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A demigod (or demi-god), meaning half-god, is originally a Greek mythological figure whose one parent was a god and whose other parent was human; as such, demigods are human-god hybrids. Examples of well-known demigods include the Greek hero Heracles (Roman Hercules), the Celtic hero Cuchulain, and the Sumerian king Gilgamesh.
Greek demigods 
Part of the dual nature of Greek heroes that gave rise to the modern demigod conception of them is that one parent is a mortal, and another is a god. This scenario is also occasionally embellished with the theme of double paternity: the hero's mother lying with king and god in the same night (the mother of Theseus, for example) or to be visited secretly by the god (like Danaë, mother of Perseus), and the seed of the two fathers is mixed in her womb. Thus the heroes have liminal qualities that enable them to have great strength, to cross the threshold between the worlds of the living and the dead yet return safely, and to mediate long after their death between human and divine.
The fact that male deities of Greek myth had far more notable children with mortals than the female goddesses can be attributable to the Greek male-dominated society being reflected in their religion. Zeus, primarily, and also Poseidon, all had a multitude of affairs with mortal women, with Zeus having to shield them from his wife Hera after she was alerted to the infidelity. The females were expected to remain loyal to their husbands, while the males were almost expected to take multiple lovers, meaning that far more of the demigods in Greek myths were born on earth to human mothers than on Olympus to divine mothers.
These hybrids were stronger, braver, and quicker than other mortals, accomplishing super-human feats only possible because of their divine parent. They would go out of their way to prove their valor, often engaging monsters or beasts far too powerful for any normal human to defeat, for the sole purpose of spreading their name. Others, such as Heracles, fought to reclaim lost honor. Theseus fought to save his homeland, killing the Minotaur to stop the flow of sacrifices that were taken from Athens on a yearly basis to feed the beast.
Zeus became the father of many heroes as a result of his dalliances, and after death they were accorded honors, especially among those Greeks who claimed to be their descendants and to have claims on the protection and patronage of a god. The veneration of heroes was part of chthonic rites in the religion of Greece. Such demigods were always mortal, but were preeminent among humans, and some had unusual powers. An exception was Heracles, who was accepted in the passage of time among the Twelve Olympians.
Structurally, mythic narratives of such heroic figures falls into the genre of Romance, as Northrop Frye defined and described it. Alexander the Great encouraged the myth makers in his retinue to spread the legend of his "secret" Olympian paternity. His legend survived the end of Antiquity; a cycle of medieval romances developed around his legend.
Hindu demigods 
In the Hindu religion, demigod is used to refer to deities who were once human and later became devas (gods) and are worshiped as such. Worship of the demigods is often different from worship of the regular gods such as Lord Ganesha and Lord Shiva.
The heroes of the Hindu epic Mahabharata, the five Pandava brothers, fit the Western definition of demigods, but are generally not referred to as such. Queen Kunti, the wife of King Pandu, was given a mantra that, when recited, meant that one of the Gods would give her his child. When her husband was cursed to die if he ever engaged in sexual relations, Kunti used this mantra to provide her husband with children, Yudishtira (father Yama), Bhima (father Vayu) and Arjuna (father Indra). She taught this mantra to Madri, King Pandu's other wife, and she conceived twin boys, Nakula and Sahadeva (fathers the Asvins). Queen Kunti had previously conceived another son, Karna, when she had tested the mantra out—despite her protests, Surya the sun god was compelled by the mantra to impregnate her.
The Vaishnavites (who often translate deva as "demigod") cite various verses that speak of the devas' subordinate status. For example, the Rig Veda (1.22.20) states, oṃ tad viṣṇoḥ paramam padam sadā paśyanti sūrayaḥ: "All the suras (i.e., the devas) look always toward the feet of Lord Vishnu." Similarly, in the Vishnu Sahasranama the concluding verses state: "The Rishis (great sages), the ancestors, the devas, the great elements, in fact all things moving and unmoving constituting this universe, have originated from Narayana," (i.e., Vishnu). Thus the Devas are stated to be subordinate to Vishnu, or God.
A. C. Bhaktivedanta Swami Prabhupada, the founder of the International Society for Krishna Consciousness (ISKCON) translated the Sanskrit word "deva" as "demigod" in his literature when the term referred to a God other than the Supreme Lord. This is because the ISKCON tradition teaches that there is only one Supreme Lord and that all others are but His servants. In order to emphasize their subservience, Prabhupada used the word "demigod" as a translation of deva. However, there are at least three occurrences in the eleventh chapter of Bhagavad-Gita where the word deva is used to refer to Lord Krishna; here Prabhupada translates it as "Lord". The word deva can be used to refer to the Supreme Lord, celestial beings and saintly souls depending on the context. This is similar to the word Bhagavan which is translated according to different contexts.
In the Bhagavad Gita Krishna himself states that worshipers of deities other than the Supreme Lord, Vishnu, are incorrect (Gita 9.23) as such worship leads only to temporal benefits, rather than to the Lord Himself (Gita 7.23). Krishna also says: "Whatever deity or form a devotee worships, I make his faith steady. However, their wishes are granted only by Me." (Gita: 7:21-22) Elsewhere in the Gita Lord Krishna states: "O Arjuna, even those devotees who worship other lesser deities (e.g., devas, for example) with faith, they also worship Me, but in an improper way because I am the Supreme Being. I alone am the enjoyer of all sacrificial services (Seva, Yajna) and Lord of the universe." (Gita: 9:23)
See also 
- "Online Etymology Dictionary". Etymonline.com. Retrieved 2012-11-07.
- Ruck and Staples 1984, part 3; Kerenyi 1959.