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The word "hylomorphism" is a 19th century term formed from the Greek words ὑλη hyle, "wood, matter" and μορφή, morphē, "form."
Matter and form 
Aristotle defines X's matter as "that out of which" X is made. For example, letters are the matter of syllables. Thus, "matter" is a relative term: an object counts as matter relative to something else. For example, clay is matter relative to a brick because a brick is made of clay, whereas bricks are matter relative to a brick house.
Change is analyzed as a material transformation: matter is what undergoes a change of form. For example, consider a lump of bronze that's shaped into a statue. Bronze is the matter, and this matter loses one form (that of a lump) and gains a new form (that of a statue).
According to Aristotle's theory of perception, we perceive an object by receiving its form with our sense organs. Thus, forms include complex qualia such as colors, textures and flavors, not just shapes.
Substantial form, accidental form, and prime matter 
Medieval philosophers who used Aristotelian concepts frequently distinguished between substantial forms and accidental forms. A substance necessarily possesses at least one substantial form. It may also possess a variety of accidental forms. For Aristotle, a "substance" (ousia) is an individual thing—for example, an individual man or an individual horse. The substantial form of substance S consists of S's essential properties, the properties that S's matter needs in order to be the kind of substance that S is. In contrast, S's accidental forms are S's non-essential properties, properties that S can lose or gain without changing into a different kind of substance.
In some cases, a substance's matter will itself be a substance. If substance A is made out of substance B, then substance B is the matter of substance A. However, what is the matter of a substance that is not made out of any other substance? According to Aristotelians, such a substance has only "prime matter" as its matter. Prime matter is matter with no substantial form of its own. Thus, it can change into various kinds of substances without remaining any kind of substance all the time.
Body–soul hylomorphism 
Basic theory 
Aristotle applies his theory of hylomorphism to living things. He defines a soul as that which makes a living thing alive. Life is a property of living things, just as knowledge and health are. Therefore, a soul is a form—that is, a property or set of properties—belonging to a living thing. Furthermore, Aristotle says that a soul is related to its body as form to matter.
Hence, Aristotle argues, there is no problem in explaining the unity of body and soul, just as there is no problem in explaining the unity of wax and its shape. Just as a wax object consists of wax with a certain shape, so a living organism consists of a body with the property of life, which is its soul. On the basis of his hylomorphic theory, Aristotle rejects the Pythagorean doctrine of reincarnation, ridiculing the notion that just any soul could inhabit just any body.
According to Timothy Robinson, it is unclear whether Aristotle identifies the soul with the body's structure. According to one interpretation of Aristotle, a properly organized body is already alive simply by virtue of its structure. However, according to another interpretation, the property of life—that is, the soul—is something in addition to the body's structure. Robinson uses the analogy of a car to explain this second interpretation. A running car is running not only because of its structure but also because of the activity in its engine. Likewise, according to this second interpretation, a living body is alive not only because of its structure but also because of an additional property: the soul is this additional property, which a properly organized body needs in order to be alive. John Vella uses Frankenstein's monster to illustrate the second interpretation: the corpse lying on Frankenstein's table is already a fully organized human body, but it is not yet alive; when Frankenstein activates his machine, the corpse gains a new property, the property of life, which Aristotle would call the soul.
Living bodies 
Some scholars have pointed out a problem facing Aristotle's theory of soul-body hylomorphism. According to Aristotle, a living thing's matter is its body, which needs a soul in order to be alive. Similarly, a bronze sphere's matter is bronze, which needs roundness in order to be a sphere. Now, bronze remains the same bronze after ceasing to be a sphere. Therefore, it seems that a body should remain the same body after death. However, Aristotle implies that a body is no longer the same body after death. Moreover, Aristotle says that a body that has lost its soul is no longer potentially alive. But if a living thing's matter is its body, then that body should be potentially alive by definition.
One approach to resolving this problem relies on the fact that a living body is constantly losing old matter and gaining new matter. Your five-year-old body consists of different matter than does your seventy-year-old body. If your five-year-old body and your seventy-year-old body consist of different matter, then what makes them the same body? The answer is presumably your soul. Because your five-year-old body and your seventy-year-old body share your soul—that is, your life—we can identify them both as your body. Apart from your soul, we cannot identify what collection of matter is your body. Therefore, your body is no longer your body after it dies.
Another approach to resolving the problem relies on a distinction between "proximate" and "non-proximate" matter. When Aristotle says that the body is matter for a living thing, he may be using the word "body" to refer to the matter that makes up the fully organized body, rather than the fully organized body itself. Unlike the fully organized body, this "body" remains the same thing even after death. In contrast, when he says that the body is no longer the same body after its death, he is using the word "body" to refer to the fully organized body, which (according to this interpretation) does not remain the same thing after death.
Aristotle says that the intellect (nous), the ability to think, has no bodily organ (in contrast with other psychological abilities, such as sense-perception and imagination). In fact, he says that it is not mixed with the body and suggests that it can exist apart from the body. This seems to contradict Aristotle's claim that the soul is a form or property of the body. To complicate matters further, Aristotle distinguishes between two kinds of intellect or two parts of the intellect. These two intellectual powers are traditionally called the "passive intellect" and the "active intellect" or "agent intellect". Thus, interpreters of Aristotle have faced the problem of explaining how the intellect fits into Aristotle's hylomorphic theory of the soul.
According to one interpretation, a person's ability to think (unlike his other psychological abilities) belongs to some incorporeal organ distinct from his body. This would amount to a form of dualism. However, according to some scholars, it would not be a full-fledged Cartesian dualism. This interpretation creates what Robert Pasnau has called the "mind-soul problem": if the intellect belongs to an entity distinct from the body, and the soul is the form of the body, then how is the intellect part of the soul?
Another interpretation rests on the distinction between the passive intellect and the agent intellect. According to this interpretation, the passive intellect is a property of the body, while the agent intellect is a substance distinct from the body. Some proponents of this interpretation think that each person has his own agent intellect, which presumably separates from the body at death. Others interpret the agent intellect as a single divine being, perhaps the Unmoved Mover, Aristotle's God.
A third interpretation relies on the theory that an individual form is capable of having properties of its own. According to this interpretation, the soul is a property of the body, but the ability to think is a property of the soul itself, not of the body. If that is the case, then the soul is the body's form and yet thinking need not involve any bodily organ.
Medieval modifications 
Medieval theologians, newly exposed to Aristotle's philosophy, applied hylomorphism to Christian doctrines such as the transubstantiation of the Eucharist's bread and wine into the body and blood of Jesus. Theologians such as Duns Scotus and Thomas Aquinas developed Christian applications of hylomorphism.
Plurality vs. unity of substantial form 
Many medieval theologians and philosophers followed Aristotle in seeing a living being's soul as that being's form—specifically, its substantial form. However, they disagreed about whether X's soul is X's only substantial form. Some medieval thinkers argued that X's soul is X's only substantial form, responsible for all of the features of X's body. In contrast, other medieval thinkers argued that a living being contains at least two substantial forms—(1) the shape and structure of its body, and (2) its soul, which makes its body alive.
Thomistic dualism 
Thomas Aquinas claimed that X’s soul was X’s only substantial form, although X also had numerous accidental forms that accounted for X’s nonessential features. Aquinas defined a substantial form as that which makes X's matter constitute X, which in the case of a human being is rational capacity. He attributed all other features of a human being to accidental forms. However, Aquinas did not claim that the soul was identical to the person. He held that a proper human being is a composite of form and matter, specifically prime matter. Form and matter taken separately may retain some of the attributes of a human being but are nonetheless not identical to that person. So a dead body is not actually or potentially a human being.
Eleanore Stump describes Aquinas's theory of the soul in terms of "configuration". The body is matter that is "configured", i.e. structured, while the soul is a "configured configurer". In other words, the soul is itself a configured thing, but it also configures the body. A dead body is merely matter that was once configured by the soul. It does not possess the configuring capacity of a human being.
Aquinas believed that rational capacity was a property of the soul alone, not of any bodily organ. However, he did believe that the brain had some basic cognitive function. Aquinas’s attribution of rational capacity to the soul allowed him to claim that disembodied souls could retain their rational capacity, although he was adamant that such a state was unnatural.
Teleology and ethics 
Aristotle holds a teleological worldview: he sees the universe as inherently purposeful. Basically, Aristotle claims that potentiality exists for the sake of actuality. Thus, matter exists for the sake of receiving its form, and an organism has sight for the sake of seeing. Now, each thing has certain potentialities as a result of its form. Because of its form, a snake has the potential to slither. Hence, we can say that the snake ought to slither. The more a thing achieves its potential, the more it succeeds in achieving its purpose.
Aristotle bases his ethical theory on this teleological worldview. Because of his form, a human being has certain abilities. Hence, his purpose in life is to exercise those abilities as well and as fully as possible. Now, the most characteristic human ability, which is not included in the form of any other organism, is the ability to think. Therefore, the best human life is a life lived rationally.
Modern physics 
"In the experiments about atomic events we have to do with things and facts, with phenomena that are just as real as any phenomena in daily life. But atoms and the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts ... The probability wave ... mean[s] tendency for something. It's a quantitative version of the old concept of potentia from Aristotle's philosophy. It introduces something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."
See also 
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