
- Martin, D.B. (1999). The Corinthian Body. Yale University Press. pp. 8–9. ISBN 9780300081725. LCCN lc94044947.
- Berkovitz, Joseph (2008). "Action at a Distance in Quantum Mechanics". In Edward N. Zalta. The Stanford Encyclopedia of Philosophy (Winter 2008 ed.).
- Taliaferro, C.; Draper, P.; Quinn, P.L. (2010). A Companion to Philosophy of Religion. Blackwell Companions to Philosophy. John Wiley & Sons. pp. 84,87. ISBN 9781405163576. LCCN 2009037505.
- Lockett, L. (2011). Anglo-Saxon Psychologies in the Vernacular and Latin Traditions. Toronto Anglo-Saxon Series. University of Toronto Press. pp. 287–289. ISBN 9781442642171. LCCN 2011378491.
- Taliaferro, C.; Draper, P.; Quinn, P.L. (2010). A Companion to Philosophy of Religion. Blackwell Companions to Philosophy. John Wiley & Sons. p. 292. ISBN 9781405163576. LCCN 2009037505.